Extended bridge XY force sensor

Abstract

The invention relates to an extended bridge XY force sensor. A force sensor includes a beam having a longitudinal central axis and a neutral axis extending along a surface of the beam parallel to the central axis. The first half-bridge includes a stretch resistor. The second half-bridge includes a stretch resistor. The third half-bridge includes a compression resistor. The fourth half-bridge includes a compression resistor. The half-bridges are arranged on the surface of the beam such that four different combinations of three half-bridges can be used to make redundant measurements of the orthogonal component of the force applied to the beam. The redundant measurement may be used to identify a fault of one or more resistors.

Description

[0001] This application is a divisional application of Chinese Patent Application No. 2020800938650 (PCT / US2020 / 060636), titled "Extended Bridge XY Force Sensor", with an international filing date of November 15, 2020 and an entry into the national stage on July 12, 2022.

[0002] Rights of priority

[0003] This application is a continuation of, and claims the priority benefit of, U.S. Patent Application Serial No. 62 / 936,349, filed November 15, 2019, U.S. Patent Application Serial No. 62 / 936,350, filed November 15, 2019, and U.S. Patent Application Serial No. 62 / 936,351, filed November 15, 2019, each of which is hereby incorporated by reference in its entirety. Background Art

[0004] Force sensing and feedback during minimally invasive surgery can provide a better sense of immersion, realism, and intuitiveness for the surgeon performing the surgery. To achieve optimal haptic rendering performance and accuracy, a force sensor can be placed on a surgical instrument and as close as possible to the interacting anatomical tissue. One method is to embed a force sensor at the distal end of the surgical instrument shaft, forming an electrical strain gauge on the force transducer by, for example, laying a conductive sheet with a cut circuit pattern, printing, or additive deposition processes, to measure the strain applied to the surgical instrument.

[0005] FIG. 1 is a schematic diagram showing a conventional force sensor that includes a rectangular beam having four full Wheatstone bridges (full bridges). A typical bridge circuit includes a circuit topology where two circuit branches (usually in parallel with each other) are bridged by a third branch between the first two branches to provide an offset voltage at some intermediate point between the two branches. The illustrative force sensor includes two full bridges on each of two adjacent orthogonal sides of the beam to measure forces orthogonal to the longitudinal axis of the beam. The beam can be fixed to the distal portion of the surgical instrument shaft to sense forces orthogonal to the longitudinal axis of the shaft. For example, a force applied perpendicular to one side of the beam (i.e., an X or Y force) can be determined by subtracting the force measurement values determined by the full bridges at the proximal and distal portions of that side of the beam.

[0006] A force sensor can withstand various different strain sources, including: orthogonal forces, torques, off-axis forces, off-axis torques, compression / tension, torsion, ambient temperature, and gradient temperature to be measured. Each example full bridge can cancel out the following stresses: temperature, torsion, off-axis force, and off-axis torque. Each individual full bridge output can indicate the stress caused by force, torque, and compression / tension. In the example force sensor, subtracting the output value generated by the proximal full bridge formed on the same side from the output value generated by the distal full bridge on one side can cancel out the torque, thereby generating an output value representing the orthogonal force to be measured.

[0007] The force sensor of a surgical instrument is crucial for ensuring patient safety. Therefore, force sensor error detection may be required to prevent injury by detecting force sensor failures. One method of error detection is to provide additional full bridges to generate redundant force measurement values that can be compared to detect errors. However, the limited space on the beam side makes it impractical to add more full bridges on one side. In addition, some manufacturing processes are typically limited to forming bridges on at most two sides. Forming bridges on four sides significantly increases the manufacturing cost. Summary of the Invention

[0008] The force sensor includes a beam having four Wheatstone half bridges ("half bridges") located on the beam surface. The beam includes a proximal portion and a distal portion, a longitudinal central axis, and a neutral axis extending parallel to the central axis along the beam surface. The first and second half bridges include tensile resistors. The third and fourth half bridges include compressive resistors. The first and third half bridges are arranged along a first side axis. The second and fourth half bridges are arranged along a second side axis. The first and second side axes extend along the beam surface on opposite sides of the neutral axis and are equidistant from the neutral axis and parallel to the neutral axis.

[0009] Each of four combinations of three half bridges can be used to generate a separate measurement value of the orthogonal component of the force applied to the beam. Comparison of the separate measurement values provides an indication of whether one or more half bridges are faulty. The fault is reported as a sensor error. Description of the Drawings

[0010] In the drawings, which are not necessarily to scale, the same numbers may describe similar components in different views. Similar numbers with different letter suffixes may represent different instances of similar components. The drawings generally illustrate, by way of example and not limitation, the various embodiments discussed herein.

[0011] FIG. 1 is a schematic diagram showing an example existing force sensor, which includes a rectangular beam having four full Wheatstone bridges (full bridges).

[0012] Figure 2 is an illustrative side view of a distal portion of a surgical instrument having an elongated shaft, on which a force sensor beam is mounted.

[0013] Figure 3A is an illustrative perspective view of an example force sensor including a rectangular beam with two extended Wheatstone bridge circuits on each of two adjacent sides of the rectangular beam.

[0014] Figure 3B Shows Figure 3A An illustrative perspective view of a force sensor further illustrating an imaginary first plane and an imaginary second plane.

[0015] Figure 3C Shows Figure 3A An illustrative perspective view of a force sensor further illustrating an imaginary third plane and an imaginary fourth plane.

[0016] Figure 4 yes Figures 3A - 3B An illustrative proximal cross-sectional view of an example beam showing the intersection of imaginary planes at the longitudinal center axis.

[0017] Figure 5A is a side view showing the arrangement of resistors on the first side 308 of the beam.

[0018] Figure 5B is a side view showing the placement of resistors on the second side of the beam.

[0019] Figure 6A is an illustrative side view of an example beam showing a first example circuit layout topology of an example full Wheatstone bridge.

[0020] Figure 6B is an illustrative first schematic circuit diagram representation of a full Wheatstone bridge layout topology.

[0021] Figure 7A is an illustrative side view of an example beam showing a second example circuit layout topology of an example full Wheatstone bridge.

[0022] Figure 7B is an illustrative first schematic circuit diagram representation of a second full Wheatstone bridge layout topology.

[0023] Figure 8A is an illustrative planar side view of two adjacent sides of an example beam showing the layout of the first and second full Wheatstone bridges and the routing of the center conductor traces.

[0024] Figure 8B yes Figure 8A An illustrative first schematic circuit diagram of a first and a second full-Wheatstone bridge is shown.

[0025] Figure 9A yes Figure 4Explanatory cross-sectional end view of an exemplary beam, which indicates resistors on a first side and indicates a first planar force and a second planar force.

[0026] Figure 9B is an explanatory force diagram that indicates the X and Y force components of the first planar force applied to the first proximal resistor and the first distal resistor in response to an applied force.

[0027] Figure 9C is an explanatory force diagram that indicates the X and Y force components of the second planar force applied to the second proximal resistor and the second distal resistor in response to an applied force.

[0028] Figure 10 is Figure 4 Explanatory cross-sectional end view of an exemplary beam, which indicates resistors on a second side of the beam and indicates a third planar force and a fourth planar force.

[0029] Figure 11 is an explanatory diagram showing a metal sheet with a cut-out that defines an exemplary resistor for assembly into respective bridge circuits on adjacent first and second sides of the beam.

[0030] Figure 12A is a schematic diagram showing the process of winding first and second regions around first and second sides of the metal sheet that surrounds the beam.

[0031] Figure 12B is an explanatory perspective view of the beam, which shows the first and second regions of the metal sheet laid on respective first and second sides of the exemplary beam.

[0032] Figures 13A - 13B Shows an explanatory top perspective view ( Figure 13A ) and a bottom perspective view ( Figure 13B ) of an exemplary force sensor that includes a rectangular beam with two four-strain gauge resistors coupled in two half Wheatstone bridge circuits located on each of two opposite sides of the rectangular beam.

[0033] Figure 14A Shows an explanatory first exemplary half-bridge circuit layout that has proximally and distally serially electrically coupled strain gauge resistors and has a voltage node coupled between them.

[0034] Figure 14B is an explanatory first schematic circuit representation of the first half-bridge circuit layout.

[0035] Figure 15A Shows an explanatory second exemplary half-bridge circuit layout that has proximally and distally serially electrically coupled compression gauge strain resistors and has a voltage node coupled between them.

[0036] Figure 15B It is an illustrative second schematic circuit diagram representation of the second half - bridge circuit layout.

[0037] Figure 16 It shows the first and second imaginary planes Figures 13A - 13B An illustrative proximal - direction cross - sectional view of an exemplary beam.

[0038] Figure 17A It is a side view of the beam, which shows Figures 13A - 13B the first side of the beam of

[0039] Figure 17B It is a side view of the beam, which shows Figures 13A - 13B the opposite second side of the beam of

[0040] Figure 18A It is an illustrative proximal - direction cross - sectional view of an exemplary beam, which indicates the second and third plane strain forces applied to the second and third half - bridges.

[0041] Figure 18B It is an illustrative force diagram indicating the X - force component and Y - force component of the second plane strain force on the second half - bridge.

[0042] Figure 18C It is an illustrative force diagram indicating the X - force component and Y - force component of the third plane strain force applied to the third half - bridge.

[0043] Figure 19 It is an illustrative proximal - direction cross - sectional view of an exemplary beam, which indicates the first and fourth plane strain forces applied to the first and fourth half - bridges.

[0044] Figure 20 It is an illustrative proximal - direction cross - sectional view of an exemplary beam, which indicates the first and second plane strain forces applied to the first and second half - bridges.

[0045] Figure 21 It is an illustrative proximal - direction cross - sectional view of an exemplary beam, which indicates the third and fourth plane strain forces applied to the third and fourth half - bridges.

[0046] Figure 22 It shows an illustrative top - down perspective view of an exemplary force sensor, which includes a rectangular beam having two tensile resistor half - bridge circuits and two compressive resistor half - bridge circuits on its first side.

[0047] Figure 23 It is Figure 22 An illustrative proximal - direction cross - sectional view of an exemplary beam of

[0048] Figure 24 Is Figure 22 A side view of the first side of an exemplary beam, on which two tensile resistor half - bridges and two compressive resistor half - bridges are located.

[0049] Figure 25 Is an illustrative cross - sectional end view of the exemplary beam, which indicates the first planar strain force and the second planar strain force applied to the first and second half - bridges.

[0050] Figure 26 Is an illustrative cross - sectional end view of the exemplary beam, which indicates the first planar strain force and the second planar strain force applied to the third and fourth half - bridges.

[0051] Figure 27 Is an illustrative cross - sectional end view of the exemplary beam, which indicates the first planar strain force and the fourth planar strain force applied to the first and fourth half - bridges.

[0052] Figure 28 Is an illustrative cross - sectional end view of the exemplary beam, which indicates the second planar strain force and the third planar strain force applied to the second and third half - bridges.

[0053] Figure 29 Is an illustrative cross - sectional end view of the exemplary beam, which indicates the forces applied to three exemplary half - bridges located thereon.

[0054] Figure 30 Is an illustrative diagram showing a computer system configured to monitor voltage measurements of a force sensor.

[0055] Figure 31 Is an illustrative flowchart representing an exemplary diagnostic process for detecting the occurrence of a faulty strain - gauge resistor within a force sensor.

[0056] Figures 32A - 32B Shows an illustrative top perspective view of an exemplary force sensor ( Figure 32A ) and a bottom perspective view ( Figure 32B ), the exemplary force sensor including a rectangular beam having Wheatstone bridge circuits on two opposite sides thereof.

[0057] Figure 33 Is Figures 32A - 32B An illustrative proximal - direction cross - sectional view of the exemplary beam.

[0058] Figure 34A Is a side view of the beam, which shows the first side of the beam.

[0059] Figure 34B Is a side view of the beam, which shows the second side of the beam.

[0060] Figure 35AIs an illustrative side view of an exemplary beam, which shows a first exemplary layout of a first full Wheatstone bridge circuit.

[0061] Figure 35B Is an illustrative first schematic circuit diagram representation of a first full Wheatstone bridge layout topology.

[0062] Figure 36A Is an illustrative side view of an exemplary beam, which shows an alternative second exemplary layout of a first full Wheatstone bridge circuit.

[0063] Figure 36B Is an illustrative first schematic circuit diagram representation of an alternative exemplary second layout topology of a first full Wheatstone bridge circuit.

[0064] Figure 37A Is an illustrative side view of an exemplary beam, which shows an exemplary first circuit layout of a second full Wheatstone bridge circuit located on a second side of the beam.

[0065] Figure 37B Is an illustrative schematic circuit diagram representation of a first exemplary layout of a second full bridge circuit.

[0066] Figure 37C Is an illustrative side view of an exemplary beam, which shows an exemplary second layout of a second exemplary full Wheatstone bridge located on a second side of beam 3304.

[0067] Figure 37D Is an illustrative schematic circuit diagram representation of a second exemplary layout of a second full bridge circuit.

[0068] Figure 38A Is an illustrative side view of an exemplary beam, which shows an extended layout of a Wheatstone bridge and shows the routing of a center conductor trace.

[0069] Figure 38B Is Figure 38A An illustrative first schematic circuit diagram representation of the first and second full Wheatstone bridges.

[0070] Figure 39A Is Figure 33 An illustrative cross-sectional end view of an exemplary beam of, which indicates resistors on a first side and indicates a first planar force and a second planar force.

[0071] Figure 39B Is an illustrative force diagram, which indicates the X force component and the Y force component of a first planar force applied to a first proximal resistor and a first distal resistor in response to an applied force.

[0072] Figure 39C Is an illustrative force diagram, which indicates the X force component and the Y force component of a second planar force applied to a second proximal resistor and a second distal resistor in response to an applied force.

[0073] Figure 40 is Figure 33 An illustrative proximal direction cross-sectional view of an exemplary beam's indicating resistor indicating an X-axis force.

[0074] Figure 41 Is an illustrative diagram showing a metal sheet with a cutout that defines an exemplary resistor for assembly into respective first and second full Wheatstone bridges on the first and second opposite-facing sides of a beam.

[0075] Figure 42A Is an illustrative diagram showing the process of winding a metal sheet around an exemplary beam to position a first set of resistors on a first side of the beam and a second set of resistors on a second side of the beam.

[0076] Figure 42B Is a schematic top perspective view of a beam with a metal sheet wound around three sides of the beam.

[0077] Figure 42C Is an illustrative bottom perspective view of a beam with a metal sheet wound around three sides of the beam.

[0078] Figure 43 Is an illustrative cross-sectional view of a beam. Detailed Description

[0079] Extended bridge adjacent side XY force sensor

[0080] Figure 2 Is an illustrative side view of a distal portion of an exemplary surgical instrument 202 having an elongate shaft 204 and a force sensor 205 shown in a partially cutaway manner. The force sensor 205 is mounted to the distal portion of the shaft 204 and includes a beam 206 having a plurality of strain gauge resistors 212 located thereon. The surgical instrument 202 includes an end effector 208, for example, the end effector 208 can include articulating jaws. During a surgical procedure, the end effector 208 contacts anatomical tissue, which can cause forces in the X, Y, or Z directions to be applied to the force sensor 206 and can cause torques, for example, such as a torque M about the Y-axis. Y The force sensor 205, including a longitudinal axis 210, can be used to measure X and Y forces perpendicular to the longitudinal axis 210.

[0081] Figure 3A Is an illustrative perspective view of an exemplary force sensor 302 that includes a rectangular beam 304 having extended Wheatstone bridge circuits on each of two adjacent sides. The first full Wheatstone bridge 352 (indicated by the dashed line) includes a first (R P1 )、second (R D1 )、third (R P2) and fourth (R D2 ) resistors. The second full Wheatstone bridge 354 (indicated by the dashed line) includes a fifth (R P3 ), sixth (R D3 ), seventh (R P4 ) and eighth (R D4 ) resistors. In the example first full Wheatstone bridge 352, the first and second resistors are coupled in the first half-bridge, while the third and fourth resistors are coupled in the second half-bridge. In the example second full Wheatstone bridge, the fifth and sixth resistors are coupled in the third half-bridge, while the seventh and eighth resistors are coupled in the fourth half-bridge. The (X, Y, Z) beam coordinate system 305 is shown to explain the force directions with respect to the beam 304. The example beam 304 may have a rectangular cross-section with flat / planar sides. More specifically, the example beam may have a square cross-section. The beam 304 includes a proximal beam portion 304P and a distal beam portion 304D and includes a longitudinal central axis 306 extending between the proximal beam portion and the distal beam portion. The force sensor 302 includes example resistors R P1 -R P4 and R D1 -R D4 .

[0082] The resistors can be placed on the beam 304 manually or using an automated machine, and the resistors can be adhered to the beam using an adhesive such as epoxy. Alternatively, the resistors can be directly deposited and laser-etched onto the beam 304. In both cases, the circuit can be completed externally using wire bonding and flexible printed circuits.

[0083] The first proximal strain gauge resistor (“resistor”) R P1 and the second proximal resistor R P2 are located at the proximal beam portion 304P of the first side 308 of the beam 304. The first distal resistor R D1 and the second distal resistor R D2 are located at the distal beam portion of the first side 308 of the beam 304. As described below, the first set of resistors R P1 -R P2 and R D1 -R D2 located on the first side 308 of the beam are arranged in a first extended full Wheatstone bridge. The third proximal resistor R P3 and the fourth proximal resistor R P4 are located at the proximal beam portion 304P of the second side 310 of the beam 304. The third distal resistor R D3 and the fourth distal resistor R D4at the distal beam portion 304D on the second side 310 of the beam 304. The first side 308 of the exemplary beam 304 is adjacent to the second side 310 of the exemplary beam 304. As described below, the second set of resistors R P3 -R P4 and R D3 -R D4 are arranged in a second extended full Wheatstone bridge.

[0084] As more fully explained below, the first and second full bridge circuits are "unrolled" in that portions of each full bridge circuit are laterally spaced from each other on the beam 304. For example, each full bridge can include two half bridges that are laterally extended and separated from each other. An advantage of laterally extended and separated half bridges is that, for example, the conductor traces that couple the resistors to a bias voltage or couple the resistors to each other can be routed through the middle of the face of the beam 304 or near the neutral axis of the beam on each face of the beam. Alternatively, in a beam with a circular cross-section (not shown), the conductor traces can advantageously be routed along the neutral axis of the respective half bridges. This routing helps to reduce the strain in the traces, thereby improving the accuracy of the sensor by rejecting unwanted signals. As more fully explained below, the first and second proximal resistors R P1 、R P2 and the first and second distal resistors R D1 、R D2 on the first side 308 of the beam are used as Y-direction force sensor elements, while the third and fourth proximal resistors R P3 、R P4 and the third and fourth distal resistors R D3 、R D4 on the second side 310 of the beam are used as X-direction force sensor elements.

[0085] Each of the resistors R P1 -R P4 and R D1 -R D4 is the same type of strain gauge resistor. More specifically, in the exemplary force sensor 302 described herein, the resistors R P1 -R P4 and R D1 -R D4is a tensile type gauge resistor for measuring tensile strain. In an alternative example force sensor, the set of resistors can be a compressive type gauge resistor for measuring compressive strain. As used herein, a reference to a set of resistors having a "matching type" refers to a set of resistors in which all resistors are tensile resistors or all resistors are compressive resistors. Resistors having a matching type are more likely to have similar sensitivities and performance, making the sensor more suitable and effective for low signal-to-noise situations where common mode rejection is critical. Generally, although tensile or compressive gauge resistors can be used to determine forces in the X and Y directions orthogonal to each other, tensile strain gauge resistors are typically more sensitive than compressive gauge resistors.

[0086] Figure 3B illustrates Figure 3A an illustrative perspective view of a force sensor 302, which further illustrates a hypothetical first plane P1 and a hypothetical second plane P2. A first proximal resistor R P1 and a first distal resistor R D1 are disposed on a first side of a beam 304 within the first hypothetical plane P1, a central axis 306 extends within the first hypothetical plane P1, and the plane P1 defines a first lateral side axis 312 at the location along which the first plane P1 intersects the first side 308 of the beam 304. The first lateral axis 312 and the central axis 306 extend parallel to each other. An example first lateral side axis 312 extends through the first proximal resistor R P1 and through the first distal resistor R D1 . Further, the example first lateral side axis 312 bisects the example first proximal resistor R P1 and bisects the example first distal resistor R D1 .

[0087] Still referring Figure 3B , a second proximal resistor R P2 and a second distal resistor R D2 are disposed on a first side of the beam 304 within the second hypothetical plane P2, the central axis 306 extends within the plane P2, and the plane P2 defines a second lateral side axis 314 at the location along which the second plane P2 intersects the first side 308. The second lateral axis 314 and the central axis 306 extend parallel to each other. An example second lateral side axis 314 extends through the second proximal resistor R P2 and through the second distal resistor R D2 . Further, the example second lateral side axis 314 bisects the example second proximal resistor R P2 and bisects the example second distal resistor R D2 .

[0088] Figure 3Cshows Figure 3A An illustrative perspective view of the force sensor 302, which further shows a hypothetical third plane P3 and a hypothetical fourth plane P4. The third proximal resistor R P3 and the third distal resistor R D3 are arranged on the second side 310 (adjacent to the first side 308) of the beam 304 within the third hypothetical plane P3, the central axis 306 extends in this plane P3, and the third hypothetical plane P3 defines a third lateral axis 316 at the position on the second side 310 of the beam 304, and the third plane P3 intersects the second side 310 along this position. The exemplary third lateral axis 316 extends through the third proximal resistor R P3 and through the third distal resistor R D3 . Further, the exemplary third axis bisects the exemplary third proximal resistor R P3 and bisects the exemplary third distal resistor R D3 .

[0089] Still referring to Figure 3C , the fourth proximal resistor R P4 and the fourth distal resistor R D4 are arranged on the second side 310 of the beam 304 within the fourth hypothetical plane P4, the central axis 306 extends in this plane P4, and the plane P4 defines a fourth lateral axis 318 at the position on the second side 310 of the beam 304 where the fourth plane P4 intersects the second side 310 of the beam 304, and the fourth hypothetical plane P4 includes the central axis 306. The exemplary fourth lateral axis 318 extends through the fourth proximal resistor R P4 and through the fourth distal resistor R D4 . More specifically, the exemplary fourth lateral axis bisects the exemplary fourth proximal resistor R P4 and bisects the exemplary first distal resistor R D4 .

[0090] Figure 4 is Figures 3A - 3B An illustrative proximal direction cross-sectional view of an exemplary beam 304, which shows the intersection of the hypothetical planes at the longitudinal central axis 306. Figure 5A is a side view showing the arrangement of the resistors R P1 -R P2 , R D1 -R D2 on the first side 308 of the beam 304. Figure 5B is a side view showing the arrangement of the resistors R P3 -R P4 , R D3 -R D4 on the second side 310 of the beam 304.

[0091] Reference Figure 4 , a proximal end view of the beam 304 shows a side view of imaginary first to fourth planes P1 - P4 intersecting along the longitudinal central axis 306. A (X, Y, Z) beam coordinate system 305 is shown to explain the direction of forces relative to the beam 304. Note that in Figure 4 , the Z - axis is shown as emerging from the page. The first plane P1 and the second plane P2 are separated from each other about the central axis by a first separation angle A1. The second and third imaginary planes are separated from each other by a second separation angle B1. In the exemplary force sensor 302, the first separation angle is equal to the second separation angle.

[0092] Reference Figure 5A , the first plane P1 is shown as extending through a first proximal resistor R P1 and a first distal resistor R D1 , which are arranged along a first lateral side axis 312 on the first side 308 of the beam 304, and the second plane P2 is shown as extending through a second proximal resistor R P2 and a second distal resistor R D2 , which are arranged along a second lateral side axis 314 on the first side 308 of the beam 304. A (X, Y, Z) beam coordinate system 305 is shown to explain the direction of forces relative to the beam 304. Note that in Figure 5A , the X - axis is shown as pointing into the page. The magnitude of the first separation angle A1 corresponds to the lateral spacing distance between the first lateral side axis 312 and the second lateral side axis 314 at the first side 308 and, thus, corresponds to the lateral spacing between a first pair of resistors including the first proximal and distal resistors R P1 、R D1 and a second pair of resistors including the second proximal and distal resistors R P2 、R D2 . In the exemplary force sensor 302, the first lateral side axis 312 and the second lateral side axis 314 are equidistant from the neutral axis 315 of the first side 308 of the beam 304, which extends within the first side surface and is equidistant from the opposite lateral edges of the first side 308, although an equidistant spacing is not required.

[0093] Reference Figure 5B , the third plane P3 is shown as extending through a third proximal resistor R arranged along a third lateral side axis 316 on the second side 310 of the beam 304 P3 and a third distal resistor R D3 , and the fourth plane P4 is shown as extending through a fourth proximal resistor R arranged along a fourth lateral side axis 318 of the beam 304 on the second side 310 of the beam 304 P4 and a fourth distal resistor R D4. The (X, Y, Z) beam coordinate system 305 is shown to explain the force directions relative to the beam 304. Note that in Figure 5B , the Y axis is shown as emerging from the page. The magnitude of the second separation angle B1 corresponds to the lateral spacing distance between the third lateral side axis 316 and the fourth lateral side axis 318 at the second side 310, and thus corresponds to the lateral spacing between the third resistor pair including the third proximal and distal resistors R P3 , R D3 and the fourth resistor pair including the arranged fourth proximal and distal resistors R P4 , R D4 . In the exemplary force sensor 302, the third lateral side axis 316 and the fourth lateral side axis 318 are equidistant from the neutral axis 319 of the second side 310 of the beam 304, which extends within the second side surface and is equidistant from the opposite lateral edges of the second side 310.

[0094] Thus, the first pair of resistors R P1 , R D1 and the second pair of resistors R P2 , R D2 are laterally extended and separated and located on the first side 308 of the beam 304. In the exemplary beam 304, the first pair of resistors is positioned to align with the first lateral side axis 312 and the second pair or more resistors are positioned to align with the second lateral side axis 314, and the first and second lateral side axes are laterally spaced equidistant from the neutral axis 315 of the first side of the beam 304 and on opposite sides of the neutral axis 315. More specifically, the first pair of resistors is positioned to align with the first lateral side axis 312 and the second pair or more resistors are positioned to align with the second lateral side axis 314. In addition, the third pair of resistors R P3 , R D3 and the fourth pair of resistors R P4 , R D4 are laterally extended and separated and located on the second side 310 of the beam 304. In the exemplary beam 304, the third pair of resistors is positioned to align with the third lateral side axis 316, and the fourth pair or more resistors are positioned to align with the fourth lateral side axis 318, and the first and second lateral side axes 316, 318 are laterally spaced equidistant from the neutral axis 319 of the second side of the beam 304 and on opposite sides of the neutral axis 319. More specifically, the third pair of resistors is positioned to align with the third lateral side axis 316 and the fourth pair or more resistors are positioned to align with the fourth lateral side axis 318.

[0095] In the exemplary force sensor, the proximal and distal resistors that are part of the same full bridge are laterally aligned. In addition, in the exemplary force sensor, the spacing between the first and second lateral side axes matches the spacing between the third and fourth lateral side axes. In the exemplary force sensor, the proximal resistor RP1 -R P4 is positioned at a matching longitudinal location on the beam. In the exemplary force sensor, the distal resistor R D1 -R D4 is positioned at a matching longitudinal location on the beam.

[0096] As explained below, the resistors of the first bridge 352 are arranged laterally separated to measure a force in a first direction perpendicular to the beam central axis 306 based on a bias off-axis force applied along the first plane P1 and the second plane P2. Similarly, based on measuring an off-axis force applied along the second and third planes P3, P4, the resistors of the second bridge 354 are arranged laterally to measure a force in a second direction perpendicular to the beam central axis 306 and perpendicular to the first direction. As Figure 8A shown, the lateral separation of the resistors of the first bridge 352 enables the routing of the first center conductor trace 356 parallel to the beam central axis 306 in the region of the beam 304 between the proximal and distal resistors of the first bridge 352. Similarly, the lateral separation of the resistors of the second bridge 352 enables the routing of the second center conductor trace 358 parallel to the beam central axis 306 in the region of the beam 304 between the proximal and distal resistors of the second bridge 354.

[0097] Figure 6A is an illustrative side view of an exemplary beam 304, which shows an illustrative first layout topology of an exemplary full Wheatstone bridge 602. The first exemplary full Wheatstone bridge layout includes resistors R P1 -R P2 and R D1 -R D2 . In the exemplary force sensor 304, the resistors R P1 -R P2 and R D1 -R D2 located on the first side 308 of the beam 304 can be coupled in accordance with the topology of the first full Wheatstone bridge layout. Similarly, the resistors R P3 -R P4 and R D3 -R D4 located on the second side 310 of the beam 304 can be coupled in accordance with the topology of the first full Wheatstone bridge layout. The first Wheatstone bridge layout is coupled to an input bias voltage conductor (EP, EN) and an output voltage conductor (Vo-, Vo+) in a first configuration. Figure 6B is an illustrative first schematic circuit diagram 604 representation of the full Wheatstone bridge layout topology. Referring Figures 6A - 6B , the first proximal resistor R P1 is electrically coupled between a positive first DC potential (EP) and a second (also referred to as "negative" potential) output Vo-. The second proximal resistor R P2Electrically coupled between a negative second DC potential (EN) and a second output Vo-. A first distal resistor R D1 Electrically coupled between a positive first DC potential (EP) and a first output Vo+ (also referred to as the "positive" output). A second distal resistor R D2 Electrically coupled between a negative second DC potential (EN) and a first output Vo+.

[0098] Figure 7A Is an illustrative side view of an exemplary beam 304, which shows a second circuit layout topology of an exemplary full Wheatstone bridge 702. The second exemplary full Wheatstone bridge layout includes resistors R P1 -R P2 and R D1 -R D2 . In the exemplary force sensor 304, the resistors R P1 -R P2 and R D1 -R D2 located on the first side 308 of the beam 304 can be coupled in accordance with the topology of the second full Wheatstone bridge layout. Similarly, the resistors R P3 -R P4 and R D3 -R D4 located on the second side 310 of the beam 304 can be coupled in accordance with the topology of the second full Wheatstone bridge layout. The second Wheatstone bridge layout is coupled to input bias voltage conductors (EP, EN) and output voltage conductors (Vo-, Vo+) in a second configuration. Figure 7B Is an illustrative first schematic circuit diagram 704 representation of the second full Wheatstone bridge layout topology. Referring to Figures 7A - 7B , a first proximal resistor R P1 is electrically coupled between a positive first DC potential (EP) and a first output Vo+. A second proximal resistor R P2 is electrically coupled between a positive first DC potential (EP) and a second output Vo-. A first distal resistor R D1 is electrically coupled between a negative second DC potential (EN) and a first output Vo+. A second distal resistor R D2 is electrically coupled between a negative second DC potential (EN) and a second output Vo-.

[0099] Generally speaking, Figure 6A the layout in Figure 7A is more suitable for reducing the number of traces that must span the length of the beam and can also reduce the effect of trace pick-up strain. On the other hand, if the force sensor uses half-bridge voltage measurement, then

[0100] Figure 8AIs an illustrative plan side view of two adjacent sides of the exemplary beam 304, which shows the unfolded layout of the first and second full Wheatstone bridges 352, 354 and the routing of the center conductor traces 356, 358 that extend within the center of the bridge, between the proximal and distal resistors of the bridge. The first bridge 352 is located at the first side 304-1 of the beam 304. The second bridge 354 is located at the second side 304-2 of the beam 304. The first side 304-1 and the second side 304-2 share the side edge 303 of the beam 304.

[0101] The first full Wheatstone bridge 352 includes R P1 、R P2 and the distal resistors R D1 、R D2 and has a first neutral axis 362 that extends parallel to the beam axis 306 between the proximal resistors R P1 、R P2 and the distal resistors R D1 、R D2 In the exemplary first bridge, the first neutral line is equidistant from each of R P1 and R P2 and is equidistant from each of R D1 and R D2 The first bridge 352 is longitudinally separated, where the proximal resistors R P1 、R P2 are longitudinally separated from the distal resistors R D1 、R D2 The first bridge is laterally expanded, where the proximal resistors R P1 、R P2 are laterally expanded and separated and the distal resistors R D1 、R D2 are laterally expanded and separated from each other. The second full Wheatstone bridge 354 has a first neutral axis 364 that extends along the outer surface of the beam 304 parallel to the beam axis 306 between the proximal resistors R P3 、R P4 and the distal resistors R D3 、R D4 In the exemplary second bridge, the second neutral line is equidistant from each of R P3 and R P4 and is equidistant from each of R D3 and R D4 The second bridge 354 is longitudinally separated, where the proximal resistors R P3 、R P4 are longitudinally separated from the distal resistors R D3 、R D4 The second bridge is laterally expanded, where the proximal resistors R P3 、R P4Laterally-spaced-apart and distal resistors R D3 、R D4 are laterally-spaced apart from each other.

[0102] It should be understood that since the resistors of the first full Wheatstone bridge 352 are laterally-spaced apart, they do not occupy the first neutral axis 362. Similarly, since the resistors of the second full Wheatstone bridge 354 are laterally-spaced apart, they do not occupy the second neutral axis 364. Accordingly, the conductor traces can be routed close to and parallel to the first and second neutral axes 362, 364, which can reduce the strain applied to the traces. Additionally, routing the traces along the neutral axes of the bridge circuits can be easier to fabricate, manufacture, or assemble.

[0103] An example first full bridge includes a first set of center conductor traces 356 that longitudinally extend along a center portion of the first bridge 352, parallel to the first neutral axis 362, along an outer surface 304-1 of the beam 304 between a pair of proximal resistors R P1 、R P2 and a pair of distal resistors R D1 、R D2 . The first set of center traces 356 includes a trace segment 356-1 coupled to the first positive output voltage VO1+. The first set of center traces 356 includes a trace segment 356-2 coupled to the first negative voltage output VO1-. The first set of center traces 356 includes a trace segment 356-3 coupled to the negative voltage potential EN.

[0104] Similarly, an example second full bridge includes a second set of center conductor traces 358 that longitudinally extend along a center portion of the second bridge 354, parallel to the second neutral axis 364, along an outer surface 304-2 of the beam 304 between a pair of proximal resistors R P3 、R P4 and a pair of distal resistors R D3 、R D4 . The second set of center traces 358 includes a trace segment 358-1 coupled to the second positive output voltage VO2+. The second set of center traces 358 includes a trace segment 358-2 coupled to the second negative voltage output VO2-. The second set of center traces 358 includes a trace segment 358-3 coupled to the negative voltage potential EN.

[0105] Figure 8B is Figure 8A An illustrative first schematic circuit diagram representation of the first and second full Wheatstone bridges. The first full Wheatstone bridge 352 includes R P1 and R D1 coupled between EP and ENTo provide a first half - bridge voltage divider circuit, the first half - bridge voltage divider circuit includes a trace conductor coupled to a first positive output voltage VO1+. The first full Wheatstone bridge 352 further includes Rs coupled between EP and EN P2 and Rs D2 To provide a second half - bridge voltage divider circuit, the second half - bridge voltage divider circuit includes a trace conductor coupled to a first negative output voltage VO1-. The second full Wheatstone bridge 354 includes Rs coupled between EP and EN P3 and Rs D3 To provide a third half - bridge voltage divider circuit, the third half - bridge voltage divider circuit includes a trace conductor coupled to a second negative output voltage VO2-. The second full Wheatstone bridge 354 further includes Rs coupled between EP and EN P4 and Rs D4 To provide a fourth half - bridge voltage divider circuit, the fourth half - bridge voltage divider circuit includes a trace conductor coupled to a second positive output voltage VO2+.

[0106] Figure 9A is Figure 4 An illustrative cross - sectional end view of an example beam 304, which indicates resistors on a first side and indicates a first planar force FP1 and a second planar force FP2. Figure 9B Indicates the orthogonal X - force component and Y - force component of the first planar force FP1 applied to a first proximal resistor R P1 and a first distal resistor R D1 in response to an applied force F. An illustrative force diagram. Figure 9C Indicates the X - force component and Y - force component of the second planar force FP2 applied to a second proximal resistor R P2 and a second distal resistor R D2 in response to an applied force F. An illustrative force diagram.

[0107] In the example force sensor 302, the resistance values of the first pair of resistors R P1 、R D1 are the same as those of the second pair of resistors R P2 、R D2Resistance value matching. In the exemplary force sensor 302, the first and second pairs of resistors are positioned on the exemplary beam 304 such that an applied force F applied to the exemplary beam 304 applies a first plane strain force FP1 to the first pair of resistors within the first plane P1 and a second plane strain force FP2 to the second pair of resistors within the second plane P2. It should be understood that the first plane strain force FPl is an off-axis force because it is a force applied along the first lateral side axis 312 that is laterally offset from the neutral axis 315 of the first bridge 352. Similarly, it should be understood that the second plane strain force FP2 is an off-axis force because it is a force applied along the second lateral side axis 314 that is laterally offset from the neutral axis 315 of the first bridge 352. The first and second pairs of resistors are positioned on the exemplary beam 304 such that the magnitude of the components of the first plane strain force FP1 matches the magnitude of the components of the second plane strain force FP2. The force directions of the first plane strain force FP1 and the second plane strain force FP2 are separated from each other by a first separation angle "A".

[0108] One advantage of using the same type of strain gauge resistor is that the magnitude of the force applied perpendicular to the central axis 306 of the beam 304 can be determined based on the difference in the magnitudes of the off-axis forces applied to different half-bridges of the full bridge located on the beam. In the exemplary force sensor 302, the Y-direction force component FY of the force F applied to the beam 304 Y can be determined based on the difference between the first off-axis force FP1 and the second off-axis force FP2 as follows.

[0109] Let A be the angle between P1 and P2.

[0110] Let the X axis bisect the angle A. Thus, the angle between P1 and X is A / 2, and the angle between P2 and X is A / 2.

[0111] Let θ be the angle between the X axis and the applied force F.

[0112] The force F along the X axis x = F cosθ

[0113] The force F along the y axis y = F sinθ

[0114] Referring to Figure 9B , the force along P1 = F x cos A / 2 + F y cos(90 + A / 2) = FP1

[0115] Referring to Figure 9C , the force along P2 = F x cos A / 2 + F y cos(90 - A / 2) = FP2

[0116] FP1 = F x cos(A / 2) + F y cos(90 + A / 2)

[0117] FP2 = F x cos(A / 2) + F y cos(90 - A / 2)

[0118] Using cos(θ) = -cos(180 - θ)

[0119] We get

[0120] FP2 = F x cos(A / 2) - F y cos(90 + A / 2)

[0121] When we subtract FP1 and FP2

[0122] We get FP1 - FP2 = F x cos(A / 2) + F y cos(90 + A / 2)

[0123] -F x cos(A / 2) + F y cos(90 + A / 2)

[0124] Therefore, FP1 - FP2 = 2F y cos(90 + A / 2)

[0125] Therefore, FP1 - FP2 ∝ F y

[0126] Therefore, the difference between FP1 and FP2 is proportional to the Y - direction force component F Y exerted on the beam by the applied force F

[0127] Furthermore, it should be understood that

[0128] F Y αV S1O+ –V S1O- ,

[0129] where V S1O+ is the positive output voltage of the first bridge circuit 352, V S1O- is the negative output voltage, and V S1O+ -V S1O- is the voltage offset generated by the first bridge circuit 352 located on the first side 308 of the beam 304

[0130] Figure 10 is Figure 4Exemplary cross-sectional end view of an exemplary beam that indicates resistors on a second side 310 of the beam 304 and indicates third-plane X-forces and fourth-plane X-forces. In the exemplary force sensor 302, the third pair of resistors R P3 , R D3 have a resistance value that matches the resistance value of the fourth pair of resistors R P4 , R D4 . In the exemplary force sensor 302, the third and fourth pairs of resistors are positioned on the exemplary beam 304 such that an applied force applied to the exemplary beam 304 applies a third-plane strain force FP3 to the third pair of resistors P3 in the third plane and applies a fourth-plane strain force FP4 to the fourth pair of resistors in the fourth plane P4. It should be understood that the third-plane strain force FP3 is an off-axis force because it is a force applied along the third lateral side axis 316, which is laterally offset from the neutral axis 315 of the second bridge 354. Similarly, it should be understood that the fourth-plane strain force FP4 is an off-axis force because it is a force applied along the fourth lateral side axis 318, which is laterally offset from the neutral axis 315 of the second bridge 354. The third and fourth pairs of resistors are positioned on the exemplary beam 304 such that the magnitude of the components of the third-plane strain force FP3 matches the magnitude of the components of the fourth-plane strain force FP4. The force directions of the third-plane strain force FP3 and the fourth-plane strain force FP4 are separated from each other by a second separation angle A.

[0131] In this example, the difference between FP3 and FP4 is proportional to the X-direction force component F X applied to the beam by the applied force F. Those skilled in the art will understand that the process for determining the difference between FP3 and FP4 is based on the above description of determining the difference between FP1 and FP2.

[0132] In addition, it should be understood that

[0133] F X = FP3 – FP4

[0134] F X αV S2O+ – V S2O- ,

[0135] where V S2O+ is the positive output voltage, V S2O- is the negative output voltage of the second bridge 354, and V S2O+ - V S2O- is the voltage offset generated by the second bridge circuit 354 on the second side 310 of the beam 304.

[0136] Figure 11 is a schematic diagram showing the metal sheet 1102, which includes defining the exemplary resistor R P1 - RP4 and R D1 -R D4 The cutouts of are for assembly into corresponding first and second full Wheatstone bridges on adjacent first side 308 and second side 310 of beam 304. The first region 1104 of the metal sheet 1102 includes resistors R for coupling in a first full bridge configuration located on the first side 308 of beam 304 P1 -R P2 and R D1 -R D2 . The second region 1106 of the metal sheet 1102 includes resistors R for coupling in a second full bridge configuration located on the second (Y-axis) side of the exemplary beam P3 -R P4 and R D3 -R D4 . The first and second regions are separated by a fold line 1108.

[0137] Figure 12A represents folding the metal sheet 1102 at the fold line 1108 to wrap the first and second regions of the metal sheet around the beam 304 to position the first pair of resistors R P1 -R P2 and R D1 -R D2 at the first side 308 of the beam 304 and to position the second pair of resistors R P3 -R P4 and R D3 -R D4 at the second side 310 of the beam 304. Figure 12B is an illustrative perspective view of beam 304 showing the first and second regions 1104 - 1106 of the metal sheet 1102 laid over the corresponding first and second sides 308 - 310 of the exemplary beam 304. In the exemplary rectangular beam, the first and second sides include adjacent sides of the beam. The metal sheet 1102 may be glued or welded to the beam 304 or a combination of both. During attachment, care is taken to align the metal sheet 1102 with the beam 304.

[0138] Redundant half - bridge XY force sensor

[0139] In sensors with four half - bridges and all the same type of gauges on the first side and the opposite side, subtracting the half - bridge voltages of two adjacent half - bridges provides a force measurement along an axis parallel to the plane of all gauges having two half - bridges. There are four ways to provide two measurements of F x and F y .

[0140] Figures 13A - 13B shows an illustrative first - side perspective view of an exemplary force sensor 2302 ( Figure 13A ) and a second - side perspective view (Figure 13B ), the force sensor includes a rectangular beam 2304, in which two strain gauge resistors R P1 -R P4 、R D1 -R D4 are coupled in two half Wheatstone bridge circuits ("half bridges") located on each of two opposite sides of the rectangular beam. Figure 13B The second side 308 of the beam 2304 shown in Figure 13A faces in a direction opposite to the direction faced by the first side 308 of the beam 2304 shown in

[0141] Reference Figure 13A , a first proximal strain gauge resistor ("resistor") R P1 and a second proximal resistor R P2 are located at the proximal beam portion 2304P of the first side 308 of the beam 2304. A first distal resistor R D1 and a second distal resistor R D2 are located at the distal beam portion 2304D of the first side 308 of the beam 2304. As explained in the following reference Figures 14A - 14B , 15A-15B, a first pair of resistors R P1 -R D1 are serially electrically coupled and arranged in the first half bridge, and a second pair of resistors R P2 -R D2 are serially electrically coupled and arranged in the second half bridge.

[0142] Reference Figure 13B , a third proximal resistor R P3 and a fourth proximal resistor R P4 are located at the proximal beam portion 2304P of the second side 2310 (also referred to as the "opposite" side) of the beam 2304 that faces in the opposite direction to the direction faced by the first side 308 of the beam 2304. A third distal resistor R D3 and a fourth distal resistor R D4 are located at the distal beam portion 2304D of the opposite second side 2310 of the beam 2304. As explained in the following reference Figures 14A - 14B , 15A-15B, a third pair of resistors R P3 -R D3 are serially electrically coupled and arranged in the third half bridge, and a fourth pair of resistors RP4 -R D4 The first and second half bridges are electrically coupled in series and arranged in a fourth half bridge.

[0143] Figure 14A 24 is an illustrative side view of an example beam including a first example half-bridge circuit layout 2402 having proximal and distal tensile gauge strain resistors RTP, RTD electrically coupled in series and having a voltage node coupled therebetween. The first example half-bridge circuit layout 2402 includes input bias voltage conductors (EP, EN) and proximal and distal tensile resistors RT P , RT D The output voltage node (Vo) is between . Figure 14B is an illustrative first schematic circuit diagram 2404 representation of a first half-bridge circuit layout 2402. Figures 14A - 14B , proximal tensile resistor RT P The far-side pull resistor RT is electrically coupled between the positive first DC potential (EP) and the output voltage node Vo. D is electrically coupled between the negative second DC potential (EN) and the output voltage node Vo. In the example force sensor 2302, each of the first, second, third, and fourth half bridges has a Figures 14A - 14B Layout 2402 and circuit schematic 2404 are shown in FIG.

[0144] Figure 15A is an illustrative side view of an example beam showing a second example half-bridge circuit layout 2502 having proximal and distal compression gauge strain resistors RC electrically coupled in series. P ,RC D and having a voltage node coupled therebetween. The second example half-bridge circuit layout 2502 includes input bias voltage conductors (EP, EN) and compression resistors RC at the proximal and distal sides. P ,RC D The output voltage node (Vo) is between . Figure 15B is an illustrative second schematic circuit diagram 2504 representation of a second half-bridge circuit layout 2502. Figures 15A - 15B , near side compression resistor RC P The far side compression resistor RC is electrically coupled between the positive first DC potential (EP) and the output voltage node Vo. D is electrically coupled between the negative second DC potential (EN) and the output voltage node Vo. In another example force sensor 2302, each of the first, second, third, and fourth half bridges has a Figures 15A - 15B Layout 2502 and circuit schematic 2504 are shown in FIG.

[0145] like Figures 14A - 14B andFigures 15A - 15B As shown, each half - bridge of the exemplary force sensor 2302 includes a pair of strain - gauge resistors of a matching type, which matching type can be tensile ( Figures 14A - 14B ) or compressive ( Figures 15A - 15B ). As used herein, referring to a set of resistors having a "matching type" means a set of resistors where all resistors are tensile resistors or all resistors are compressive resistors. Although either tensile or compressive gauge resistors can be used to determine forces in the X - and Y - directions, generally, tensile strain - gauge resistors are more sensitive than compressive gauge resistors.

[0146] Referring again to Figures 13A - 13B , as more fully explained below, the voltage offset between the first half - bridge voltage at the first voltage node between the first pair of resistors R P1 and R D1 and the second half - bridge voltage at the second voltage node between the second pair of resistors R P2 and R D2 can be used to measure the X - direction force applied to the beam 2304. Additionally, the voltage offset between the third half - bridge voltage at the third voltage node between the third pair of resistors R P3 and R D3 and the fourth half - bridge voltage at the fourth voltage node between the fourth pair of resistors R P4 and R D4 can be used to measure the X - direction force applied to the beam 2304. Thus, the first, second, third, and fourth half - bridges together provide a redundant measure of the X - direction force on the beam.

[0147] In addition, as more fully explained below, the voltage offset between the first half - bridge voltage at the first voltage node between the first pair of resistors R P1 and R D1 and the fourth half - bridge voltage at the fourth voltage node between the fourth pair of resistors R P4 and R D4 can be used to measure the Y - direction force applied to the beam 2304. Additionally, the offset between the second half - bridge voltage at the second voltage node between the second pair of resistors R P2 and R D2 and the third half - bridge voltage at the third voltage node between the third pair of resistors R P3 and R D3 can be used to measure the Y - direction force applied to the beam 2304.

[0148] Thus, the first, second, third, and fourth half - bridges together can provide a redundant measure of the X - direction force on the beam 2304 and can provide a redundant measure of the Y - direction force on the beam 2304. The resistors R P1 - R P4 and R D1 - RD4 A fault in any one of them results in a difference between the X-direction force measurement values determined using the first and second half-bridges on the one hand and the X-direction force measurement values determined using the third and fourth half-bridges on the other hand. Similarly, for the resistors R P1 -R P4 and R D1 -R D4 A fault in any one of them results in a difference between the Y-direction force measurement values determined using the first and fourth half-bridges on the one hand and the Y-direction force measurement values determined using the second and third half-bridges on the other hand.

[0149] Still referring to Figure 13A , the first proximal resistor R P1 and the first distal resistor R D1 are arranged on the first side 308 of the beam 2304 within the first imaginary plane P1, the central axis 306 extending in this plane P1, and the plane P1 defining a first lateral side axis 2312 at the position where the first plane P1 intersects the first side 308 of the beam 2304. The first lateral side axis 2312 and the central axis 306 extend parallel to each other. An example first lateral side axis 2312 extends through the first proximal resistor R P1 and through the first distal resistor R D1 . More specifically, in the example force sensor, the example first lateral side axis 2312 bisects the example first proximal resistor R P1 and bisects the example first distal resistor R D1 .

[0150] Referring to Figure 13A , the second proximal resistor R P2 and the second distal resistor R D2 are arranged on the first side 308 of the beam within the second imaginary plane P2, the central axis 306 extending in this plane P2, and the plane P2 defining a second lateral side axis 2314 at the position where the second plane P2 intersects the first side. The second lateral axis 2314 and the central axis 306 extend parallel to each other. An example second lateral side axis 2314 extends through the second proximal resistor R P2 and through the second distal resistor R D2 . More specifically, in the example force sensor, the example second lateral side axis 2314 bisects the example second proximal resistor R P2 and bisects the example second distal resistor R D2 .

[0151] Referring to Figure 13B , the third proximal resistor R P3 and the third distal resistor R D3The example third lateral side axis 2316 extends through the third proximal resistor R P3 and through the third remote resistor R D3 More specifically, in the example force sensor, the example third lateral axis 2316 bisects the example third proximal resistor R P3 and bisects the example third remote resistor R D3 .

[0152] refer to Figure 13B , the fourth proximal resistor R P4 and the fourth remote resistor R D4 The example fourth lateral side axis 2318 extends through the fourth proximal resistor R P4 and through the fourth far resistor R D4 More specifically, in the example force sensor, the example fourth lateral axis bisects the example fourth proximal resistor R P4 and bisects the example first remote resistor R D4 .

[0153] Figure 16 yes Figures 13A - 13B An illustrative proximal cross-sectional view of an example beam 2304 showing first and second imaginary planes P1 , P2 . Figure 17A is a side view of beam 2304, which shows Figures 13A - 13B The first side 308 of the beam includes a first (R P1 ) and the second (R D1 ) and a second resistor and includes a third (R P2 ) and the fourth (R D2 ) resistor. Figure 17B is a side view of beam 2304, which shows Figures 13A - 13B The opposite second side 308 of the beam includes a second bridge including a fifth (R P3 ) and the sixth (R D3 ) resistor, and a seventh (RP4 ) and the eighth (R D4 ) resistor.

[0154] The resistors can be placed on the beam 2304 manually or using an automated machine, and the resistors can be adhered to the beam using an adhesive such as epoxy. Alternatively, the resistors can be directly deposited and laser-etched onto the beam 2304. In both cases, the circuitry can be completed externally using wire bonding and flexible printed circuits.

[0155] Referring Figure 16 , a proximal end view of the beam 2304 shows a side view of a first plane P1 and a second plane P2 intersecting each other along a central axis 306 that extends within the first and second planes. The first plane P1 extends through the first and third half-bridges HB1, HB3 and through the central axis 306. The second plane P1 extends through the second and fourth half-bridges HB2, HB4 and through the central axis 306. The portions of the first plane P1 and the second plane P2 that extend through the respective first and second half-bridges HB1, HB2 intersect the central axis 306 at a first separation angle A1. The portions of the first plane P1 and the second plane P2 that extend through the respective third and fourth half-bridges HB3, HB4 also intersect the central axis 306 at the first separation angle A1.

[0156] Referring Figure 17A , the first plane P1 is shown as extending through the first half-bridge HB1 that includes a first proximal resistor R P1 and a first distal resistor R D1 arranged along a first lateral side axis 2312 on a first side 308 of the beam 2304, and the second plane P2 is shown as extending through the second half-bridge HB2 that includes a second proximal resistor R P2 and a second distal resistor R D2 arranged along a second lateral side axis 2314 on the first side 308 of the beam 2304. The magnitude of the first separation angle A1 corresponds to the lateral spacing distance between the first and second lateral side axes 2312, 2314 at the first side 308, and thus corresponds to the lateral spacing between the first half-bridge HB1 that includes the first proximal and distal resistors R P1 , R D1 and the second resistor pair that includes the second proximal and distal resistors R P2 , R D2 . In the exemplary force sensor 2302, the first lateral side axis 2312 and the second lateral side axis 2314 are equidistant from the neutral axis of the first side of the beam 2304, which is equidistant from the first and second lateral side edges 2312, 2314 of the first side 308 of the beam 2304.

[0157] ReferringFigure 17B The first plane P1 is shown as extending through the third half - bridge HB3, which includes a third proximal resistor R P3 and a third distal resistor R D3 that are arranged on the second side 2310 of the beam 2304 along a third lateral side axis 2316, and the second plane P2 is shown as extending through the fourth half - bridge HB4, which includes a fourth proximal resistor R P4 and a fourth distal resistor R D4 that are arranged on the second side 2310 of the beam 2304 along a fourth lateral side axis 2318. The magnitude of the first separation angle A1 corresponds to the lateral spacing distance between the third and fourth lateral side axes 2316 - 2318 at the second side 2310 of the beam 2304 and, thus, corresponds to the lateral spacing between the third half - bridge HB3 that includes a third resistor pair comprising RP3, RD3 and the fourth half - bridge HB4 that includes a fourth resistor pair comprising R P4 、R D4 . In the example force sensor, the third lateral side axis 2316 and the fourth lateral side axis 2318 are equidistant from the neutral axis of the second side 2310 of the beam 2304, which is equidistant from the third and fourth lateral side edges 2316, 2318 of the second side 2310 of the beam 2304.

[0158] The half - bridges HB1 - HB4 are laterally positioned symmetrically with respect to the beam 2304. The separation angle A1 between the first half - bridge and the second half - bridge matches the first separation angle A1 between the third half - bridge HB3 and the fourth half - bridge HB4. Additionally, in the example force sensor 2302, the spacing between the first lateral side axis 2312 and the second lateral side axis 2314 matches the spacing between the third lateral side axis 2316 and the fourth lateral side axis 2318, although an equidistant spacing is not required. The half - bridges HB1 - HB4 are longitudinally positioned symmetrically along the beam 2304. The proximal resistors R P1 -R P4 are positioned at matching longitudinal positions of the beam. In the example force sensor, the distal resistors R D1 -R D4 are positioned at matching longitudinal positions of the beam.

[0159] Figure 18A is Figures 13A - 13B an illustrative proximal - direction cross - sectional view of an example beam 2304 that indicates the second plane strain force FP2 and the third plane strain force FP3 applied to the respective second and third half - bridges HB2, HB3 by a force F applied to the beam 2304. In Figure 18A the example beam, the second and third half - bridges HB2, HB3 contain only tensile resistors. Figure 18Bis an illustrative force diagram indicating the X-force component and Y-force component of the second planar strain force FP2 applied to the second half-bridge HB2 in response to an applied force F, the half-bridge HB2 including a second proximal resistor R P2 and a second distal resistor R D2 . Figure 18C is an illustrative force diagram indicating the orthogonal X-force component and Y-force component of the third planar strain force FP3 applied to the third half-bridge HB3 in response to an applied force, the half-bridge HB3 including a third proximal resistor R P3 and a third distal resistor R D3 .

[0160] In the example force sensor 2302, the second pair of resistors R P2 、R D2 of the second half-bridge HB2 have resistance values that match the resistance values of the third pair of resistors R P3 、R D3 of the third half-bridge HB3. In the example force sensor 2302, the second and third half-bridges HB2, HB3 are positioned on the example beam 2304 such that an applied force applied to the example beam 2304 applies the second planar strain force FP2 to the second half-bridge HB2 within the second plane P2 and applies the third planar strain force FP3 to the third half-bridge HB3 within the third plane P3. It should be understood that the second planar strain force FP2 is an off-axis force because it is a force applied along the second lateral side axis 2314. Similarly, it should be understood that the third planar strain force FP3 is an off-axis force because it is a force applied along the third lateral side axis 2316. In the example force sensor 2302, the second and third half-bridges HB2, HB3 are positioned on the example beam 2304 such that the magnitudes of the components of the second planar strain force FP2 match the magnitudes of the components of the third planar strain force FP3.

[0161] One advantage of using the same type of strain gauge resistor is that the magnitude of the force applied perpendicular to the central axis 306 of the beam 2304 can be determined based on the difference in the magnitudes of the off-axis forces applied to different half-bridges of the full bridge located on the beam. In the example force sensor 2302, the magnitude of the Y-direction force component F Y applied to the beam 2304 by the applied force F can be determined as follows based on the difference between the first off-axis force FP2 and the second off-axis force FP3.

[0162] Let A be the angle between P2 and P3.

[0163] Let the X-axis bisect the angle A. Thus, the angle between P2 and X is A / 2, and the angle between P3 and X is A / 2.

[0164] Let θ be the angle between the X-axis and the applied force F.

[0165] The force F along the X-axisx = F cosθ

[0166] The force F along the y-axis y = F sinθ

[0167] Reference Figure 18B , the force along P2 = F x cos A / 2 + F y cos(90 + A / 2) = FP2

[0168] Reference Figure 18C , the force along P3 = F x cos A / 2 + F y cos(90 - A / 2) = FP3

[0169] FP2 = F x cos A / 2 + F y cos(90 + A / 2)

[0170] FP3 = F x cos A / 2 + F y cos(90 - A / 2)

[0171] Using cos(θ) = -cos(180 - θ)

[0172] We get

[0173] FP3 = F x cos A / 2 - F y cos(90 + A / 2)

[0174] When we subtract FP1 and FP2

[0175] We get FP2 – FP3 = F x cos A / 2 + F y cos(90 + A / 2)

[0176] -F x cos A / 2 + F y cos(90 + A / 2)

[0177] Therefore, FP2 – FP2 = 2F y cos(90 + A / 2)

[0178] Therefore, FP2 – FP3 ∝ F y

[0179] Therefore, the difference between FP2 and FP3 is proportional to the Y-direction force component F of the applied force F on the beam Y is proportional to

[0180] In addition, it should be understood that

[0181] F Y = FP2 - FP2

[0182] F Y αV O2 –V O3

[0183] where V O2 is the output voltage of HB2, V O3 is the output voltage of HB3.

[0184] Figure 19 is Figures 13A - 13B An illustrative proximal direction cross-sectional view of an example beam that indicates the first and fourth plane strain forces FP1 and FP4 applied to the respective first and fourth half-bridges HB1, HB4 by a force F applied to beam 2304. In Figure 19 the example beam, the first and fourth half-bridges HB1, HB4 contain only tensile resistance resistors. In example force sensor 2302, the first pair of resistors R P1 , R D1 of the first half-bridge HB1 have a resistance value that matches the resistance value of the fourth pair of resistors R P4 , R D4 of the fourth half-bridge HB4. In example force sensor 2302, the first and fourth half-bridges HB1, HB4 are positioned on example beam 2304 such that an applied force F applied to example beam 2304 applies a first plane strain force FP1 to the first half-bridge HB1 within the first plane P1 and applies a fourth plane strain force FP4 to the fourth half-bridge HB4 within the second plane P4. In example force sensor 2302, the first and fourth half-bridges HB1, HB4 are positioned on example beam 2304 such that the component magnitude of the first plane strain force FP1 matches the magnitude of the component of the fourth plane strain force FP4.

[0185] In this example, the difference between FP1 and FP4 is proportional to the force component F Y in the Y direction of the beam applied by the applied force F. Those skilled in the art will understand that the process for determining the difference between FP1 and FP4 is based on the description above for determining the difference between FP2 and FP3.

[0186] Furthermore, it should be understood that

[0187] F Y = FP1 – FP4

[0188] F Y αV O1 –V O4

[0189] where V O1is the output voltage of HB1, V O4 is the output voltage of HB4.

[0190] Figure 20 is Figures 13A - 13B An illustrative proximal direction cross-sectional view of exemplary beam 2304 that indicates first and second planar strain forces FP1 and FP2 applied to respective first and second half-bridges HB1, HB2 by a force applied to beam 2304. In exemplary force sensor 2302, a first pair of resistors R P1 , R D1 of first half-bridge HB1 have a resistance value that matches the resistance value of a second pair of resistors R P2 , R D2 of second half-bridge HB2. In exemplary force sensor 2302, first and second half-bridges HB1, HB2 are positioned on exemplary beam 2304 such that an applied force applied to exemplary beam 2304 applies a first planar strain force FP1 to first half-bridge HB1 within first plane P1 and a second planar strain force FP2 to second half-bridge HB2 within second plane P2. It should be understood that first planar strain force FP1 is an off-axis force because it is a force applied along first lateral side axis 2312. Similarly, it should be understood that second planar strain force FP2 is an off-axis force because it is a force applied along second lateral side axis 2314. First and second half-bridges HB1, HB2 are positioned on exemplary beam 2304 such that the magnitude of first planar strain force FP1 X matches the magnitude of second planar strain force FP2. The force direction of first planar strain force FP1 X and first plane P1 are separated from each other by a first separation angle A1.

[0191] In this example, the difference between FP1 and FP2 is proportional to the X-direction force component FX of the force F applied to the beam. Those skilled in the art will understand that the process for determining the difference between FP1 and FP2 is based on the description above for determining the difference between FP2 and FP3.

[0192] In addition, it should be understood that

[0193] F X = FP1 - FP2

[0194] F X αV O1 – V O2

[0195] where V O1 is the output voltage of HB1 and V O2 is the output voltage of HB2. Figure 21 is Figures 13A - 13BExemplary proximal direction cross-sectional view of exemplary beam 2304, which indicates the force F applied to the beam X applied to the third and fourth plane strain forces FP3 and FP4 of the corresponding third and fourth half-bridges HB3, HB4. In the exemplary force sensor 2302, the third pair of resistors R of the third half-bridge HB3 P3 、R D3 have resistance values that match those of the fourth pair of resistors R of the fourth half-bridge HB4 P4 、R D4 In the exemplary force sensor 2302, the third and fourth half-bridges HB3, HB4 are positioned on the exemplary beam 2304 such that the applied force applied to the exemplary beam 2304 applies the third plane strain force FP3 to the third half-bridge HB3 within the third plane P3 and applies the fourth plane strain force FP4 to the fourth half-bridge HB4 within the fourth plane P4. It should be understood that the third plane strain force FP3 is an off-axis force because it is a force applied along the third lateral side axis 2316. Similarly, it should be understood that the fourth plane strain force FP4 is an off-axis force because it is a force applied along the fourth lateral side axis 2318. In the exemplary force sensor 2302, the third and fourth half-bridges HB3, HB4 are positioned on the exemplary beam 2304 such that Figure 21 the magnitude of is Figures 13A - 13B exemplary beam 2304 which indicates the force F applied to the beam X applied to the third and fourth plane strain forces FP3 and FP4 of the corresponding third and fourth half-bridges HB3, HB4. Exemplary proximal direction cross-sectional view.

[0196] In this example, the difference between FP3 and FP4 is proportional to the X-direction force component F of the force F applied to the beam X skilled in the art will understand that the process for determining the difference between FP3 and FP4 is based on the description above for determining the difference between FP2 and FP3.

[0197] In addition, it should be understood that

[0198] F X = FP3 – FP4

[0199] F X αV O3 – V O4

[0200] where V O3 is the output voltage of HB3, and V O4 is the output voltage of HB4.

[0201] Therefore, assuming that all resistors R P1 -R P4 and RD1 -R D4 Works normally

[0202] F X αV O1 –V O2 = V O3 –V O4 and F Y αV O1 –V O4 = V O2 –V O3

[0203] In addition, it should be understood that F X and F Y can be more generally determined based on each of the following four combinations of three half - bridges (HB) listed in Table 1 below.

[0204] Table 1

[0205] HB combination number <![CDATA[Suitable for determining F X and F Y of the HB combination]]> 1 HB1, HB2, HB3 2 HB1, HB2, HB4 3 HB3, HB4, HB2 4 HB4, HB3, HB1

[0206] Therefore, the half - bridge combinations in Table 1 above can be used to perform redundancy determination on F X and F Y Based on the comparison of the F X and F Y values determined based on the above - mentioned half - bridge combinations, it can be used to determine whether the force sensor 2304 contains a faulty resistor. If even a single resistor fails, then all four combinations will produce different Fx and Fy values, indicating a fault. Since all four HBs produce different results when a fault occurs, it is impossible to determine which resistor has failed. Adding one or more additional half - bridges to the beam can be used to achieve a fault - tolerant design because the comparison of five or more combinations of three bridges can be used to determine which half - bridge is defective, so the measurement values from the defective half - bridge can be ignored.

[0207] Redundant single - sided XY force sensor

[0208] An example single - sided XY force sensor includes a beam that includes four half - bridges located on one side of it. Two of the half - bridges are of one of the compression types, and two of the half - bridges are of the tension type. Since the compression and tension strain gauge resistors measure strains that occur in opposite directions in response to a force applied to the beam, the measured values of the combination of three half - bridges located on the same side of the beam can be used to measure the X - direction force and the Y - direction force, where one of the three half - bridges has a different type of strain gauge resistor than the other two. The example single - sided XY force sensor can perform redundant XY measurements, where the example single - sided XY force sensor includes four half - bridges, two of which are of the compression type and two of which are of the tension type.

[0209] In a sensor having four half - bridges and all the same type of gauges on a first side and an opposite side, subtracting the half - bridge voltages of two adjacent half - bridges provides a force measurement value along an axis parallel to the plane of all the gauges having two half - bridges. There are four ways to provide two measurements of Fx and Fy.

[0210] Figures 13A - 13B Illustrative first - side perspective view ( Figure 13A ) and second - side perspective view ( Figure 13B ) of an exemplary force sensor 2302 are shown, the force sensor including a rectangular beam 2304 in which two four - strain - gauge resistors R P1 - R P4 、R D1 - R D4 are coupled in two half - Wheatstone bridge circuits (“half - bridges”) located on each of two opposite sides of the beam. Figure 13B The second side 308 of the beam 2304 shown in Figure 13A faces in a direction opposite to the direction faced by the first side 308 of the beam 2304 shown in

[0211] Reference Figure 13A , a first proximal strain - gauge resistor (“resistor”) R P1 and a second proximal resistor R P2 are located at the proximal beam portion 2304P of the first side 308 of the beam 2304. A first distal resistor R D1 and a second distal resistor R D2 are located at the distal beam portion 2304D of the first side 308 of the beam 2304. As explained in the following reference Figures 14A - 14B , 15A - 15B, a first pair of resistors R P1 - R D1 are serially electrically coupled and arranged in a first half - bridge, while a second pair of resistors R P2 - R D2 are serially electrically coupled and arranged in a second half - bridge.

[0212] Reference Figure 13B , a third proximal resistor R P3 and a fourth proximal resistor R P4At the proximal beam portion 2304P of the second side 2310 (also referred to as the "opposite" side) of the beam 2304 that faces in the opposite direction to the direction faced by the first side 308 of the beam 2304. The third distal resistor R D3 and the fourth distal resistor R D4 are located at the distal beam portion 2304D of the opposite second side 2310 of the beam 2304. As explained in the following references Figures 14A - 14B 、15A - 15B, the third pair of resistors R P3 -R D3 are serially electrically coupled and arranged in the third half - bridge, and the fourth pair of resistors R P4 -R D4 are serially electrically coupled and arranged in the fourth half - bridge which is arranged in the fourth half - bridge.

[0213] Figure 14A is an illustrative side view of an example beam that includes a first example half - bridge circuit layout 2402, which has proximally and distally serially electrically coupled strain gauges RT P 、RT D and has a voltage node coupled therebetween. The first example half - bridge bridge circuit layout 2402 includes input bias voltage conductors (EP, EN) and outputs a voltage node (V P 、RT D between the proximal and distal strain gauges RT o ). Figure 14B is an illustrative first schematic circuit diagram 2404 representation of the first half - bridge circuit layout 2402. Referring to Figures 14A - 14B , the proximal strain gauge RT P is electrically coupled between a positive first DC potential (EP) and the output voltage node V o . The distal strain gauge RT D is electrically coupled between a negative second DC potential (EN) and the output voltage node V o . In the example force sensor 2302, each of the first, second, third, and fourth half - bridges has the layout 2402 and circuit schematic 2404 as represented in Figures 14A - 14B .

[0214] Figure 15A is an illustrative side view of an example beam showing a second example half - bridge circuit layout 2502, which has proximally and distally serially electrically coupled compression gauges RC P 、RC D and has a voltage node coupled therebetween. The second example half - bridge bridge circuit layout 2502 includes input bias voltage conductors (EP, EN) and between the proximal and distal compression gauges RC P 、RCD Between the output voltage node (Vo). Figure 15B Is an illustrative second schematic circuit diagram 2504 representation of the second half-bridge circuit layout 2502. Refer to Figures 15A - 15B , the proximal compression resistor RC P Is electrically coupled between the positive first DC potential (EP) and the output voltage node Vo. The distal compression resistor RC D Is electrically coupled between the negative second DC potential (EN) and the output voltage node Vo. In another example force sensor 2302, each of the first, second, third, and fourth half-bridges has the layout 2502 and circuit schematic 2504 represented in Figures 15A - 15B .

[0215] As Figures 14A - 14B And Figures 15A - 15B Shown, each half-bridge of the example force sensor 2302 includes a pair of strain gauge resistors of a matching type, which matching type can be tensile type ( Figures 14A - 14B ) or compressive type ( Figures 15A - 15B ). As used herein, referring to a set of resistors having a "matching type" means a set of resistors where all the resistors are tensile resistors or all the resistors are compressive resistors. Although both tensile or compressive strain gauge resistors can be used to determine forces in the X and Y directions, generally, tensile strain gauge resistors are more sensitive than compressive strain gauge resistors.

[0216] Referring again to Figures 13A - 13B , as more fully explained below, the voltage offset between the first half-bridge voltage at the first voltage node between the first pair of resistors R P1 、R D1 And the second half-bridge voltage at the second voltage node between the second pair of resistors R P2 、R D2 Can be used to measure the X-direction force applied to the beam 2304. Additionally, the voltage offset between the third half-bridge voltage at the third voltage node between the third pair of resistors R P3 、R D3 And the fourth half-bridge voltage at the fourth voltage node between the fourth pair of resistors R P4 、R D4 Can be used to measure the X-direction force applied to the beam 2304. Thus, the first, second, third, and fourth half-bridges together provide a redundant measure of the X-direction force on the beam.

[0217] In addition, as more fully explained below, the voltage offset between the first half-bridge voltage at the first voltage node between the first pair of resistors R P1 、R D1 And the fourth half-bridge voltage at the fourth voltage node between the fourth pair of resistors R P4 、R D4The voltage offset between the fourth half-bridge voltages at the fourth voltage node therebetween can be used to measure the Y-direction force applied to the beam 2304. Additionally, the offset between the second half-bridge voltage at the second voltage node between the second pair of resistors R P2 and R D2 and the third half-bridge voltage at the third voltage node between the third pair of resistors R P3 and R D3 can be used to measure the Y-direction force applied to the beam 2304.

[0218] Thus, the first, second, third, and fourth half-bridges together are capable of providing a redundant measure of the X-direction force on the beam 2304 and are capable of providing a redundant measure of the Y-direction force on the beam 2304. A failure of any one of the resistors R P1 -R P4 and R D1 -R D4 results in a difference between the X-direction force measurement determined using the first and second half-bridges on the one hand and the X-direction force measurement determined using the third and fourth half-bridges on the other hand. Similarly, a failure of any one of the resistors R P1 -R P4 and R D1 -R D4 results in a difference between the Y-direction force measurement determined using the first and fourth half-bridges on the one hand and the Y-direction force measurement determined using the second and third half-bridges on the other hand.

[0219] Still referring to Figure 13A , the first proximal resistor R P1 and the first distal resistor R D1 are arranged on the first side 308 of the beam 2304 within the first imaginary plane P1, the central axis 306 extending in this plane P1, and the plane P1 defining a first lateral side axis 2312 at the position on the first side 308 of the beam 2304 where the first plane P1 intersects therewith. The first lateral side axis 2312 and the central axis 306 extend parallel to each other. An example first lateral side axis 2312 extends through the first proximal resistor R P1 and through the first distal resistor R D1 . More specifically, in the example force sensor, the example first lateral side axis 2312 bisects the example first proximal resistor R P1 and bisects the example first distal resistor R D1 .

[0220] Referring to Figure 13A , the second proximal resistor R P2 and the second distal resistor R D2On the first side 308 of the beam disposed within the second imaginary plane P2, the central axis 306 extends within this plane P2, and the plane P2 defines a second lateral axis 2314 at the position where the plane P2 intersects the first side 308 of the beam 2304. The second lateral axis 2314 and the central axis 306 extend parallel to each other. An example second lateral axis 2314 extends through the second proximal resistor R P2 and through the second distal resistor R D2 . More specifically, in the example force sensor, the example second lateral axis 2314 bisects the example second proximal resistor R P2 and bisects the example second distal resistor R D2 .

[0221] Reference Figure 13B , the third proximal resistor RP3 and the third distal resistor R D3 are disposed on the opposite second side 2310 of the beam 2304 within the first imaginary plane P1, the central axis 306 extends within this plane P1, and the plane P1 defines a third lateral axis 2316 at the position where the plane P1 intersects the second side 2310 of the beam 2304. An example third lateral axis 2316 extends through the third proximal resistor R P3 and through the third distal resistor R D3 . More specifically, in the example force sensor, the example third lateral axis 2316 bisects the example third proximal resistor R P3 and bisects the example third distal resistor R D3 .

[0222] Reference Figure 13B , the fourth proximal resistor R P4 and the fourth distal resistor R D4 are disposed on the opposite second side 2310 of the beam 2304 within the second imaginary plane P2, the central axis 306 extends within this plane P2, and the plane P2 defines a fourth lateral axis 2318 at the position where the plane P2 intersects the second side 2310 of the beam 2304, and the plane P2 includes the central axis 306. An example fourth lateral axis 2318 extends through the fourth proximal resistor R P4 and through the fourth distal resistor R D4 . More specifically, in the example force sensor, the example fourth lateral axis bisects the example fourth proximal resistor R P4 and bisects the example first distal resistor R D4 .

[0223] Figure 16 is Figures 13A - 13BExemplary proximal direction cross-sectional view of beam 2304, showing first and second imaginary planes P1, P2. Figure 17A is a side view of beam 2304, showing Figures 13A - 13B a first side 308 of the beam, which includes a first resistor (R P1 ) and a second resistor (R D1 ) coupled in a first half-bridge HB1 and includes a third resistor (R P2 ) and a fourth resistor (R D2 ) coupled in a second half-bridge HB2. Figure 17B is a side view of beam 2304, showing Figures 13A - 13B an opposite second side 308 of the beam, which includes a second bridge that includes a fifth resistor (R P3 ) and a sixth resistor (R D3 ) coupled in a third half-bridge HB3, and includes a seventh resistor (R P4 ) and an eighth resistor (R D4 ) coupled in a fourth half-bridge HB4.

[0224] The resistors can be placed on beam 2304 manually or using automated machinery, and the resistors can be adhered to the beam using an adhesive such as epoxy. Alternatively, the resistors can be directly deposited and laser-etched onto beam 2304. In both cases, the circuit can be completed externally using wire bonding and flexible printed circuits.

[0225] Referring Figure 16 , a proximal direction end view of beam 2304 shows side views of a first plane P1 and a second plane P2 intersecting each other along a central axis 306 that extends within the first and second planes. The first plane P1 extends through the first and third half-bridges HB1, HB3 and through the central axis 306. The second plane P1 extends through the second and fourth half-bridges HB2, HB4 and through the central axis 306. The portions of the first plane P1 and the second plane P2 that extend through the respective first and second half-bridges HB1, HB2 intersect at the central axis 306 at a first separation angle A1. The portions of the first plane P1 and the second plane P2 that extend through the respective third and fourth half-bridges HB3, HB4 also intersect at the central axis 306 at the first separation angle.

[0226] Referring Figure 17A , the first plane P1 is shown extending through the first half-bridge HB1, which includes a first proximal resistor R P1 and a first distal resistor R D1and the second plane P2 is shown as extending through the second half bridge HB2, which includes a second proximal resistor R arranged on the first side 308 of the beam 2304 along the second lateral side axis 2314 P2 and a second distal resistor R D2 . The magnitude of the first separation angle A1 corresponds to the lateral spacing distance between the first and second lateral side axes 2312, 2314 at the first side 308, and thus corresponds to the lateral spacing between the first half bridge HB1 including the first proximal and distal resistors R P1 、R D1 and the second resistor pair including the second proximal and distal resistors R P2 、R D2 . In the exemplary force sensor 2302, the first lateral side axis 2312 and the second lateral side axis 2314 are equidistant from the neutral axis of the first side of the beam 2304, which is equidistant from the first and second lateral side edges 2312, 2314 of the first side 308 of the beam 2304.

[0227] Reference Figure 17B , the first plane P1 is shown as extending through the third half bridge HB3, which includes a third proximal resistor R arranged on the second side 2310 of the beam 2304 along the third lateral side axis 2316 P3 and a third distal resistor R D3 , and the second plane P2 is shown as extending through the fourth half bridge HB4, which includes a fourth proximal resistor R arranged on the second side 2310 of the beam 2304 along the fourth lateral side axis 2318 P4 and a fourth distal resistor R D4 . The magnitude of the first separation angle A1 corresponds to the lateral spacing distance between the third and fourth lateral side axes 2316 - 2318 at the second side 2310 of the beam 2304, and thus corresponds to the lateral spacing between the third half bridge HB3 including the third resistor pair including R P3 、R D3 and the fourth half bridge HB4 including the fourth resistor pair including R P4 、R D4 . In the exemplary force sensor, the third lateral side axis 2316 and the fourth lateral side axis 2318 are equidistant from the neutral axis of the second side 2310 of the beam 2304, which is equidistant from the third and fourth lateral side edges 2316, 2318 of the second side 2310 of the beam 2304.

[0228] The half - bridges HB1 - HB4 are positioned transversely symmetrically about the beam 2304. The separation angle A1 between the first and second half - bridges matches the first separation angle A1 between the third and fourth half - bridges HB3 - HB4. Additionally, in the exemplary force sensor 2302, the spacing between the first lateral side axis 2312 and the second lateral side axis 2314 matches the spacing between the third lateral side axis 2316 and the fourth lateral side axis 2318, although an equidistant spacing is not required. The half - bridges HB1 - HB4 are positioned longitudinally symmetrically along the beam 2304. The proximal resistors R P1 -R P4 are positioned at matching longitudinal positions of the beam. In the exemplary force sensor, the distal resistors R D1 -R D4 are positioned at matching longitudinal positions of the beam.

[0229] Figure 18A is Figures 13A - 13B an illustrative proximal - direction cross - sectional view of the exemplary beam 2304, which indicates the second plane - strain force FP2 and the third plane - strain force FP3 applied to the corresponding second and third half - bridges HB2, HB3 by the force F applied to the beam 2304. In Figure 18A the exemplary beam, the second and third half - bridges HB2, HB3 contain only tensile resistors. Figure 18B is an illustrative force - diagram indicating the X - force component and the Y - force component of the second plane - strain force FP2 applied to the second half - bridge HB2 in response to the applied force F, where the half - bridge HB2 includes the second proximal resistor R P2 and the second distal resistor R D2 . Figure 18C is an illustrative force - diagram indicating the orthogonal X - force component and the Y - force component of the third plane - strain force FP3 applied to the third half - bridge HB3 in response to the applied force, where the half - bridge HB3 includes the third proximal resistor R P3 and the third distal resistor R D3 .

[0230] In the exemplary force sensor 2302, the resistance values of the second pair of resistors R P2 、R D2 of the second half - bridge HB2 are the same as those of the third pair of resistors R P3 、R D3Resistance value matching. In the exemplary force sensor 2302, the second and third half-bridges HB2, HB3 are positioned on the exemplary beam 2304 such that an applied force applied to the exemplary beam 2304 applies a second planar strain force FP2 to the second half-bridge HB2 within the second plane P2 and a third planar strain force FP3 to the third half-bridge HB3 within the third plane P3. It should be understood that the second planar strain force FP2 is an off-axis force as it is a force applied along the second lateral side axis 2314. Similarly, it should be understood that the third planar strain force FP3 is an off-axis force as it is a force applied along the third lateral side axis 2316. In the exemplary force sensor 2302, the second and third half-bridges HB2, HB3 are positioned on the exemplary beam 2304 such that the magnitude of the components of the second planar strain force FP2 matches the magnitude of the components of the third planar strain force FP3.

[0231] One advantage of using the same type of strain gauge resistors is that the magnitude of the force applied perpendicular to the central axis 306 of the beam 2304 can be determined based on the difference in the magnitudes of the off-axis forces applied to different half-bridges of the full bridge located on the beam. In the exemplary force sensor 2302, the Y-direction force component F Y applied to the beam 2304 by the applied force F can be determined as follows based on the difference between the first off-axis force FP2 and the second off-axis force FP3.

[0232] Let A be the angle between P2 and P3.

[0233] Let the X axis bisect the angle A degrees. Thus, the angle between P2 and X is A / 2, and the angle between P3 and X is A / 2.

[0234] Let θ be the angle between the X axis and the applied force F.

[0235] The force F along the X axis x = F cosθ

[0236] The force F along the y axis y = F sinθ

[0237] Refer to Figure 18B , the force along P2 = F x cos A / 2 + F y cos(90 + A / 2) = FP2

[0238] Refer to Figure 18C , the force along P3 = F x cos A / 2 + F y cos(90 - A / 2) = FP3

[0239] FP2 = F x cos A / 2 + F y cos(90 + A / 2)

[0240] FP3 = F x cosA / 2 + F y cos(90 - A / 2)

[0241] Using cos(θ) = -cos(180 - θ)

[0242] We obtain

[0243] FP3 = F x cosA / 2 - F y cos(90 + A / 2)

[0244] When we subtract FP1 and FP2

[0245] We obtain FP2 – FP3 = F x cosA / 2 + F y cos(90 + A / 2)

[0246] -F x cosA / 2 + F y cos(90 + A / 2)

[0247] Therefore, FP2 – FP2 = 2F y cos(90 + A / 2)

[0248] Therefore, FP2 – FP3 ∝ F y

[0249] Therefore, the difference between FP2 and FP3 is proportional to the Y - direction force component F of the applied force F on the beam Y is proportional to

[0250] In addition, it should be understood that

[0251] F Y = FP2 - FP2

[0252] F Y αV O2 –V O3

[0253] where V O2 is the output voltage of HB2, and V O3 is the output voltage of HB3

[0254] Figure 19 is Figures 13A - 13B An illustrative proximal - direction cross - sectional view of an example beam, which indicates the first planar strain force FP1 and the fourth planar strain force FP4 applied to the corresponding first and fourth half - bridges HB1, HB4 by the force F applied to the beam 2304. In Figure 19In the exemplary beam, the first and fourth half - bridges HB1, HB4 contain only tensile - resistance resistors. In the exemplary force sensor 2302, the first pair of resistors R P1 , R D1 of the first half - bridge HB1 have a resistance value that matches the resistance value of the fourth pair of resistors R P4 , R D4 of the fourth half - bridge HB4. In the exemplary force sensor 2302, the first and fourth half - bridges HB1, HB4 are positioned on the exemplary beam 2304 such that the applied force F applied to the exemplary beam 2304 applies a first plane - strain force FP1 to the first half - bridge HB1 within the first plane P1 and a fourth plane - strain force FP4 to the fourth half - bridge HB4 within the second plane P4. In the exemplary force sensor 2302, the first and fourth half - bridges HB1, HB4 are positioned on the exemplary beam 2304 such that the component magnitude of the first plane - strain force FP1 matches the magnitude of the component of the fourth plane - strain force FP4.

[0255] In this example, the difference between FP1 and FP4 is proportional to the force component F Y applied to the beam in the Y - direction by the applied force F. Those skilled in the art will understand that the process for determining the difference between FP1 and FP4 is based on the above description for determining the difference between FP2 and FP3.

[0256] Furthermore, it should be understood that

[0257] F Y = FP1 – FP4

[0258] F Y αV O1 – V O4

[0259] where V O1 is the output voltage of HB1 and V O4 is the output voltage of HB4.

[0260] Figure 20 is Figures 13A - 13B an illustrative proximal - direction cross - sectional view of the exemplary beam 2304, which indicates the first plane - strain force FP1 and the second plane - strain force FP2 applied to the respective first and second half - bridges HB1, HB2 by the force applied to the beam 2304. In the exemplary force sensor 2302, the first pair of resistors R P1 , R D1 of the first half - bridge HB1 have a resistance value that matches the resistance value of the second pair of resistors R P2 , R D2Resistance value matching. In the exemplary force sensor 2302, the first and second half - bridges HB1, HB2 are positioned on the exemplary beam 2304 such that an applied force applied to the exemplary beam 2304 applies a first planar strain force FP1 to the first half - bridge HB1 within the first plane P1 and a second planar strain force FP2 to the second half - bridge HB2 within the second plane P2. It should be understood that the first planar strain force FP1 is an off - axis force because it is a force applied along the first lateral side axis 2312. Similarly, it should be understood that the second planar strain force FP2 is an off - axis force because it is a force applied along the second lateral side axis 2314. The first and second half - bridges HB1, HB2 are positioned on the exemplary beam 2304 such that the magnitude of the first planar strain force FP1 X matches the magnitude of the second planar strain force FP2. The force direction of the first planar strain force FP1 X and the first plane P1 are separated from each other by a first separation angle A1.

[0261] In this example, the difference between FP1 and FP2 is proportional to the X - direction force component FX of the force F applied to the beam. Those skilled in the art will understand that the process for determining the difference between FP1 and FP2 is based on the above description for determining the difference between FP2 and FP3.

[0262] In addition, it should be understood that,

[0263] F X = FP1 - FP2

[0264] F X αV O1 –V O2

[0265] where V O1 is the output voltage of HB1, and V O2 is the output voltage of HB2. Figure 21 is Figures 13A - 13B an illustrative proximal - direction cross - sectional view of the exemplary beam 2304, which indicates the third planar strain force FP3 and the fourth planar strain force FP4 applied to the corresponding third and fourth half - bridges HB3, HB4 by the force F X applied to the beam. In the exemplary force sensor 2302, the resistance values of the third pair of resistors R P3 , R D3 of the third half - bridge HB3 are the same as the resistance values of the fourth pair of resistors R P4 , R D4The resistance values are matched. In the example force sensor 2302, the third and fourth half - bridges HB3, HB4 are positioned on the example beam 2304 such that an applied force applied to the example beam 2304 applies a third plane - strain force FP3 to the third half - bridge HB3 within the third plane P3 and a fourth plane - strain force FP4 to the fourth half - bridge HB4 within the fourth plane P4. It should be understood that the third plane - strain force FP3 is an off - axis force as it is a force applied along the third lateral side axis 2316. Similarly, it should be understood that the fourth plane - strain force FP4 is an off - axis force as it is a force applied along the fourth lateral side axis 2318. In the example force sensor 2302, the third and fourth half - bridges HB3, HB4 are positioned on the example beam 2304 such that Figure 21 the magnitude of Figures 13A - 13B the example beam 2304 indicates the force F applied to the beam X illustrative proximal - direction cross - sectional view of the third plane - strain force FP3 and the fourth plane - strain force FP4 applied to the corresponding third and fourth half - bridges HB3, HB4.

[0266] In this example, the difference between FP3 and FP4 is proportional to the X - direction force component F of the force F applied to the beam X A person skilled in the art will understand that the process for determining the difference between FP3 and FP4 is based on the above description of determining the difference between FP2 and FP3.

[0267] In addition, it should be understood that

[0268] F X = FP3 – FP4

[0269] F X αV O3 – V O4

[0270] where V O3 is the output voltage of HB3, and V O4 is the output voltage of HB4.

[0271] Therefore, assuming that all resistors R P1 - R P4 and R D1 - R D4 are operating normally,

[0272] F X αV O1 – V O2 = V O3 – V O4 and F Y αV O1 – V O4 = V O2 – VO3

[0273] In addition, it should be understood that F X and F Y can be determined more generally based on each of the following four combinations of three half - bridges (HB) listed in Table 1 below.

[0274] Table 1

[0275]

[0276]

[0277] Therefore, the half - bridge combinations in Table 1 above can be used to perform redundancy determination for F X and F Y . The comparison of the F X and F Y values determined based on the above - mentioned half - bridge combinations can be used to determine whether the force sensor 2304 contains a faulty resistor. If even a single resistor fails, then all four combinations will produce different Fx and Fy values, indicating a fault. Since all four HBs produce different results when a fault occurs, it is not possible to determine which resistor has failed. Adding one or more additional half - bridges to the beam can be used to implement a fault - tolerant design because the comparison of five or more combinations of three bridges can be used to determine which half - bridge is defective, and thus the measurement values from the defective half - bridge can be ignored.

[0278] Redundant Unilateral XY Force Sensor

[0279] An example unilateral XY force sensor includes a beam that includes four half - bridges located on one side thereof. Two of the half - bridges are of one of the compression types, while two of the half - bridges are of the tension type. Since compression and tension strain gauge resistors measure strains that occur in opposite directions in response to a force applied to the beam, the measured values of the combination of three half - bridges located on the same side of the beam can be used to measure the X - direction force and the Y - direction force, where one of the three half - bridges has a different strain gauge resistor type from the other two. An example unilateral XY force sensor includes four half - bridges, two of which are of the compression type and two of which are of the tension type, and this example unilateral XY force sensor can perform redundant XY measurements.

[0280] However, generally speaking, based on any three of the four half - bridge measured values, it will be possible to measure Fx, Fy, and the temperature gradient. For a beam with four half - bridges (two of the tension type and two of the compression type), there are four ways to select three of the four half - bridges, and thus, we can obtain four measured values of Fx and Fy, providing redundancy in the measured values.

[0281] Figure 22Shows an exemplary top perspective view of an exemplary force sensor 21102, which includes a rectangular beam 21104 that includes two exemplary tensile resistor half - bridges and two exemplary compressive resistor half - bridges located on its outer first side surface 21108. The exemplary beam 21104 includes a flat first side surface 21108. The beam 21104 includes a proximal beam portion 21104P and a distal beam portion 21104D and includes a central axis 21106 extending between the proximal beam portion and the distal beam portion. The two exemplary tensile half - bridges have Figures 14A - 14B a first circuit layout 2402 and a first circuit schematic 2404. The two exemplary compressive half - bridges have Figures 15A - 15B a second circuit layout 2502 and a second circuit schematic 2504.

[0282] The first pair of tensile resistors includes a first proximal tensile resistor RT P1 located at the proximal beam portion 21104P and a first distal tensile resistor RT D1 located at the distal beam portion 21104D. The first proximal tensile resistor RT P1 and the first distal tensile resistor RT D1 are serially electrically coupled and arranged in the first tensile half - bridge HB1 T . The second pair of tensile resistors includes a second proximal tensile resistor (RT P2 ) located at the proximal beam portion 21104P and a second distal tensile resistor (RT D2 ) located at the distal beam portion 21104D. The second proximal tensile resistor RT P2 and the second distal tensile resistor RT D2 are serially electrically coupled and arranged in the second tensile half - bridge HB2 T . The first pair of compressive resistors includes a first proximal compressive resistor (RC P1 ) located at the proximal beam portion 21104P and a first distal compressive resistor (RC D1 ) located at the distal beam portion 21104D. The first proximal compressive resistor (RC P1 ) and the first distal compressive resistor (RC D1 ) are serially electrically coupled and arranged in the third compressive resistor half - bridge HB3 C . The second pair of compressive resistors includes a second proximal compressive resistor resistor (RC P2 ) located at the proximal beam portion 21104P and a second distal compressive resistor resistor (RC D2 ) located at the distal beam portion 21104D. The second proximal compressive resistor (RC P2 ) and the second distal compressive resistor (RC D2 ) are serially electrically coupled and arranged in the fourth compressive resistor half - bridge HB4C in

[0283] As will be understood from the illustrative Figures 14A - 14B and Figures 15A - 15B explanation and as more fully explained below, the corresponding output voltage nodes are located between each of the corresponding first pair of tensile resistors RT T of HB1 P1 , RT D1 , HB2 T of the corresponding second pair of tensile resistors RT P2 , RT D2 , HB3 C of the corresponding first pair of compressive resistors RC P1 , RC D1 and HB4 T of the corresponding second pair of compressive resistors RC P2 , RC D2 The voltage offset between certain combinations of these different output voltages can be used to determine a redundancy measure of the X force applied to the beam. The voltage offset between certain combinations of these different output voltages can be used to determine a redundancy measure of the Y force applied to the beam. A failure of any one of the resistors RT P1 , RT P2 , RT D1 , RT D2 , RC P1 , RC P2 , RC D1 , RC D2 , RC

[0284] Still referring to Figure 22 , the first proximal tensile resistor RT P1 , the first distal tensile resistor RT D1 , the first proximal compressive resistor RC P1 and the first distal compressive resistor RC D1 are arranged on the first side 21108 of the beam in the first imaginary plane P1, the central axis 21108 extends in this plane P1, and the plane P1 defines a first lateral axis 21112 at the position where it intersects the first side 21108 of the beam 21104 on the first side 21108 of the beam. The first lateral axis 21112 and the central axis 21106 extend parallel to each other. An example first lateral axis 21112 extends through the first proximal and distal tensile resistors RT P1 -RT D1and passes through first proximal and distal compression resistors RC P1 -RC D1 。An example first lateral side axis 21112 bisects the example first proximal and distal tensile resistors and the example first proximal and distal compression resistors.

[0285] A second proximal tensile resistor RT P2 、a second distal tensile resistor RT D2 、a second proximal compression resistor RC P2 and a second distal compression resistor RC D2 are arranged on a first side 21108 of a beam 21104 within a second imaginary plane P2, a central axis 21106 extending within the plane P2, and the plane P2 defining a second lateral side axis 21114 at a location on the first side 21108 of the beam 21104 where the second plane P2 intersects the first side 21108. The second lateral side axis 21114 and the central axis 21106 extend parallel to each other. The example second lateral side axis 21114 extends through the second proximal and distal tensile resistors RT P2 -RT D2 and passes through the second proximal and distal compression resistors RC P2 -RC D2 。The example second lateral side axis 21114 bisects the example second proximal and distal tensile resistors and the example second proximal and distal compression resistors.

[0286] Figure 23 is Figure 22 an illustrative proximal direction cross-sectional view of an example beam 21104. The proximal direction end view of the beam shows a side view of a first plane P1 and a second plane P2 intersecting each other along a central axis 21106, the central axis 21106 extending within the first and second planes. A first and a third half-bridge HB1 T 、HB3 C are longitudinally aligned along one lateral edge of the beam 21104, and a second and a fourth half-bridge HB2 T 、HB4 C are longitudinally aligned along an opposite edge of the beam 21104. A portion of the first plane extending through the half-bridge circuits HB1 T 、HB3 C and a portion of the second plane P2 extending through the half-bridge circuits HB2 T 、HB4 C intersect at the central axis 306 at a first separation angle B1.

[0287] Figure 24 is Figure 22 a side view of a first side 21108 of an outer surface of an example beam 21104, two tensile resistor half-bridges HB1T and HB2 T and two compression resistor half - bridges HB3 C and HB4 C are located on this first side. The first plane FP1 is shown as extending through the first tensile resistor half - bridge HB1 P1 including the first proximal and distal tensile resistors and the proximal resistor RT D1 and RT T and through the third compression resistor half - bridge HB3 P1 including the first proximal and distal compression resistors RC D1 and RC C . The second plane P2 is shown as extending through the second tensile resistor half - bridge HB2 P2 including the second proximal and distal tensile resistors and the proximal resistor RT D2 and RT T and through the fourth compression resistor half - bridge HB4 P2 including the second proximal and distal compression resistors RC D2 and RC C . The magnitude of the first separation angle B1 corresponds to the lateral spacing distance at the first side 21108 between the first lateral side axis 21112 and the second lateral side axis 21114, and thus corresponds to, on the one hand, the first pair of tensile resistors R P1 and R D1 and the first pair of compression resistors RC P1 and RC D1 and, on the other hand, the second pair of tensile resistors R P2 and R D2 and the second pair of compression resistors RC P2 and RC D2 . In the exemplary force sensor 21102, the first lateral side axis 21112 and the second lateral side axis 21114 are equidistant from the neutral axis 21115 extending within the surface of the first side 21108 of the beam 21104, parallel to the central axis 21106 and equidistant from the opposite lateral edges of the first side 21108.

[0288] The resistors of the first and third half - bridges HB1 T and HB3 C are staggered. RC D1 is aligned with the first lateral side axis 21112 between RT D1 and RT P1 . RT P1 is aligned along the first lateral side axis 21112 between RC D1 and RC P1 .

[0289] The second and fourth half - bridges HB2T and HB4 C The resistors of are staggered. RC D4 with RT D2 and RT P2 is aligned with the second lateral axis 21114 between RTs. RT P2 Along RC D3 and RC P4 is aligned with the second lateral axis 21114 between them.

[0290] The first voltage node V O1 is coupled between the first pair of tensile resistors RT D1 and RT P1 The second voltage node V O2 is coupled between the second pair of tensile resistors RT D2 and RT P2 The third voltage node V O3 is coupled between the first pair of compressive resistors RC D1 and RC P1 The fourth voltage node V O4 is coupled between the second pair of compressive resistors RC D2 and RC P2 between them.

[0291] In the exemplary force sensor, the first and second proximal tensile resistors RT P1 , RT P2 are positioned at matching longitudinal positions of the beam 21104. In the exemplary force sensor, the first and second distal tensile resistors RT D1 , RT D2 are positioned at matching longitudinal positions of the beam 21104. Similarly, in the exemplary force sensor, the first and second proximal compressive resistors RC P1 , RC P2 are positioned at matching longitudinal positions of the beam 21104. In the exemplary force sensor, the first and second distal compressive resistors RC D1 , RC D2 are positioned at matching longitudinal positions of the beam 21104.

[0292] Figure 25 is Figure 22 An illustrative cross-sectional end view of the exemplary beam 21104, which indicates the first plane strain force FP1 and the second plane strain force FP2 applied to the corresponding first and second tensile resistor half-bridges HB1 T , HB2 T by the force F applied to the beam 21104. In the exemplary force sensor 21102, the first pair of resistors RT T of the first half-bridge HB1 P1 , RT D1has a resistance value that matches that of the second half-bridge HB2 T of the second pair of resistors RT P2 、RT D2 In the exemplary force sensor 21102, the first and second half-bridges HB1 T 、HB2 T are positioned on the exemplary beam 21104 such that an X-direction force applied to the exemplary beam 21104 applies a first plane strain force FPl to the first half-bridge HB1 within the first plane P1 T and applies a second plane strain force FP2 to the second half-bridge HB2 within the second plane P2 T . HB1 T and HB2 T can be used to determine the X-direction component of the applied force by determining the difference between the plane forces.

[0293] Figure 26 is Figure 22 an illustrative cross-sectional end view of the exemplary beam 21104, which indicates the first plane strain force FP1 and the second plane strain force FP2 applied to the corresponding third and fourth compressive resistor half-bridges HB3 C 、HB4 C by the force applied to the beam 21104. In the exemplary force sensor 21102, the third and fourth compressive half-bridges HB3 C 、HB4 C are positioned on the exemplary beam 21104 such that the applied force applied to the exemplary beam 21104 applies a third plane strain force FP3 to the third compressive half-bridge HB3 within the first plane P1 C and applies a fourth plane strain force FP4 to the fourth compressive half-bridge HB4 within the second plane P2 C . HB3 C and HB4 C can be used to determine the X-direction component of the applied force by determining the difference between the plane forces.

[0294] Figure 27 is Figure 22 an illustrative cross-sectional end view of the exemplary beam 21104, which indicates that the first plane strain force FP1 and the fourth plane strain force FP2 are applied to the corresponding first tensile resistor half-bridge HB1 T and the fourth compressive resistor half-bridge HB4 C by the force applied to the beam 21104. In the exemplary force sensor 21102, the first tensile and fourth compressive half-bridges HB1 T 、HB4 CPositioned on exemplary beam 21104 such that the applied force applied to exemplary beam 21104 applies a first plane strain force FP1 to a first tensile half-bridge HB1 within a first plane P1 T and a fourth plane strain force FP4 to a fourth compressive half-bridge HB4 within a second plane P2 C . HB1 T and HB4 C can be used with one of HB2 T or HB3 C to determine the Y-direction component of the applied force, as explained below with reference to Figure 29 .

[0295] Figure 28 is Figure 22 an illustrative cross-sectional end view of exemplary beam 21104 that indicates reverse second plane strain force FP2 and third plane strain force FP3 applied to corresponding second tensile and third compressive resistor half-bridges HB2 T , HB3 C by the force applied to beam 21104. In exemplary force sensor 21102, second tensile and third compressive half-bridges HB2 T , HB3 C are positioned on exemplary beam 21104 such that the applied force applied to exemplary beam 21104 applies a third plane strain force FP2 to a third compressive half-bridge HB3 within a first plane P1 C and a second plane strain force FP2 to a second tensile half-bridge HB2 within a second plane P2 T . HB2 T and HB3 C are used with one of HB1 T or HB4 C to determine the Y-direction component of the applied force, as explained below with reference to Figure 29 .

[0296] Determining force components by subtracting off-axis force components does not work for half-bridges with different resistor types because compressive and tensile resistors have mismatched sensitivities. However, in exemplary sensor 21102 that includes tensile resistor type half-bridges and compressive resistor type half-bridges, any combination of three half-bridges can be used to determine the F X component and F Y component of the applied force F, which are orthogonal to each other, as explained with reference to Figure 29 below.

[0297] Figure 29 is an illustrative cross-sectional end view of exemplary beam 21504 that indicates the application to three exemplary half-bridges HB A , HBB , HB C The force of. In the following explanation, the two half - bridges can be of the same type (tensile resistor type or compressive resistor type), while the third half - bridge can be of the same type or the opposite type. It should be noted that different from the beam 21102 with four half - bridges on one side, the beam 21504 has two half - bridges HB Figure 22 and HB A and HB B , both of which are located on the same side of the beam and have a third half - bridge HB C on the opposite side of the beam. Those skilled in the art will understand the following process of determining the F x and F Y components of the applied force F based on the force measurement values using three half - bridges, where the two half - bridges with matching resistor types are independent of the circumferential position of the half - bridges on the beam and independent of the half - bridge type, and this matching resistor type can match or not match the resistor type of the third half - bridge.

[0298] Suppose the applied force F=(F X , F Y ).

[0299] Then the force,

[0300] FP1 = F X cosθ1+F Y sinθ1 (1)

[0301] FP2 = F X cosθ2+F Y sinθ2 (2)

[0302] FP3 = F X cosθ3+F Y sinθ3 (3)

[0303] Let V1, V2, V3 be the output voltages of HB A , HB B , HB C .

[0304] Then,

[0305] V1 = g1FP1+VΔT (4)

[0306] V2 = g2FP2+VΔT (5)

[0307] V3 = g3FP3+VΔT (6)

[0308] where VΔT is the voltage caused by the temperature gradient along the half - bridge; gi is the sensitivity / gain of the HB to the force along FPi.

[0309] Substituting (1), (2), and (3) into (4), (5), and (6), we get

[0310] V1 = g1cosθ1F X + g1sinθ1F Y + VΔT (7)

[0311] V2 = g2cosθ2F X + g2sinθ2F Y + VΔT (8)

[0312] V3 = g3cosθ3F X + g3sinθ3F Y + VΔT (9)

[0313] The values of gi and θi are known through design or calibration. Therefore, the unknowns are F X 、F Y and VΔT. We have three equations and three unknowns. This is a straightforward linear algebra problem.

[0314] F X = (V1(g3sinθ3 – g2sinθ2) + V2(g1sinθ1 – g3sinθ3) + V3(g2sinθ2 – g1sinθ1)) / DEN (10)

[0317] F Y = (V1(g2cosθ2 – g3cosθ3) + V2(g3cosθ3 - g1cosθ1) + V3(g1cosθ1 – g2cosθ2)) / DEN (11)

[0320] Where:

[0321] DEN = g2g3(sinθ2cosθ3 – cosθ2sinθ3) - g1g3(sinθ1cosθ3 – cosθ1sinθ3) + g1g2(sinθ1cosθ2 – cosθ1sinθ2)

[0324] HB i The value of gi depends on the type of HB.

[0325] If we assume that the sensitivity of all strain gauges HBs is g, then the following is gi

[0326] If we assume that the value of gi for the strain gauge HB is g; if HB is a compression gauge, then the value of gi is -ρg, where ρ is the Poisson's ratio of the material.

[0327] Therefore, it can be understood that F X and F YIt can be determined based on each of the following four combinations of three half - bridges (HB) listed in Table 2 below.

[0328] Table 2

[0329] HB Combination Number <![CDATA[Suitable for determining F X and F Y HB combination]]> 1 <![CDATA[HB1 T 、HB2 T 、HB3 C > 2 <![CDATA[HB3 C 、HB4 C 、HB1 T > 3 <![CDATA[HB2 T 、HB3 C 、HB4 C > 4 <![CDATA[HB1 T 、HB4 C 、HB2 T >

[0330] The following uses the reference Figure 29 described process to determine Figure 26 Example F of the example X and F Y example of force components.

[0331] This example assumes the values in Table 3 are as follows:

[0332] Table 3

[0333] Half - bridge Angle Sensitivity / Gain <![CDATA[HB1 T > θ1 = 90 - θ g1 = g <![CDATA[HB2 T > θ2 = 90 + θ g2 = g <![CDATA[HB3 C > θ3 = 90 - θ g3 = -ρg <![CDATA[HB4 C > θ4 = 90 + θ g4 = -ρg

[0334] The value θ is Figure 26 the half - angle (A / 2) between the FP1 and FP2 force planes in. The g value is the sensitivity of the strain gauge half - bridge.

[0335] In this example, we use HB1 T 、HB2 T and HB3 C to determine, using equations (10), (11),

[0336] FX = (V1 – V2) / 2gsinθ

[0337] FY = (V1(1 - ρ)+V2(1 + ρ)-2V3) / 2gcosθ(1 + ρ)

[0338] Therefore, the half - bridge combinations in Table 2 above can be used for redundant determination of F X and F Y . The comparison of the F X and F Y values determined based on the above - mentioned half - bridge combinations can be used to determine whether the force sensor 21102 contains a faulty resistor. If even a single resistor fails, then all four combinations will produce different Fx and Fy values, indicating a fault. Since all four HBs produce different results when a fault occurs, it is not possible to determine the faulty resistor.

[0339] Figure 30 is an explanatory diagram showing a computer system 21902 configured to monitor the voltage measurements of the force sensor 2302. The example computer system 21902 includes a display screen 21904. The computer system 21902 is configured to receive the voltage measurements V O1 、V O2, V O3 and V O4 . Figure 31 is an illustrative flowchart 22000 showing an example diagnostic process for detecting a failed strain gauge resistor in force sensors 2302 or 21102. The computer system 21902 is configured with computer-readable instructions to perform the steps of diagnostic process 22000. At block 22002, the computer system receives voltage measurements V O1 , V O2 , V O3 and V O4 . At block 22004, it is determined whether the respective F X values for each of HB combinations 1 - 4 in Table 1 match and whether the respective F Y values match. More specifically, for example, the computer system 21902 uses the voltage measurements from HB1, HB2, HB3, and HB4 to determine F X and F Y . If the values match, the control flow returns to block 22002. If the values do not match, block 22006 sends an electronic signal to report an error. In the example computer system 21902, the electronic signal causes an error message to be displayed on the display screen 21904. It should be understood that process 200 can also be performed for sensor 21102 and combinations 1 - 4 of Table 2.

[0340] Extended bridge opposite side XY force sensor

[0341] Figures 32A - 32B shows an exemplary top perspective view ( Figure 32A ) and a bottom perspective view ( Figure 32B ) of an example force sensor 3302, which includes a rectangular beam 3304 with a Wheatstone bridge circuit ("full bridge") located on two opposite sides thereof. The first full Wheatstone bridge includes first (R P1 ), second (R D1 ), third (R P2 ), and fourth (R D2 ) resistors. The second bridge includes fifth (R P3 ), sixth (R D3 ), seventh (R P4 ), and eighth (R D4 ) resistors. In the example first full Wheatstone bridge 3352, the first and second resistors are coupled in the first half-bridge, while the third and fourth resistors are coupled in the second half-bridge. Figure 32B The second side 3308 of the beam 3304 shown in Figure 32AThe direction opposite to the direction faced by the first side 3308 of the beam 3304 shown. The (X, Y, Z) beam coordinate system 3305 is shown to explain the force direction with respect to the beam 3304. The exemplary beam 3304 may have a rectangular cross-section with flat sides. More specifically, the exemplary beam may have a square cross-section. The beam 3304 includes a proximal beam portion 3304P and a distal beam portion 3304D and includes a longitudinal central axis 3306 extending between the proximal beam portion and the distal beam portion. Reference Figure 32A , the first proximal strain gauge resistor (“resistor”) R P1 and the second proximal resistor R P2 are located at the proximal beam portion 3304P of the first side 3308 of the beam 3304. The first distal resistor R D1 and the second distal resistor R D2 are located at the distal beam portion 3304D of the first side 3308 of the beam 3304. The resistors R P1 -R P2 and R D1 -R D2 are arranged in a first extended full Wheatstone bridge as described below, where the first pair of resistors R P1 -R D1 and the second pair of resistors P P2 -R D2 are positioned laterally apart from each other on opposite sides of the first side neutral axis 3315. Reference Figure 32B , the third proximal strain gauge resistor (“resistor”) R P3 and the fourth proximal resistor R P4 are located at the proximal portion of the second side (also referred to as the “opposite” side) of the beam. The third distal resistor R D3 and the fourth distal resistor R D4 are located at the distal portion of the second side of the beam. The resistors R P3 -R P4 and R D3 -R D4 are arranged in a second pair of split full-Wheatstone bridges aligned with the third axis 3319 which is the neutral axis of the second side of the beam.

[0342] As more fully explained below, the first and second full-bridge circuits are "spread out" because portions of each bridge circuit are laterally spaced apart from each other on the beam 3304. For example, each full bridge can include two half bridges that are laterally spread apart from each other. An advantage of laterally spread-apart half bridges is that, for example, conductor traces that couple resistors to a bias voltage or couple resistors to each other can be routed through the middle of the face of the beam 3304 or near the neutral axis of the beam on each face of the beam. Alternatively, in a beam having a circular cross-section (not shown), the conductor traces can be advantageously routed along the neutral axis of the respective half bridges. This routing helps reduce the strain on the traces, thereby improving the accuracy of the sensor by rejecting unwanted signals.

[0343] The resistors can be placed on the beam 3304 manually or using an automated machine, and the resistors can be adhered to the beam using an adhesive such as epoxy. Alternatively, the resistors can be directly deposited and laser-etched onto the beam 3304. In both cases, the circuit can be completed externally using wire bonding and flexible printed circuits.

[0344] As more fully explained below, a first pair of resistors R P1 -R P2 and a second pair of resistors R D1 -R D2 located on a first side 3304 of the beam are used as Y-direction force sensor elements, and a third pair of resistors R P3 -R P4 and a fourth pair of resistors R D3 -R D4 located on an opposite second side of the beam are used as X-direction force sensor elements. Referring again to Figure 32A , a first proximal resistor R P1 and a first distal resistor R D1 are arranged on a first side 3308 of the beam 3304 within a first imaginary plane P1 in which a longitudinal central axis 3306 extends and the plane P1 defines a first lateral side axis 3312 at the location where the first plane P1 intersects the first side 3308 of the beam 3304. The first lateral axis 3312 and the central axis 3306 are parallel to each other and extend parallel to a first side neutral axis 3315. An example first lateral side axis 3312 extends through the first proximal resistor R P1 and through the first distal resistor R D1 . Further, the example first lateral side axis 3312 bisects the example first proximal resistor R P1 and bisects the example first distal resistor R D1 .

[0345] Still referring to Figure 32A , a second proximal resistor RP2 and a second distal resistor R D2 is disposed on the opposite first side 3308 of the beam 3304 that is within the second imaginary plane P2, the longitudinal central axis 3306 extends within the plane P2 and the plane P2 defines a second lateral axis 3314 at the position where the plane P2 intersects the first side 3308 along the first side 3308 of the beam 3304. The second lateral axis 3314 and the central axis 3306 are parallel to each other and extend parallel to the first side neutral axis 3315. An example second lateral axis 3314 extends through the second proximal resistor R P2 and through the second distal resistor R D2 . Further, the example second lateral axis 3314 bisects the example second proximal resistor R P2 and bisects the example second distal resistor R D2 .

[0346] The first pair of resistors R P1 -R D1 and the second pair of resistors R P2 -R D2 each resistor in is the same type of strain gauge resistor. More specifically, in the example force sensor 3302 described herein, the resistors R P1 -R D1 and R P2 -R D2 are tensile-type gauge resistors for measuring tensile strain. In an alternative example force sensor, the first and second pairs of resistors can be compression-type gauge resistors for measuring compressive strain. As used herein, referring to a set of resistors having a "matching type" means a set of resistors where all the resistors are either tensile resistors or all the resistors are compressive resistors. Resistors having a matching type are more likely to have similar sensitivities and performance, thus making the sensor more suitable for low signal-to-noise situations where common-mode rejection is crucial and performing better. Generally, although tensile or compressive gauge resistors can be used to determine forces in the X and Y directions, generally, tensile strain gauge resistors are more sensitive than compressive gauge resistors.

[0347] Reference Figure 32B , the third pair of resistors R P3 -R D3 and the fourth pair of resistors R P4 -R D4 are disposed along a third axis 3319 on the second opposite side 3310 of the beam 3304. The third axis 3319 on the second side is a neutral axis that extends within the second side surface, is parallel to the central axis 3306, and is equidistant from the lateral edges of the second side. The third and fourth pairs of resistors include resistors of non-matching types. Specifically, R P3 , R P4One of them is a tensile resistor, the other is a compressive resistor, and R D3 、R D4 One of them is a tensile resistor, the other is a compressive resistor. The pitch between the tensile gauge and the compressive gauge is also matched.

[0348] Figure 33 is Figures 32A - 32B An illustrative proximal-direction cross-sectional view of exemplary beam 3304. Figure 34A is a side view of the beam showing the first side 3308 of beam 3304. Figure 34B is a side view of the beam showing the second side 3310 of beam 3304.

[0349] Referring to Figure 33 , the proximal-direction end view of beam 3304 shows a side view of a first plane P1 and a second plane P2 intersecting each other along the longitudinal central axis 3306, and the central axis 3306 extends within the first plane P1 and the second plane P2. The (X, Y, Z) beam coordinate system 3305 is shown to explain the force direction with respect to beam 3304. Note that in Figure 33 , the Z axis is shown as emerging from the page. The first plane P1 and the second plane P2 are separated from each other by a first separation angle A1 about the central axis 3306.

[0350] Referring to Figure 34A , a first lateral side axis 3312 is shown as extending through a first proximal resistor R P1 and a first distal resistor R D1 on the first side 3308 of beam 3304. Note that in Figure 34A , the X axis extends into the page. A second lateral side axis 3314 is shown as extending through a second proximal resistor R P2 and a second distal resistor R D2 on the first side 3308 of beam 3304. The magnitude of the first separation angle A1 corresponds to the lateral spacing distance between the first side axis 3312 and the second side axis 3314 at the first side 3308, and thus corresponds to the lateral spacing between the first resistor pair R P1 、R D1 and the second resistor pair R P2 、R D2 . In the exemplary force sensor, the first lateral side axis 3312 and the second lateral side axis 3314 are equidistant from a first side neutral axis 3315 that extends within the first side surface of the beam and is equidistant from the opposite lateral edges of the first side 3308.

[0351] Referring to Figure 34B , resistors R P3 -R P4 and RD3 -R D4 Aligned along a third axis 3319 that extends within a second side of the beam 3304 and is equidistant from opposite lateral edges of the second side 3310. Note that in Figure 34A the X axis emerges from the page.

[0352] As explained below, the resistors of the first bridge circuit are arranged laterally separated to measure a force in a first direction perpendicular to the beam center axis 3306 based on the application of a bias neutral axis force along a first plane P1 and a second plane P2. As Figure 37A shown, the lateral separation of the resistors of the first bridge 3352 enables the routing of the first center conductor trace 3356 parallel to the beam center axis 3306 in a region of the beam 3304 between the proximal and distal resistors of the full Wheatstone bridge.

[0353] Figure 35A is an illustrative side view of an example beam 3304 that shows a first example layout of a first full Wheatstone bridge 3602 that includes resistors R P1 -R P2 and R D1 -R D2 The first Wheatstone bridge layout is coupled in a first configuration to input bias voltage conductors (EP, EN) and output voltage conductors (Vo-, Vo+). Figure 35B is an illustrative first schematic circuit diagram 3604 representation of the first full Wheatstone bridge layout topology. Referring to Figures 35A - 35B the first proximal resistor R P1 is electrically coupled between a positive first DC potential (EP) and a second (also referred to as "negative" potential) output Vo-. The second proximal resistor R P2 is electrically coupled between a negative second DC potential (EN) and the second output Vo-. The first distal resistor R D1 is electrically coupled between a positive first DC potential (EP) and a first output Vo+ (also referred to as the "positive" output). The second distal resistor R D2 is electrically coupled between a negative second DC potential (EN) and the first output Vo+.

[0354] Figure 36A is an illustrative side view of an example beam 3304 that shows an alternative second example layout of a first full Wheatstone bridge 3702 that includes resistors R P1 -R P2 and R D1 -R D2 The second Wheatstone bridge layout is coupled in a second configuration to input bias voltage conductors (EP, EN) and output voltage conductors (Vo-, Vo+). Figure 36Bis illustrated by a first illustrative schematic circuit diagram 3704 that is a second alternative example layout of a first full Wheatstone bridge circuit. Refer to Figures 36A - 36B , a first proximal resistor R P1 is electrically coupled between a positive first DC potential (EP) and a first output Vo+. A second proximal resistor R P2 is electrically coupled between the positive first DC potential (EP) and a second output Vo-. A first distal resistor R D1 is electrically coupled between a negative second DC potential (EN) and the first output Vo+. A second distal resistor R D2 is electrically coupled between the negative second DC potential (EN) and the second output Vo-.

[0355] Generally speaking, Figure 35A the layout in Figure 36A is more suitable for reducing the number of traces that must span the length of the beam and can also reduce the effect of trace pick-up strain. On the other hand, if the force sensor uses a half-bridge voltage measurement, then Figure 37A the layout in P3 -R P4 and R D3 -R D4 is an example layout of a second example full Wheatstone bridge 3802 that is located at a second side 3310 of the beam 3304 and includes resistors R P3 is proximal to the proximal resistor R P4 . The distal resistor R D3 is proximal to the distal resistor R D4 . The proximal resistor R P3 and the distal resistor R D3 are strain gauge resistors in tension, and the proximal resistor R P4 and the distal resistor R D4 are strain gauge resistors in compression. In the first layout of the second bridge shown in Figure 37A , the second bridge is coupled to input bias voltage conductors (EP, EN) and coupled to output voltage conductors (Vo-, Vo+) in a first configuration. Figure 37B is illustrated by a first illustrative schematic circuit diagram 3804 that is a first example layout of a second full bridge circuit. Refer to Figures 37A - 37B , a third proximal resistor R P3 is electrically coupled between the negative second DC potential (EN) and the first output Vo+. A fourth proximal resistor R P4 is electrically coupled between the positive first DC potential (EP) and the first output Vo+. A third distal resistor R D3 is electrically coupled between the negative second DC potential (EN) and the second output Vo-. A fourth distal resistor R D4The electrical coupling is between a positive first DC potential (EP) and a second output Vo-.

[0356] Figure 37A is an illustrative side view of an exemplary beam 3304, which shows a resistor R located at a second side 3310 of the beam 3304 and includes P3 -R P4 and R D3 -R D4 An exemplary second layout of a second example full Wheatstone bridge 3902. The proximal resistor R P3 is located proximal to the proximal resistor R P4 . The distal resistor R D3 is located proximal to the distal resistor R D4 . The proximal resistor R P3 and the distal resistor R D3 are strain gauge resistors, and the proximal resistor R P4 and the distal resistor R D4 are compression gauge resistors. In the second layout of the second bridge shown in Figure 37A the second full bridge is coupled to input bias voltage conductors (EP, EN) and to output voltage conductors (Vo-, Vo+) in a first configuration. Figure 37B is represented by an illustrative schematic circuit diagram 904 of a second example layout of a second full bridge circuit. Referring to Figures 37A - 37B , a third proximal resistor R P3 is electrically coupled between a positive first DC potential (EP) and a first output Vo+. A fourth proximal resistor R P4 is electrically coupled between a positive first DC potential (EP) and a second output Vo-. A third distal resistor R D3 is electrically coupled between a negative second DC potential (EN) and a first output Vo+. A fourth distal resistor R D4 is electrically coupled between a negative second DC potential (EP) and a second output Vo-.

[0357] Figure 38A is an illustrative side view of an exemplary beam 3304, which shows an extended layout of a Wheatstone bridge 3352 located on a first side 3308 of the beam 3304 and shows the routing of a center conductor trace 3356 extending between the proximal and distal resistors of the bridge at the center of the bridge. The bridge 3352 includes R P1 、R P2 and distal resistors R D1 、R D2 , and has a first neutral axis 3362, which is between the proximal resistors R P1 、R P2 and the distal resistors R D1 、R D2extend parallel to the beam axis 3306 therebetween. In the example bridge, the first neutral line and R P1 and R P2 are each equally spaced and are equally spaced from each of R D1 and R D2 The first bridge 3352 is longitudinally separated, wherein the proximal resistors R P1 、R P2 are longitudinally separated from the distal resistors R D1 、R D2 The first bridge extends laterally, wherein the proximal resistors R P1 、R P2 are laterally extended and separated and the distal resistors R D1 、R D2 are laterally extended and separated from each other.

[0358] It should be understood that since the resistors of the first full Wheatstone bridge 3352 are laterally extended and separated, they do not occupy the first neutral axis 3362. Accordingly, the conductor traces can be routed close to and parallel to the first neutral axis 3362, which can reduce the strain applied to the traces. Additionally, routing the traces along the neutral axis of the bridge circuit can be easier to produce, fabricate, or assemble.

[0359] The example first full bridge includes a first set of center conductor traces 3356 that extend longitudinally between the pair of proximal resistors R P1 、R P2 and the pair of distal resistors R D1 、R D2 along the center portion of the first bridge 3352, parallel to the first neutral axis 3362, and along the region of the outer surface of the beam 3304. The first set of center traces 3356 includes a trace segment 3356-1 coupled to the first positive output voltage VO1+. The first set of center traces 3356 includes a trace segment 3356-1 coupled to the first negative voltage output VO1-. The first set of center traces 3356 includes a trace segment 3356-3 coupled to the negative voltage potential EN.

[0360] Figure 38B is Figure 38A Illustrative first schematic circuit diagrams of the first and second full Wheatstone bridges. The full Wheatstone bridge 3352 includes R P1 and R D1 coupled between EP and EN to provide a first half-bridge voltage divider circuit that includes a trace conductor coupled to the first positive output voltage VO1+. The first full Wheatstone bridge 3352 further includes R P2 and R D2to provide a second half - bridge voltage divider circuit that includes a trace conductor coupled to a first negative output voltage VO1-.

[0361] Figure 39A is Figure 33 An illustrative cross - sectional end view of an exemplary beam 3304 that indicates resistors on a first side and indicates a first planar force FP1 and a second planar force FP2. Figure 39B indicates the X - force component and the Y - force component of the first planar force FP1 applied to a first proximal resistor R P1 and a first distal resistor R D1 in response to an applied force F. An illustrative force - diagram. Figure 39C indicates the X - force component and the Y - force component of the second planar force FP2 applied to a second proximal resistor R P2 and a second distal resistor R D2 in response to an applied force F. An illustrative force - diagram.

[0362] In an exemplary force sensor 3302, the resistance values of a first pair of resistors R P1 、R D1 match the resistance values of a second pair of resistors R P2 、R D2 . In an exemplary force sensor 3302, the first and second pairs of resistors are positioned on an exemplary beam 3304 such that an applied force F applied to the exemplary beam 3304 applies a first planar strain force FP1 to the first pair of resistors within a first plane P1 and applies a second planar strain force FP2 to the second pair of resistors within a second plane P2. It should be understood that the first planar strain force FPl is an off - axis force because it is a force applied along a first lateral side axis 3312 that is laterally offset from the neutral axis 3315 of a first bridge 3352. Similarly, it should be understood that the second planar strain force FP2 is an off - axis force because it is a force applied along a second lateral side axis 3314 that is laterally offset from the neutral axis 3315 of the first bridge 3352. The first and second pairs of resistors are positioned on the exemplary beam 3304 such that the magnitude of the first planar strain force FP1 matches the magnitude of the second planar strain force FP2. The force directions of the first planar strain force FP1 and the second planar strain force FP2 are separated from each other by a first separation angle “A”.

[0363] One advantage of using the same type of strain - gauge resistors is that the magnitude of a force applied perpendicular to the central axis 3306 of the beam 3304 can be determined based on the difference in the magnitudes of off - axis forces applied to different half - bridges of a full - bridge located on the beam. In an exemplary force sensor 3302, the magnitude of the Y - direction force component F Y applied to the beam 3304 by the applied force F can be determined based on the difference between a first off - axis force FP1 and a second off - axis force FP2 as follows.

[0364] Let A be the angle between P1 and P2.

[0365] Let the X-axis bisect the angle A. Thus, the angle between P1 and X is A / 2, and the angle between P2 and X is A / 2.

[0366] Let θ be the angle between the X-axis and the applied force F.

[0367] The force F along the X-axis x = F cosθ

[0368] The force F along the y-axis y = F sinθ

[0369] Reference Figure 37B , the force along P1 = F x cos A / 2 + F y cos(90 + A / 2) = FP1

[0370] Reference Figure 9C , the force along P2 = F x cos A / 2 + F y cos(90 - A / 2) = FP2

[0371] FP1 = F x cos A / 2 + F y cos(90 + A / 2)

[0372] FP2 = F x cos A / 2 + F y cos(90 - A / 2)

[0373] Using cos(θ) = -cos(180 - θ)

[0374] We get

[0375] FP2 = F x cos A / 2 - F y cos(90 + A / 2)

[0376] When we subtract FP1 and FP2

[0377] We get FP1 - FP2 = F x cos A / 2 + F y cos(90 + A / 2)

[0378] -F x cos A / 2 + F y cos(90 + A / 2)

[0379] Therefore, FP1 - FP2 = 2F ycos(90+A / 2)

[0380] Therefore, FP1 - FP2 ∝ F y

[0381] Therefore, the difference between FP1 and FP2 is proportional to the Y - direction force component FY of the applied force F on the beam Y is proportional to

[0382] In addition, it should be understood that

[0383] F Y αV S1O+ –V S1O- ,

[0384] where V S1O+ is the positive output voltage of the first bridge circuit 3352, V S1O- is the negative output voltage of the first bridge circuit 3352, and V S1O+ -V S1O- is the voltage offset generated by the first bridge circuit 3352 located on the first side 3308 of the beam 3304

[0385] Figure 40 is Figure 33 An illustrative proximal - direction cross - sectional view of an example beam 3304, which indicates the resistors R P3 , R P4 , R D3 , R D4 on the second side 3310 of an example second full - bridge 3802 or 3902, and indicates the X - axis force FX. An example full - bridge circuit is disclosed in PCT / US2018 / 061113, filed on November 14, 2018, which includes tensile and compressive resistors that are longitudinally parallel to the beam center axis and aligned along the neutral axis, and is hereby incorporated by reference in its entirety

[0386] Figure 41 is a schematic diagram showing a metal sheet 31102 that includes cuts defining example resistors R P1 -R P4 and R D1 -R D4 for assembly into corresponding first and second full - Wheatstone bridges on opposite - facing first and second sides 3308, 3310 of the beam 3304. The first region 31104 of the metal sheet 31102 includes the resistors R P1 -R P2 and R D1 -R D2is coupled within a first full bridge to be positioned at a first side 3308 of an exemplary beam. A second region 31106 of the metal sheet includes a resistor R P3 -R P4 and R D3 -R D4 is coupled within a second full bridge located at a second opposite side 3310 of the exemplary beam 3304. An intermediate third region 31108 extending between the first and second regions and sized to lie over a third intermediate side 3320 of the beam 3304 is located between the first side 3308 and the second side 3310 of the beam 3304. A first fold line 1110 separates the first region from the second region, and a second fold line 1112 separates the second region from the intermediate region.

[0387] Figure 42A is an illustrative diagram showing the process of folding the metal sheet 31102 along the first and second fold lines 1110, 1112 to wrap the metal sheet 31102 around the exemplary beam 3304 for the first, second, and third 31104, 31104, 31106 regions to place a first set of resistors R P1 -R P2 and R D1 -R D2 at the first side 3308 of the beam 3304 and to place a second set of resistors R P3 -R P4 and R D3 -R D4 at the second side 3310 of the beam 3304, and to place the intermediate third region 31108 over the third intermediate side 3320 of the beam 3304. Figure 42B is an illustrative top perspective view of the beam 3304 with the metal sheet 31102 wrapped around three of its sides. In particular, Figure 42B shows the first region 31104 of the metal sheet 31102 lying over the first side 3310 of the beam 3304 to position the first set of resistors at the first side. Figure 42C is an illustrative bottom perspective view of the beam 3304 with the metal sheet 31102 wrapped around three of its sides. In particular, Figure 42C shows the second region 31106 of the metal sheet 31102 lying over the second side 3310 of the beam 3304 to position the second set of resistors at the second side. In the exemplary rectangular beam, the first side includes a first face of the beam and the second side includes a second face opposite the first side face.

[0388] Although illustrative examples have been shown and described, numerous modifications, changes, and substitutions are contemplated in the foregoing disclosure, and in some instances, some features of the examples may be employed without corresponding use of other features. For example, rectangular beams are described herein. However, alternative example beams with circular or octagonal cross-sections may be used. More generally, example beams may be used having a second moment of area that is isotropic for all axes in a cross-sectional plane extending through a proximal portion of the beam perpendicular to the central axis of the beam and is also isotropic for all axes in a distal cross-section extending through a distal portion of the beam perpendicular to the central axis of the beam.

[0389] The second moment of area requirement is expressed as,

[0390] I X = I Y

[0391] where I X represents the moment of inertia about an arbitrarily chosen X-axis lying in a plane perpendicular to the central axis, I Y represents the moment of inertia about an axis lying in the same plane but perpendicular to the X-axis, and

[0392] I XY = 0,

[0393] where I XY represents the product moment of inertia of the cross-section of the beam.

[0394] Figure 43 is an illustrative cross-sectional view of beam 1500 having a cross-sectional area A. For the cross-section A of beam 1500,

[0395] Let I x , I y , I xy be the second moments of inertia

[0396] where I x = ∫∫x 2 dA

[0397] I y = ∫∫y 2 dA

[0398] I xy = ∫∫xydA

[0399] For a new frame tilted at an angle θ

[0400] x 1 = xcosθ + ysinθ

[0401] y 1= Y cos θ - x sin θ

[0402]

[0403] For I to be isotropic in all directions, the requirement is that

[0404] I x = I y and I xy = 0

[0405] The second area moment of inertia requirement is expressed as

[0406] I X = I Y

[0407] where I X represents the moment of inertia about an arbitrarily chosen X-axis lying in a plane perpendicular to the central axis, I Y represents the moment of inertia about an axis lying in the same plane but perpendicular to the X-axis, and

[0408] I XY = 0,

[0409] where I XY represents the product moment of inertia of the cross-section of the beam.

[0410] Example

[0411] Example 1 may include a force sensor that includes: a rectangular beam having a proximal portion and a distal portion and having a longitudinal central axis extending between the proximal portion and the distal portion; a first full-bridge circuit that includes: a first gauge resistor ("first resistor") and a second gauge resistor ("second resistor") coupled to provide a first voltage divider output; and a third gauge resistor ("third resistor") and a fourth gauge resistor ("fourth resistor") coupled to provide a second voltage divider output; a second full-bridge circuit that includes: a fifth gauge resistor ("fifth resistor") and a sixth gauge resistor ("sixth resistor") coupled to provide a third voltage divider output; and a seventh gauge resistor ("seventh resistor") and an eighth gauge resistor ("eighth resistor") coupled to provide a fourth voltage divider output; wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors have a matching resistor type; wherein the first, second, third, and fourth resistors are located on a first side of the beam such that a voltage offset between the first and second voltage divider outputs represents the magnitude of a first force applied to the beam in a first force direction perpendicular to the longitudinal axis and parallel to the surface of the beam; and wherein the fifth, sixth, seventh, and eighth resistors are located on a second side of the beam adjacent to the first side such that a voltage divider offset between the third and fourth voltage divider outputs represents the magnitude of a second force applied to the beam in a second force direction perpendicular to the longitudinal axis and perpendicular to the first force direction.

[0412] Example 2 may include the subject matter of Example 1, wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors are strain-type resistors.

[0413] Example 3 may include the subject matter of Example 1, wherein the first, third, fifth, and seventh resistors are located at the proximal portion of the beam; and wherein the second, fourth, sixth, and eighth resistors are located at the proximal portion of the beam.

[0414] Example 4 may include the subject matter of Example 3, wherein the first and third resistors have a matching value, the second and fourth resistors have a matching value, the fifth and seventh resistors have a matching value, and the sixth and eighth resistors have a matching value.

[0415] Example 5 may include the subject matter of Example 3, wherein the first and third resistors have a matching longitudinal position on the beam, the second and fourth resistors have a matching longitudinal position on the beam, the fifth and seventh resistors have a matching longitudinal position on the beam, and the sixth and eighth resistors have a matching longitudinal position on the beam.

[0416] Example 6 may include a force sensor including: a beam having a proximal portion and a distal portion and having a longitudinal central axis extending between the proximal portion and the distal portion; a first full-bridge circuit including: a first gauge resistor (“first resistor”) and a second gauge resistor (“second resistor”) coupled to provide a first voltage divider output, the first gauge resistor and the second gauge resistor being arranged to extend along a first side axis that extends along the beam parallel to the longitudinal central axis; and a third gauge resistor (“third resistor”) and a fourth gauge resistor (“fourth resistor”) coupled to provide a second voltage divider output, the third gauge resistor and the fourth gauge resistor being arranged to extend along a second side axis that extends along the beam parallel to the longitudinal central axis; a second full-bridge circuit including: a fifth gauge resistor (“fifth resistor”) and a sixth gauge resistor (“sixth resistor”) coupled to provide a third voltage divider output, the fifth gauge resistor and the sixth gauge resistor being arranged to extend along a third side axis that extends along the beam parallel to the longitudinal central axis; and a seventh gauge resistor (“seventh resistor”) and an eighth gauge resistor (“eighth resistor”) coupled to provide a fourth voltage divider output, the seventh gauge resistor and the eighth gauge resistor being arranged to extend along a fourth side axis that extends along the beam parallel to the longitudinal central axis; wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors have a matching resistor type; wherein the first and second resistors extending along the first side axis and the third and fourth resistors extending along the second side axis are positioned on the beam such that the voltage offset between the first and second voltage divider outputs represents the magnitude of a first force applied to the beam in a first force direction perpendicular to the longitudinal axis, perpendicular to the first and second side axes, and parallel to the third and fourth side axes; and wherein the fifth and sixth resistors extending along the third side axis and the seventh and eighth resistors extending along the fourth side axis are positioned on the beam such that the voltage offset between the third and fourth voltage divider outputs represents the magnitude of a second force applied to the beam in a second force direction perpendicular to the longitudinal axis, parallel to the first and second axes, and perpendicular to the third and fourth side axes.

[0417] Example 7 may include the subject matter of Example 6, wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors are strain-type resistors.

[0418] Example 8 may include the subject matter of Example 6, wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors have matching resistor values.

[0419] Example 9 may include the subject matter of Example 6, wherein the first, third, fifth, and seventh resistors are located at the proximal portion of the beam; and wherein the second, fourth, sixth, and eighth resistors are located at the proximal portion of the beam.

[0420] Example 10 may include the subject matter described in Example 6, wherein the first, third, fifth, and seventh resistors are positioned at matching longitudinal positions of the beam; and wherein the second, fourth, sixth, and eighth resistors are positioned at matching longitudinal positions of the beam.

[0421] Example 11 may include the subject matter described in Example 6, wherein the first and third resistors are located in a proximal transverse plane of the beam that is perpendicular to the central axis and has a second area moment of inertia that is isotropic for all axes within the proximal transverse plane passing through the longitudinal central axis; wherein the fifth and seventh resistors are located in a proximal transverse plane of the beam that is perpendicular to the central axis and has a second area moment of inertia that is isotropic for all axes within the proximal transverse plane passing through the longitudinal central axis; wherein the second and fourth resistors are located in a distal transverse plane of the beam that is perpendicular to the central axis and has a second area moment of inertia that is isotropic for all axes within the distal transverse plane passing through the longitudinal central axis; and wherein the sixth and eighth resistors are located in a distal transverse plane of the beam that is perpendicular to the central axis and has a second area moment of inertia that is isotropic for all axes within the distal transverse plane passing through the longitudinal central axis.

[0422] Example 12 may include the subject matter described in Example 6, wherein a first side axis extends within a first plane that includes the longitudinal central axis; wherein a first side axis extends within a first plane that includes the longitudinal central axis; wherein a second force direction bisects a first separation angle between the first plane and a second plane; wherein a third side axis extends within a third plane that includes the longitudinal central axis; wherein a fourth side axis extends within a fourth plane that includes the longitudinal central axis; and wherein a first force direction bisects a second separation angle between the third plane and the fourth plane.

[0423] Example 13 may include the subject matter described in Example 12, wherein the first separation angle is equal to the second separation angle.

[0424] Example 14 may include the subject matter described in Example 6, wherein the first gauge resistor, the second gauge resistor, the third gauge resistor, and the fourth gauge resistor are located at corresponding positions of the beam having matching cross-sections; and wherein the fifth gauge resistor, the sixth gauge resistor, the seventh gauge resistor, and the eighth gauge resistor are located at corresponding positions of the beam having matching cross-sections.

[0425] Example 15 may include the subject matter of Example 9, wherein the first gauge resistor, the second gauge resistor, the third gauge resistor, and the fourth gauge resistor are located at corresponding positions of the beam having a matching cross-section; and wherein the fifth gauge resistor, the sixth gauge resistor, the seventh gauge resistor, and the eighth gauge resistor are located at corresponding positions of the beam having a matching cross-section.

[0426] Example 16 may include a metal sheet for use with a rectangular beam having a proximal portion and a distal portion and having a longitudinal central axis extending between the proximal portion and the distal portion, the metal sheet including: a first cutout portion configured to lay on a first side surface of the beam, including: a first gauge resistor ("first resistor") and a second gauge resistor ("second resistor") coupled to provide a first voltage divider output; a third gauge resistor ("third resistor") and a fourth gauge resistor ("fourth resistor") coupled to provide a second voltage divider output; a second cutout portion configured to lay on a second side surface of the beam adjacent to the first side surface of the beam, including: a fifth gauge resistor ("fifth resistor") and a sixth gauge resistor ("sixth resistor") coupled to provide a third voltage divider output; a seventh gauge resistor ("seventh resistor") and an eighth gauge resistor ("eighth resistor") coupled to provide a fourth voltage divider output, the seventh gauge resistor and the eighth gauge resistor being arranged to extend along a fourth side axis that extends along the beam parallel to the longitudinal central axis; wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors have a matching resistor type; wherein the first, second, third, and fourth resistors arranged to lay on the first side surface of the beam are located at the first side surface of the beam such that the voltage offset between the first voltage divider output and the second voltage divider output represents the magnitude of a first force applied to the beam in a first force direction perpendicular to the longitudinal axis; and wherein the fifth, sixth, seventh, and eighth resistors arranged to lay on the second side surface of the beam adjacent to the first side surface of the beam are located on the beam such that the voltage divider offset between the third voltage divider output and the fourth voltage divider output represents the magnitude of a second force applied to the beam in a second force direction perpendicular to the longitudinal axis and perpendicular to the first force direction.

[0427] Example 17 may include the subject matter of Example 16, wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors are strain type resistors.

[0428] Example 18 may include the subject matter of Example 16, wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors have matching resistor values.

[0429] Example 19 may include the subject matter described in Example 16, wherein the first, third, fifth, and seventh resistors are arranged to be located at the proximal portion of the beam; and wherein the second, fourth, sixth, and eighth resistors are arranged to be located at the proximal portion of the beam.

[0430] Example 20 may include the subject matter described in Example 16, wherein the first, third, fifth, and seventh resistors are arranged to be positioned at the matching longitudinal positions of the beam; and wherein the second, fourth, sixth, and eighth resistors are arranged to be positioned at the matching longitudinal positions of the beam.

[0431] Example 21 may include a metal sheet for use with a beam having a proximal portion and a distal portion and having a longitudinal central axis extending between the proximal portion and the distal portion, the metal sheet including: a first cutout portion configured to lie over a first portion of the beam, which includes: a first gauge resistor (“first resistor”) and a second gauge resistor (“second resistor”) coupled to provide a first voltage divider output, the first gauge resistor and the second gauge resistor being arranged to lie over the first portion of the beam and extend along a first side axis extending along the beam parallel to the longitudinal central axis; a third gauge resistor (“third resistor”) and a fourth gauge resistor (“fourth resistor”) coupled to provide a second voltage divider output, the third gauge resistor and the fourth gauge resistor being arranged to lie over the first portion of the beam and extend along a second side axis extending along the beam parallel to the longitudinal central axis; a second cutout portion configured to lie over a second portion of the beam, which includes: a fifth gauge resistor (“fifth resistor”) and a sixth gauge resistor (“sixth resistor”) coupled to provide a third voltage divider output, the fifth gauge resistor and the sixth gauge resistor being arranged to lie over the second portion of the beam and extend along a third side axis extending along the beam parallel to the longitudinal central axis; and a seventh gauge resistor (“seventh resistor”) and an eighth gauge resistor (“eighth resistor”) coupled to provide a fourth voltage divider output, the seventh gauge resistor and the eighth gauge resistor being arranged to lie over the second portion of the beam and extend along a fourth side axis extending along the beam parallel to the longitudinal central axis; wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors have a matching resistor type; wherein the first and second resistors arranged to lie over the first portion of the beam and extend along the first side axis and the third and fourth resistors arranged to lie over the first portion of the beam and extend along the second side axis are arranged to be positioned on the beam such that the voltage offset between the first and second voltage divider outputs represents the magnitude of a first force applied to the beam in a first force direction perpendicular to the longitudinal axis, perpendicular to the first and second side axes, and parallel to the third and fourth side axes; and wherein the fifth and sixth resistors arranged to lie over the second portion of the beam and extend along the third side axis and the seventh and eighth resistors arranged to lie over the second portion of the beam and extend along the fourth side axis are arranged to be positioned on the beam such that the voltage offset between the third and fourth voltage divider outputs represents the magnitude of a second force applied to the beam in a second force direction perpendicular to the longitudinal axis, parallel to the first and second axes, and perpendicular to the third and fourth side axes.

[0432] Example 22 may include the subject matter described in Example 22, wherein a first side axis extends within a first plane that includes a longitudinal central axis; wherein the first side axis extends within a first plane that includes a longitudinal central axis; wherein a second force direction bisects a first separation angle between the first plane and a second plane; wherein a third side axis extends within a third plane that includes a longitudinal central axis; wherein a fourth side axis extends within a fourth plane that includes a longitudinal central axis; and wherein a first force direction bisects a second separation angle between the third plane and the fourth plane.

[0433] Example 23 may include the subject matter described in Example 22, wherein the first separation angle is equal to the second separation angle.

[0434] Example 24 may include a force sensor that includes: a beam having a proximal portion and a distal portion and having a longitudinal central axis extending between the proximal portion and the distal portion; a first full bridge circuit on the beam, the first full bridge circuit having a first neutral axis and including: a first half-bridge circuit including a first gauge resistor (“first resistor”) and a second gauge resistor (“second resistor”), the first gauge resistor and the second gauge resistor being arranged along a first lateral side axis parallel to the longitudinal central axis and coupled to provide a first voltage divider output; a second half-bridge circuit including a third gauge resistor (“third resistor”) and a fourth gauge resistor (“fourth resistor”), the third gauge resistor and the fourth gauge resistor being arranged along a second lateral side axis parallel to the longitudinal central axis and coupled to provide a second voltage divider output; wherein the first and second lateral side axes are laterally spaced apart from each other on opposite sides of the first neutral axis; further including: a plurality of first central conductor traces that extend parallel to the neutral axis in regions of the beam that are between the first resistor and the second resistor and between the third resistor and the fourth resistor.

[0435] Example 25 may include a force sensor that includes: a beam having a proximal portion and a distal portion and having a longitudinal central axis extending between the proximal portion and the distal portion; a first full-bridge circuit on the beam, the first full-bridge circuit having a first neutral axis and including: a first half-bridge circuit that includes a first gauge resistor (“first resistor”) and a second gauge resistor (“second resistor”), the first gauge resistor and the second gauge resistor being arranged along a first lateral side axis parallel to the longitudinal central axis and coupled to provide a first voltage divider output; a second half-bridge circuit that includes a third gauge resistor (“third resistor”) and a fourth gauge resistor (“fourth resistor”), the third gauge resistor and the fourth gauge resistor being arranged along a second lateral side axis parallel to the longitudinal central axis and coupled to provide a second voltage divider output; wherein the first and second lateral side axes are laterally spaced apart from each other on opposite sides of the first neutral axis; wherein the first, second, third, and fourth resistors have a matching resistor type; and wherein the first full-bridge circuit is arranged on the beam such that a component of a force applied in a first direction perpendicular to the longitudinal central axis can be determined based on a difference between a first off-axis force applied to the first half-bridge and a second off-axis force applied to the second half-bridge.

[0436] Example 26 includes the subject matter of claim 25, further including: a second full-bridge circuit on the beam, the second full-bridge circuit having a second neutral axis and including: a fifth gauge resistor (“fifth resistor”) and a sixth gauge resistor (“sixth resistor”), the fifth gauge resistor and the sixth gauge resistor being arranged along a third lateral side axis parallel to the longitudinal central axis and coupled to provide a third voltage divider output; and a seventh gauge resistor (“seventh resistor”) and an eighth gauge resistor (“eighth resistor”), the seventh gauge resistor and the eighth gauge resistor being arranged along a fourth lateral side axis parallel to the longitudinal central axis and coupled to provide a fourth voltage divider output; wherein the third and fourth lateral side axes are laterally spaced apart from each other on opposite sides of the second neutral axis; further including: a plurality of first central conductor traces that extend parallel to the second neutral axis in regions of the beam that are between the fifth resistor and the sixth resistor and between the seventh resistor and the eighth resistor.

[0437] Example 27 includes the subject matter of claim 26, wherein the first, second, third, and fourth resistors have a matching resistor type; wherein the first full bridge circuit is arranged on the beam such that the component of the applied force in a first direction perpendicular to the longitudinal central axis can be determined based on the difference between a first off-axis force applied to the first half bridge and a second off-axis force applied to the second half bridge; wherein the fifth, sixth, seventh, and eighth resistors have a matching resistor type; and wherein the second full bridge circuit is arranged on the beam such that the component of the applied force in a second direction perpendicular to the longitudinal central axis and perpendicular to the first direction can be determined based on the difference between a third off-axis force applied to the third half bridge and a fourth off-axis force applied to the fourth half bridge.

[0438] Example 28 includes a force sensor, comprising: a rectangular beam having a proximal portion and a distal portion and having a longitudinal central axis extending between the proximal portion and the distal portion; a first half bridge circuit including a first gauge resistor ("first resistor") and a second gauge resistor ("second resistor") coupled to provide a first voltage divider output; a second half bridge circuit including a third gauge resistor ("third resistor") and a fourth gauge resistor ("fourth resistor") coupled to provide a second voltage divider output; a third half bridge circuit including a fifth gauge resistor ("fifth resistor") and a sixth gauge resistor ("sixth resistor") coupled to provide a third voltage divider output; a fourth half bridge circuit including a seventh gauge resistor ("seventh resistor") and an eighth gauge resistor ("eighth resistor") coupled to provide a fourth voltage divider output; wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors have a matching resistor type; wherein the first, second, third, and fourth resistors are located on a first face of the beam, and the fifth, sixth, seventh, and eighth resistors are located on a second face of the beam opposite the first face of the beam such that the voltage offset between the first and second voltage divider outputs represents the magnitude of a first force applied to the beam in a first force direction perpendicular to the longitudinal axis; the voltage offset between the third and fourth voltage divider outputs represents the magnitude of the first force; the voltage offset between the first and fourth voltage divider outputs represents the magnitude of a second force applied to the beam in a second force direction perpendicular to the longitudinal axis and perpendicular to the first force direction; and the voltage offset between the second and third voltage divider outputs represents the magnitude of the second force.

[0439] Example 29 includes the subject matter of claim 28, wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors are strain type resistors.

[0440] Example 29 includes the subject matter of claim 28, wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors have matching resistor values.

[0441] Example 30 includes the subject matter of claim 28, wherein the first, third, fifth, and seventh resistors are located at the proximal portion of the beam; and wherein the second, fourth, sixth, and eighth resistors are located at the distal portion of the beam.

[0442] Example 31 includes the subject matter of claim 30, wherein the first, third, fifth, and seventh resistors are positioned at matching longitudinal positions of the beam; and wherein the second, fourth, sixth, and eighth resistors are positioned at matching longitudinal positions of the beam.

[0443] Example 32 includes a force sensor that includes: a beam having a proximal portion and a distal portion and having a longitudinal central axis extending between the proximal portion and the distal portion; a first half-bridge circuit including a first gauge resistor (“first resistor”) and a second gauge resistor (“second resistor”) coupled to provide a first voltage divider output, the first gauge resistor and the second gauge resistor being arranged to extend along a first side axis that extends along the beam parallel to the longitudinal central axis; a second half-bridge circuit including a third gauge resistor (“third resistor”) and a fourth gauge resistor (“fourth resistor”) coupled to provide a second voltage divider output, the third gauge resistor and the fourth gauge resistor being arranged to extend along a second side axis that extends along the beam parallel to the longitudinal central axis; a third half-bridge circuit including a fifth gauge resistor (“fifth resistor”) and a sixth gauge resistor (“sixth resistor”) coupled to provide a third voltage divider output, the fifth gauge resistor and the sixth gauge resistor being arranged to extend along a third side axis that extends along the beam parallel to the longitudinal central axis; a fourth half-bridge circuit including a seventh gauge resistor (“seventh resistor”) and an eighth gauge resistor (“eighth resistor”) coupled to provide a fourth voltage divider output, the seventh gauge resistor and the eighth gauge resistor being arranged to extend along a fourth side axis that extends along the beam parallel to the longitudinal central axis; wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors have a matching resistor type; wherein the first and second resistors extending along the first side axis and the third and fourth resistors extending along the second side axis are positioned on the beam such that the voltage offset between the first and second voltage divider outputs represents the magnitude of a first force applied to the beam in a first force direction perpendicular to the longitudinal axis and perpendicular to the first, second, third, and fourth side axes; wherein the fifth and sixth resistors extending along the third side axis and the seventh and eighth resistors extending along the fourth side axis are positioned on the beam such that the voltage offset between the third and fourth voltage divider outputs represents the magnitude of a first force applied to the beam in a first force direction perpendicular to the longitudinal axis and perpendicular to the first, second, third, and fourth side axes; wherein the first and second resistors extending along the first side axis and the seventh and eighth resistors extending along the fourth side axis are positioned on the beam such that the voltage offset between the first and fourth voltage divider outputs represents the magnitude of a second force applied to the beam in a second force direction perpendicular to the longitudinal axis and parallel to the first, second, third, and fourth side axes; and wherein the third and fourth resistors extending along the first side axis and the fifth and sixth resistors extending along the third side axis are positioned on the beam such that the voltage offset between the second and third voltage divider outputs represents the magnitude of a second force applied to the beam in a second force direction perpendicular to the longitudinal axis and parallel to the first, second, third, and fourth side axes.

[0444] Example 33 includes the subject matter of Example 32, wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors are strain resistors.

[0445] Example 34 includes the subject matter of Example 32, wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors have matching resistor values.

[0446] Example 35 includes the subject matter of Example 32, wherein the first, third, fifth, and seventh resistors are located at the proximal portion of the beam; and wherein the second, fourth, sixth, and eighth resistors are located at the distal portion of the beam.

[0447] Example 36 includes the subject matter of Example 35, wherein the first, third, fifth, and seventh resistors are positioned at matching longitudinal positions of the beam; and wherein the second, fourth, sixth, and eighth resistors are positioned at matching longitudinal positions of the beam.

[0448] Example 37 includes the subject matter of Example 35, wherein the first, third, fifth, and seventh resistors are located in a proximal transverse plane of the beam that is perpendicular to the central axis and has a second area moment of inertia that is isotropic for all axes within the proximal transverse plane passing through the longitudinal central axis; and wherein the second, fourth, sixth, and eighth resistors are located in a distal transverse plane of the beam that is perpendicular to the central axis and has a second area moment of inertia that is isotropic for all axes within the distal transverse plane passing through the longitudinal central axis.

[0449] Example 38 includes the subject matter of Example 32, wherein the first side axis extends within a first plane that includes the longitudinal central axis; wherein the second force direction bisects a first separation angle between the first plane and the second plane; wherein the third side axis extends within a third plane that includes the longitudinal central axis; wherein the fourth side axis extends within a fourth plane that includes the longitudinal central axis; and wherein the first force direction bisects a second separation angle between the first plane and the fourth plane.

[0450] Example 39 includes the subject matter of Claim 37, wherein the first and second angles are supplementary angles.

[0451] Example 40 includes a force sensor, which includes: a rectangular beam having a proximal portion and a distal portion and having a longitudinal central axis extending between the proximal portion and the distal portion; a first half-bridge circuit including a first gauge resistor ("first resistor") and a second gauge resistor ("second resistor") coupled to provide a first voltage divider output; a second half-bridge circuit including a third gauge resistor ("third resistor") and a fourth gauge resistor ("fourth resistor") coupled to provide a second voltage divider output; a third half-bridge circuit including a fifth gauge resistor ("fifth resistor") and a sixth gauge resistor ("sixth resistor") coupled to provide a third voltage divider output; a fourth half-bridge circuit including a seventh gauge resistor ("seventh resistor") and an eighth gauge resistor ("eighth resistor") coupled to provide a fourth voltage divider output; wherein the first, second, third, and fourth resistors are one of tensile type and compressive type, and the fifth, sixth, seventh, and eighth resistors are the other of tensile type and compressive type.

[0452] Example 41 includes the subject matter of Example 40, wherein the first, second, third, and fourth resistors are strain-type resistors, and the fifth, sixth, seventh, and eighth resistors are compressive-type resistors.

[0453] Example 42 includes the subject matter of Example 40, wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors have matching resistor values.

[0454] Example 43 includes the subject matter of Example 40, wherein the first, third, fifth, and seventh resistors are located at the proximal portion of the beam; and wherein the second, fourth, sixth, and eighth resistors are located at the proximal portion of the beam.

[0455] Example 44 includes the subject matter of Example 43, wherein the first, third, fifth, and seventh resistors are positioned at matching longitudinal positions of the beam; and wherein the second, fourth, sixth, and eighth resistors are positioned at matching longitudinal positions of the beam.

[0456] Example 45 includes a force sensor that includes: a beam having a proximal portion and a distal portion and having a longitudinal central axis extending between the proximal portion and the distal portion; a first half-bridge circuit that includes a first gauge resistor ("first resistor") and a second gauge resistor ("second resistor") coupled to provide a first voltage divider output, the first gauge resistor and the second gauge resistor being arranged to extend along a first side axis that extends along the beam parallel to the longitudinal central axis; a second half-bridge circuit that includes a third gauge resistor ("third resistor") and a fourth gauge resistor ("fourth resistor") coupled to provide a second voltage divider output, the third gauge resistor and the fourth gauge resistor being arranged to extend along a second side axis that extends along the beam parallel to the longitudinal central axis; a third half-bridge circuit that includes a fifth gauge resistor ("fifth resistor") and a sixth gauge resistor ("sixth resistor") coupled to provide a third voltage divider output, the fifth gauge resistor and the sixth gauge resistor being arranged to extend along a third side axis that extends along the beam parallel to the longitudinal central axis; a fourth half-bridge circuit that includes a seventh gauge resistor ("seventh resistor") and an eighth gauge resistor ("eighth resistor") coupled to provide a fourth voltage divider output, the seventh resistor and the eighth resistor being arranged to extend along a fourth side axis that extends along the beam parallel to the longitudinal central axis; wherein the first, second, third, and fourth resistors are tensile resistors; and wherein the fifth, sixth, seventh, and eighth resistors are compressive resistors.

[0457] Example 46 includes the subject matter of Example 45, wherein the first, second, third, and fourth resistors are tensile resistors, and the fifth, sixth, seventh, and eighth resistors are compressive resistors.

[0458] Example 47 includes the subject matter of Example 45, wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors have matching resistor values.

[0459] Example 48 includes the subject matter of Example 45, wherein the first, third, fifth, and seventh resistors are located at the proximal portion of the beam; and wherein the second, fourth, sixth, and eighth resistors are located at the proximal portion of the beam.

[0460] Example 49 includes the subject matter of Example 48, wherein the first, third, fifth, and seventh resistors are arranged to be positioned at matching longitudinal positions of the beam; and wherein the second, fourth, sixth, and eighth resistors are arranged to be positioned at matching longitudinal positions of the beam.

[0461] Example 50 includes the subject matter of Example 48, wherein the first, third, fifth, and seventh resistors are located in a proximal transverse plane of the beam, the transverse plane being perpendicular to the central axis and having a second area moment of inertia that is isotropic for all axes within the proximal transverse plane passing through the longitudinal central axis; and wherein the second, fourth, sixth, and eighth resistors are located in a distal transverse plane of the beam, the distal transverse plane being perpendicular to the central axis and having a second area moment of inertia that is isotropic for all axes within the distal transverse plane passing through the longitudinal central axis.

[0462] Example 51 includes the subject matter of claim 45, wherein a first side axis extends within a first plane including the longitudinal central axis; wherein a first side axis extends within a first plane including the longitudinal central axis; wherein a second force direction bisects a first separation angle between the first plane and a second plane; wherein a third side axis extends within a third plane including the longitudinal central axis; wherein a fourth side axis extends within a fourth plane including the longitudinal central axis; and wherein a first force direction bisects a second separation angle between the third plane and the fourth plane.

[0463] Example 52 includes the subject matter of claim 51, wherein the first and second angles are supplementary angles.

[0464] Example 53 includes a force sensor, comprising: a beam having a proximal portion and a distal portion and having a longitudinal central axis extending between the proximal portion and the distal portion; a first full bridge circuit comprising: a first gauge resistor ("first resistor") and a second gauge resistor ("second resistor") coupled to provide a first voltage divider output; a third gauge resistor ("third resistor") and a fourth gauge resistor ("fourth resistor") coupled to provide a second voltage divider output; and a second full bridge circuit comprising: a fifth gauge resistor ("fifth resistor") and a sixth gauge resistor ("sixth resistor") coupled to provide a third voltage divider output; a seventh gauge resistor ("seventh resistor") and an eighth gauge resistor ("eighth resistor") coupled to provide a fourth voltage divider output; wherein the first, second, third, and fourth resistors have a matching resistor type; wherein the fifth and sixth resistors are of one of a tensile and a compressive resistor type, and the seventh and eighth resistors are of one of a tensile and a compressive resistor type; wherein the first, second, third, and fourth resistors are located at a first side of the beam such that a voltage offset between the first and second voltage divider outputs represents a magnitude of a first force applied to the beam in a first force direction perpendicular to the longitudinal axis; and wherein the fifth, sixth, seventh, and eighth resistors are located at a second side of the beam opposite the first side of the beam such that a voltage offset between the third and fourth voltage divider outputs represents a magnitude of a second force applied to the beam in a second force direction perpendicular to the longitudinal axis and perpendicular to the first force direction.

[0465] Example 54 includes the subject matter described in Example 53, wherein the first, second, third, and fourth resistors are strain resistors.

[0466] Example 54 includes the subject matter described in Example 53, wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors have matching resistor values.

[0467] Example 55 includes the subject matter described in Example 53, wherein the first, third, fifth, and seventh resistors are located at the proximal portion of the beam; and wherein the second, fourth, sixth, and eighth resistors are located at the proximal portion of the beam.

[0468] Example 56 includes the subject matter described in Example 55, wherein the first, third, fifth, and seventh resistors are positioned at matching longitudinal positions of the beam; and wherein the second, fourth, sixth, and eighth resistors are positioned at matching longitudinal positions of the beam.

[0469] Example 57 includes a force sensor that includes: a beam having a proximal portion and a distal portion and having a longitudinal central axis extending between the proximal portion and the distal portion; a first full-bridge circuit that includes: a first gauge resistor (“first resistor”) and a second gauge resistor (“second resistor”) coupled to provide a first voltage divider output, the first gauge resistor and the second gauge resistor being arranged to extend along a first side axis that extends along the beam parallel to the longitudinal central axis; a third gauge resistor (“third resistor”) and a fourth gauge resistor (“fourth resistor”) coupled to provide a second voltage divider output, the third gauge resistor and the fourth gauge resistor being arranged to extend along a second side axis that extends along the beam parallel to the longitudinal central axis; a second full-bridge circuit that includes: a fifth gauge resistor (“fifth resistor”) and a sixth gauge resistor (“sixth resistor”) coupled to provide a third voltage divider output; and a seventh gauge resistor (“seventh resistor”) and an eighth gauge resistor (“eighth resistor”) coupled to provide a fourth voltage divider output, the seventh gauge resistor and the eighth gauge resistor being arranged to extend along a third side axis that extends along the beam parallel to the longitudinal central axis; wherein the first, second, third, and fourth resistors have a matching resistor type; wherein the fifth and sixth resistors are of one of a tensile and a compressive resistor type, and the seventh and eighth resistors are of the other of the tensile and compressive resistor types; wherein the first and second resistors extending along the first side axis and the third and fourth resistors extending along the second side axis are positioned on the beam such that a voltage offset between the first and second voltage divider outputs represents a magnitude of a first force applied to the beam in a first force direction perpendicular to the longitudinal axis and perpendicular to the first and second side axes; and wherein the fifth, sixth, seventh, and eighth resistors extending along the third side axis are positioned on the beam such that a voltage offset between the third and fourth voltage divider outputs represents a magnitude of a second force applied to the beam in a second force direction perpendicular to the longitudinal axis and parallel to the first and second side axes.

[0470] Example 58 includes the subject matter of Example 57, wherein the first, second, third, and fourth resistors are strain-type resistors.

[0471] Example 59 includes the subject matter of Example 57, wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors have matching resistor values.

[0472] Example 60 includes the subject matter of Example 57, wherein the first, third, fifth, and seventh resistors are located at the proximal portion of the beam; and wherein the second, fourth, sixth, and eighth resistors are located at the proximal portion of the beam.

[0473] Example 61 includes the subject matter described in Example 60, wherein the first, third, fifth, and seventh resistors are positioned at matching longitudinal positions of the beam; and wherein the second, fourth, sixth, and eighth resistors are positioned at matching longitudinal positions of the beam.

[0474] Example 61 includes the subject matter described in Example 57, wherein a first side axis extends in a first plane that includes a longitudinal central axis; wherein a first side axis extends in a first plane that includes a longitudinal central axis; wherein a second force direction bisects a first separation angle between the first plane and a second plane.

[0475] Example 62 includes a metal sheet for use with a rectangular beam having a proximal portion and a distal portion and having a longitudinal central axis extending between the proximal portion and the distal portion, the metal sheet including: a first cutout portion configured to lay over a first side surface of the beam, which includes: a first gauge resistor ("first resistor") and a second gauge resistor ("second resistor") coupled to provide a first voltage divider output; a third gauge resistor ("third resistor") and a fourth gauge resistor ("fourth resistor") coupled to provide a second voltage divider output; and a second cutout portion configured to lay over a second side surface of the beam opposite the first side surface of the beam, which includes: a fifth gauge resistor ("fifth resistor") and a sixth gauge resistor ("sixth resistor") coupled to provide a third voltage divider output; a seventh gauge resistor ("seventh resistor") and an eighth gauge resistor ("eighth resistor") coupled to provide a fourth voltage divider output; wherein the first, second, third, and fourth resistors have a matching resistor type; wherein the fifth and sixth resistors have one of a tensile and a compressive resistor type, and the seventh and eighth resistors have the other of the tensile and the compressive resistor type; wherein the first, second, third, and fourth resistors are arranged to lay over the first side surface of the beam such that a voltage offset between the first and second voltage divider outputs represents a magnitude of a first force applied to the beam in a first force direction perpendicular to the longitudinal axis; and wherein the fifth, sixth, seventh, and eighth resistors are arranged to lay over the second side surface of the beam opposite the first side surface of the beam such that a voltage offset between the third and fourth voltage divider outputs represents a magnitude of a second force applied to the beam in a second force direction perpendicular to the longitudinal axis and perpendicular to the first force direction.

[0476] Example 63 includes the subject matter described in Example 61, wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors are strain gauges.

[0477] Example 64 includes the subject matter described in Example 61, wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors have matching resistor values.

[0478] Example 65 includes the subject matter described in Example 61, wherein the first, third, fifth, and seventh resistors are located at the proximal portion of the beam; and wherein the second, fourth, sixth, and eighth resistors are located at the proximal portion of the beam.

[0479] Example 66 includes the subject matter described in the example, wherein the first, third, fifth, and seventh resistors are positioned at matching longitudinal positions of the beam; and wherein the second, fourth, sixth, and eighth resistors are positioned at matching longitudinal positions of the beam.

[0480] Example 68 includes a sheet of metal for use with a beam having a proximal portion and a distal portion and having a longitudinal central axis extending between the proximal portion and the distal portion, the sheet of metal including: a first cutout portion configured to lie over a first portion of the beam, which includes: a first gauge resistor (“first resistor”) and a second gauge resistor (“second resistor”) coupled to provide a first voltage divider output, the first gauge resistor and the second gauge resistor being arranged to lie over the first portion of the beam and extending along a first side axis extending along the beam parallel to the longitudinal central axis; and a third gauge resistor (“third resistor”) and a fourth gauge resistor (“fourth resistor”) coupled to provide a second voltage divider output, the third gauge resistor and the fourth gauge resistor being arranged to lie over the first portion of the beam and extending along a second side axis extending along the beam parallel to the longitudinal central axis; and a second cutout portion configured to lie over a second portion of the beam, which includes: a fifth gauge resistor (“fifth resistor”) and a sixth gauge resistor (“sixth resistor”) coupled to provide a third voltage divider output; and a seventh gauge resistor (“seventh resistor”) and an eighth gauge resistor (“eighth resistor”) coupled to provide a fourth voltage divider output, the seventh gauge resistor and the eighth gauge resistor being arranged to lie over the second portion of the beam and extending along a third side axis extending along the beam parallel to the longitudinal central axis; wherein the first, second, third, and fourth resistors have a matching resistor type; wherein the fifth and seventh resistors are strain type resistors; wherein the sixth and eighth resistors are compression type resistors; wherein the first and second resistors arranged to lie over the first portion of the beam and extending along the first side axis and the third and fourth resistors arranged to lie over the first portion of the beam and extending along the second side axis are arranged to be positioned on the beam such that the voltage offset between the first and second voltage divider outputs represents the magnitude of a first force applied to the beam in a first force direction perpendicular to the longitudinal axis and perpendicular to the first and second side axes; and wherein the fifth, sixth, seventh, and eighth resistors arranged to lie over the second portion of the beam and extending along the third side axis are arranged to be positioned on the beam such that the voltage offset between the third and fourth voltage divider outputs represents the magnitude of a second force applied to the beam in a second force direction perpendicular to the longitudinal axis and parallel to the first and second side axes; wherein the first side axis extends in a first plane including the longitudinal central axis; wherein the second side axis extends in a second plane including the longitudinal central axis; wherein the second force direction bisects a first separation angle between the first plane and the second plane.

[0481] Example 69 includes the subject matter of Example 68, wherein the first side axis extends in a first plane including the longitudinal central axis; wherein the first side axis extends in a first plane including the longitudinal central axis.

[0482] Example 70 includes a force sensor that includes: a beam that includes a proximal portion and a distal portion, a longitudinal central axis, and a neutral axis that extends parallel to the central axis along the surface of the beam; a first Wheatstone half-bridge (“half-bridge”) that includes a strain resistor; a second half-bridge that includes a strain resistor; a third half-bridge that includes a compression resistor; a fourth half-bridge that includes a compression resistor; the first and third half-bridges are arranged along a first side axis; the second and fourth half-bridges are arranged along a second side axis; the first and second side axes extend parallel to the neutral axis and are equidistant from the neutral axis along the surface of the beam on opposite sides of the neutral axis.

[0483] Example 71 includes a method of identifying a fault in the force sensor of Example 70, including: applying a force to the force sensor; measuring a pair of orthogonal components of the applied force using each of four different combinations of three half-bridges in a set, the set consisting of a first half-bridge, a second half-bridge, a third half-bridge, and a fourth half-bridge, each pair of force measurements including a first force component measurement of the applied force and a second force component measurement of the applied force, the first force component being orthogonal to the second force component; comparing the first force component measurements from each pair of force measurements; comparing the second force component measurements from each pair of force measurements; generating an electronic signal to report an error in response to a mismatch between the first force component measurement of one of a pair of force measurements and the first force component measurement of at least another of the pair of force measurements; and generating an electronic signal to report an error in response to a mismatch between the second force component measurement of one of a pair of force measurements and the second force component measurement of at least another of the pair of force measurements.

[0484] Those of ordinary skill in the art will recognize many variations, alternatives, and modifications. Accordingly, the scope of the present disclosure should be limited only by the appended claims, and it should be understood that the claims should be interpreted broadly in a manner consistent with the scope of the examples disclosed herein. The foregoing description is presented to enable any person skilled in the art to create and use a force sensor having a beam and a distributed bridge circuit. Various modifications to the examples will be apparent to those skilled in the art, and the general principles defined herein can be applied to other examples and applications without departing from the scope of the invention. In the foregoing description, numerous details are set forth for purposes of explanation. However, those of ordinary skill in the art will recognize that the invention can be practiced without the use of these specific details. In other instances, well-known processes are shown in block diagram form to avoid obscuring the description of the invention with unnecessary details. The same reference numerals may be used to denote different views of the same or similar items in different figures. Accordingly, the foregoing description and drawings of examples according to the invention are merely illustrative of the principles of the invention. Accordingly, it should be understood that those skilled in the art can make various modifications to the examples without departing from the scope of the invention, and the scope of the invention is defined by the appended claims.

Claims

1. A force sensor, comprising: a beam including a flat transverse surface and a longitudinal central axis, each longitudinally extending between a proximal portion and a distal portion, a neutral axis extending parallel to the longitudinal central axis along the transverse surface, a first lateral axis and a second lateral axis extending parallel to the neutral axis on both sides of the neutral axis along the transverse surface; and a first half - bridge circuit, a second half - bridge circuit, a third half - bridge circuit, and a fourth half - bridge circuit coupled to the flat transverse surface, wherein: a first plane is defined by the longitudinal central axis and the first lateral axis, a second plane is defined by the longitudinal central axis and the second lateral axis, the first half - bridge circuit includes a first proximal tensile strain gauge resistor and a first distal tensile strain gauge resistor arranged along the first lateral axis, the second half - bridge circuit includes a second proximal tensile strain gauge resistor and a second distal tensile strain gauge resistor arranged along the second lateral axis, the third half - bridge circuit includes a first proximal compressive strain gauge resistor and a first distal compressive strain gauge resistor arranged along the first lateral axis, the fourth half - bridge circuit includes a second proximal compressive strain gauge resistor and a second distal compressive strain gauge resistor arranged along the second lateral axis, the output of each of the first half - bridge circuit and the third half - bridge circuit in response to an external force applied to the beam indicates that a first plane strain force in the first plane is an off - axis force with respect to the beam coordinate system, the output of each of the second half - bridge circuit and the fourth half - bridge circuit in response to the external force applied to the beam indicates that a second plane strain force in the second plane is an off - axis force with respect to the beam coordinate system, and the combination of the first plane strain force indication and the second plane strain force indication indicates the magnitude and direction of the external force applied to the beam.

2. A method of controlling a device, comprising: receiving, at a computer system, a plurality of outputs from a force sensor coupled to the device, the force sensor including a first half - bridge circuit, a second half - bridge circuit, a third half - bridge circuit, and a fourth half - bridge circuit coupled to a flat transverse surface of a beam, the beam including a longitudinal central axis longitudinally extending between a proximal portion and a distal portion, a neutral axis extending along the transverse surface parallel to the longitudinal central axis, a first lateral axis and a second lateral axis extending parallel to the neutral axis on both sides of the neutral axis, wherein: a first plane is defined by the longitudinal central axis and the first lateral axis, and a second plane is defined by the longitudinal central axis and the second lateral axis, the first half - bridge circuit and the third half - bridge circuit are arranged along the first lateral axis, the second half - bridge circuit and the fourth half - bridge circuit are arranged along the second lateral axis, The plurality of outputs from the force sensor includes at least a first half-bridge circuit voltage, a second half-bridge circuit voltage, a third half-bridge circuit voltage, and a fourth half-bridge circuit voltage, wherein the first half-bridge circuit voltage is from the first half-bridge circuit or the third half-bridge circuit, and wherein the second half-bridge circuit voltage is from the second half-bridge circuit or the fourth half-bridge circuit; by the computer system, determining a first indication of a first in-plane strain force in the first plane based at least in part on the first half-bridge circuit voltage, and determining a second indication of the first in-plane strain force based at least in part on the third half-bridge circuit voltage, the first in-plane strain force being an off-axis force defined for the beam relative to the beam coordinate system; by the computer system, determining a first indication of a second in-plane strain force in the second plane based at least in part on the second half-bridge circuit voltage, and determining a second indication of the second in-plane strain force based at least in part on the fourth half-bridge circuit voltage, the second in-plane strain force being an off-axis force relative to the beam coordinate system; and by the computer system, determining a determined external force applied to the beam based on any three of the first indication of the first in-plane strain force, the second indication of the first in-plane strain force, the first indication of the second in-plane strain force, and the second indication of the second in-plane strain force.

3. A force sensor, comprising: a beam, a first bridge circuit, and a second bridge circuit, wherein: the beam includes a proximal portion, a distal portion, a first side extending between the proximal portion and the distal portion, and a second side opposite the first side extending between the proximal portion and the distal portion, a longitudinal central axis extends between the proximal portion and the distal portion, a first neutral axis extends along the first side parallel to the central axis, a first lateral side axis extends along the first side parallel to the first neutral axis, a second lateral side axis extends along the first side parallel to the first neutral axis, the first lateral side axis and the second lateral side axis are located on opposite sides of the first neutral axis, a second neutral axis extends along the second side parallel to the central axis, the first bridge circuit includes a first strain gauge resistor disposed along the first lateral side axis and a second strain gauge resistor disposed along the second lateral side axis, the second bridge circuit includes a proximal strain gauge resistor along the second neutral axis at the proximal portion of the beam and a distal strain gauge resistor along the second neutral axis at the distal portion of the beam, the strain indication measured by the first bridge circuit in response to an external force applied to the beam indicates the magnitude of the external force in a first direction perpendicular to the central axis, and the strain indication measured by the second bridge circuit in response to an external force applied to the beam indicates the magnitude of the external force in a second direction perpendicular to the central axis and orthogonal to the first direction.

4. A method of controlling a device, comprising: receiving, at a computer system, an input from a force sensor coupled to a device, wherein: The force sensor includes a beam, a first bridge circuit, and a second bridge circuit, The beam includes a proximal portion, a distal portion, a first side extending between the proximal portion and the distal portion, and a second side opposite to the first side and extending between the proximal portion and the distal portion, A longitudinal central axis extends between the proximal portion and the distal portion, A first neutral axis extends along the first side parallel to the central axis, A second neutral axis extends along the second side parallel to the central axis, A first transverse side axis extends along the first side parallel to the neutral axis, A second transverse side axis extends along the first side parallel to the neutral axis, The first transverse side axis and the second transverse side axis are located on opposite sides of the first neutral axis, The first bridge circuit includes a first strain gauge resistor arranged along the first transverse side axis and a second strain gauge resistor arranged along the second transverse side axis, The second bridge circuit includes a proximal strain gauge resistor along the second neutral axis at the proximal portion of the beam and a distal strain gauge resistor along the second neutral axis at the distal portion of the beam, The output from the force sensor includes at least a first bridge circuit voltage and a second bridge circuit voltage, The first bridge circuit voltage comes from the first bridge circuit in response to an external force applied to the beam, and The second bridge circuit voltage comes from the second bridge circuit in response to an external force applied to the beam; Determine the sensed magnitude of the external force in a first direction perpendicular to the longitudinal axis through the computer system and at least partially based on the first bridge circuit voltage; and Determine the sensed magnitude of the external force in a second direction perpendicular to the longitudinal axis and orthogonal to the first direction through the computer system and at least partially based on the second bridge circuit voltage.

5. A force sensor, comprising: A beam, a first bridge circuit, and a second bridge circuit, wherein: The beam includes a proximal portion, a distal portion, a first side extending between the proximal portion and the distal portion, and a second side adjacent to the first side and extending between the proximal portion and the distal portion, A longitudinal central axis extends between the proximal portion and the distal portion, A first neutral axis extends along the first side parallel to the central axis, A first transverse side axis extends along the first side parallel to the first neutral axis, A second transverse side axis extends along the first side parallel to the first neutral axis, The first transverse side axis and the second transverse side axis are located on opposite sides of the first neutral axis, A second neutral axis extends along the second side parallel to the central axis, A third transverse side axis extends along the second side parallel to the second neutral axis, A fourth transverse side axis extends along the second side parallel to the second neutral axis, The third transverse side axis and the fourth transverse side axis are located on opposite sides of the second neutral axis, The first bridge circuit includes a first strain gauge resistor arranged along the first lateral side axis and a second strain gauge resistor arranged along the second lateral side axis, The second bridge circuit includes a third strain gauge resistor arranged along the third lateral side axis and a fourth strain gauge resistor arranged along the fourth lateral side axis, The strain measured by the first bridge circuit in response to an external force applied to the beam indicates the magnitude of the external force in a first direction perpendicular to the longitudinal axis, and The strain measured by the second bridge circuit in response to an external force applied to the beam indicates the magnitude of the external force in a second direction perpendicular to the longitudinal axis and orthogonal to the first direction.

6. A method of controlling a device, comprising: Receiving, at a computer system, an input from a force sensor coupled to the device, wherein: The force sensor includes a beam, a first bridge circuit, and a second bridge circuit, The beam includes a proximal portion, a distal portion, a first side extending between the proximal portion and the distal portion, and a second side adjacent to the first side and extending between the proximal portion and the distal portion, A longitudinal central axis extends between the proximal portion and the distal portion, A first neutral axis extends along the first side parallel to the central axis, A first lateral side axis extends along the first side parallel to the neutral axis, A second lateral side axis extends along the first side parallel to the neutral axis, The first lateral side axis and the second lateral side axis are located on opposite sides of the first neutral axis, A second neutral axis extends along the second side parallel to the central axis, A third lateral side axis extends along the second side parallel to the second neutral axis, A fourth lateral side axis extends along the second side parallel to the second neutral axis, The third lateral side axis and the fourth lateral side axis are located on opposite sides of the second neutral axis, The first bridge circuit includes a first strain gauge resistor arranged along the first lateral side axis and a second strain gauge resistor arranged along the second lateral side axis, The second bridge circuit includes a third strain gauge resistor arranged along the third lateral side axis and a fourth strain gauge resistor arranged along the fourth lateral side axis, The output from the force sensor includes at least a first bridge circuit voltage and a second bridge circuit voltage, The first bridge circuit voltage is from the first bridge circuit in response to an external force applied to the beam, and The second bridge circuit voltage is from the second bridge circuit in response to an external force applied to the beam; Determining, by the computer system and at least partially based on the first bridge circuit voltage, the strain measured by the first bridge circuit, the strain indicating the magnitude of the external force in a first direction perpendicular to the longitudinal axis; and Determining, by the computer system and at least partially based on the second bridge circuit voltage, the strain measured by the second bridge circuit, the strain indicating the magnitude of the external force in a second direction perpendicular to the longitudinal axis and orthogonal to the first direction.

7. A force sensor, comprising: A beam, a first bridge circuit, and a second bridge circuit, wherein: The beam includes a proximal portion, a distal portion, a first side extending between the proximal portion and the distal portion, and a second side opposite the first side and extending between the proximal portion and the distal portion, A longitudinal central axis extends between the proximal portion and the distal portion, A first neutral axis extends along the first side parallel to the central axis, A first transverse side axis extends along the first side parallel to the neutral axis, A second transverse side axis extends along the first side parallel to the neutral axis, The first transverse side axis and the second transverse side axis are located on opposite sides of the first neutral axis, A second neutral axis extends along the second side parallel to the central axis, A third transverse side axis extends along the second side parallel to the second neutral axis, A fourth transverse side axis extends along the second side parallel to the second neutral axis, The third transverse side axis and the fourth transverse side axis are located on opposite sides of the second neutral axis, The first bridge circuit includes a first proximal strain gauge resistor arranged along the first transverse side axis and a second proximal strain gauge resistor arranged along the second transverse side axis, The second bridge circuit includes a third proximal strain gauge resistor arranged along the third transverse side axis and a fourth proximal strain gauge resistor arranged along the fourth transverse side axis, The first proximal strain gauge resistor, the second proximal strain gauge resistor, the third proximal strain gauge resistor, and the fourth proximal strain gauge resistor are located at the proximal portion of the beam, and The strain measured by the first bridge circuit in response to an external force applied to the beam and the strain measured by the second bridge circuit in response to the external force applied to the beam indicate the magnitude of the external force in a first direction perpendicular to the longitudinal axis and the magnitude of the external force in a second direction perpendicular to the longitudinal axis and orthogonal to the first direction.

8. A method of controlling a device, comprising: Receiving, at a computer system, an input from a force sensor coupled to the device, wherein: The force sensor includes a beam, a first bridge circuit, and a second bridge circuit, The beam includes a proximal portion, a distal portion, a first side extending between the proximal portion and the distal portion, and a second side opposite the first side and extending between the proximal portion and the distal portion, A longitudinal central axis extends between the proximal portion and the distal portion, A first neutral axis extends along the first side parallel to the central axis, A first transverse side axis extends along the first side parallel to the neutral axis, A second transverse side axis extends along the first side parallel to the neutral axis, The first transverse side axis and the second transverse side axis are located on opposite sides of the first neutral axis, A second neutral axis extends along the second side parallel to the central axis, A third transverse side axis extends along the second side parallel to the second neutral axis, A fourth transverse side axis extends along the second side parallel to the second neutral axis, The third lateral axis and the fourth lateral axis are located on opposite sides of the second neutral axis, The first bridge circuit includes a first proximal strain gauge resistor arranged along the first lateral axis and a second proximal strain gauge resistor arranged along the second lateral axis, The second bridge circuit includes a third proximal strain gauge resistor arranged along the third lateral axis and a fourth proximal strain gauge resistor arranged along the fourth lateral axis, The first proximal strain gauge resistor, the second proximal strain gauge resistor, the third proximal strain gauge resistor, and the fourth proximal strain gauge resistor are located at the proximal portion of the beam, and The output from the force sensor includes at least a first bridge circuit voltage of the first bridge circuit and a second bridge circuit voltage of the second bridge circuit, and The first bridge circuit voltage and the second bridge circuit voltage are at least partially based on an external force applied to the beam; and The sensed magnitude of the external force in a first direction perpendicular to the longitudinal axis and the sensed magnitude of the external force in a second direction perpendicular to the longitudinal axis and orthogonal to the first direction are determined by the computer system and at least partially based on the first bridge circuit voltage and the second bridge circuit voltage.

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