Expansion Bridge XY Force Sensor

Abstract

A force sensor includes a beam having a longitudinal center axis and a neutral axis extending along a surface of the beam parallel to the center axis. A first half-bridge includes a tensile resistor. A second half-bridge includes a tensile resistor. A third half-bridge includes a compression resistor. A fourth half-bridge includes a compression resistor. The half-bridges are arranged on the surface of the beam so that orthogonal components of a force applied to the beam can be redundantly measured using four different combinations of three half-bridges. The redundant measurements can be used to identify failure of one or more resistors.

Description

[0001] Priority rights

[0002] This application is a continuation of and claims the benefit of priority of U.S. patent application serial number 62 / 936,349 filed on November 15, 2019 and U.S. patent application serial number 62 / 936,350 filed on November 15, 2019 and U.S. patent application serial number 62 / 936,351 filed on November 15, 2019, each of which is incorporated herein by reference in its entirety. Background Art

[0003] Force sensing and feedback during minimally invasive surgical procedures can bring better immersion, realism, and intuitiveness to the surgeon performing the procedure. For optimal tactile rendering performance and accuracy, force sensors can be placed on the surgical instrument as close as possible to the interacting anatomical tissue. One approach is to embed a force sensor at the distal end of the surgical instrument shaft and form an electrical strain gauge on the force transducer, such as by laying a conductive sheet with a cut circuit pattern, printing, or additive deposition process, to measure the strain applied to the surgical instrument.

[0004] FIG. 1 is a schematic diagram of an existing force sensor including a rectangular beam having four full Wheatstone bridges (full bridges). A typical bridge circuit includes a circuit topology in which two circuit branches (usually connected in parallel to 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. An 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 force measurements determined by the full bridges of the proximal and distal portions of that side of the beam.

[0005] The force sensor can be subjected to a variety of different strain sources, including: normal forces to be measured, moments, off-axis forces, off-axis moments, compression / tension, torsion, ambient temperature, and gradient temperature. Each example full bridge can offset the following stresses: temperature, torsion, off-axis forces, and off-axis moments. Each individual full bridge output can indicate stresses caused by forces, moments, and compression / tension. In the example force sensor, the output value generated by the proximal full bridge formed on one side can be subtracted from the output value generated by the distal full bridge on the same side to offset the moment, thereby generating an output value representing the normal force to be measured.

[0006] Surgical instrument force sensors are critical to ensuring patient safety. Therefore, force sensor error detection may be required to prevent injury by detecting force sensor failure. One method of error detection is to provide additional full bridges to produce redundant force measurements that can be compared to detect errors. However, limited space on the side of the beam can make it impractical to add more full bridges on one side. In addition, some manufacturing processes are often limited to forming bridges on two sides at most. Forming bridges on four sides significantly increases manufacturing costs. Summary of the invention

[0007] The force sensor includes a beam having four Wheatstone half bridges ("half bridges") located on a beam surface. The beam includes a proximal portion and a distal portion, a longitudinal center axis, and a neutral axis extending along the beam surface parallel to the center axis. The first and second half bridges include tension resistors. The third and fourth half bridges include compression resistors. The first and third half bridges are arranged along a first lateral axis. The second and fourth half bridges are arranged along a second lateral axis. The first and second lateral axes extend along the beam surface parallel to the neutral axis and equidistant from the neutral axis on opposite sides of the neutral axis.

[0008] Each of the four combinations of the three half-bridges can be used to produce a separate measurement of the orthogonal components of the force applied to the beam. Comparison of the separate measurements provides an indication of whether one or more of the half-bridges is faulty. Faults are reported as sensor errors. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] In the accompanying drawings, which are not necessarily drawn to scale, the same numerals may describe similar components in different views. Similar numerals with different letter suffixes may represent different instances of similar components. The accompanying drawings generally illustrate various embodiments discussed herein by way of example and not limitation.

[0010] FIG. 1 is a schematic diagram showing an example prior art force sensor including a rectangular beam having four full Wheatstone bridges (full bridges).

[0011] Figure 2 is an illustrative side view of a distal portion of a surgical instrument having an elongated shaft with a force sensor beam mounted thereon, according to some examples.

[0012] 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.

[0013] Figure 3B Shows Figure 3A An illustrative perspective view of a force sensor further illustrating an imaginary first plane and an imaginary second plane.

[0014] Figure 3C Shows Figure 3A An illustrative perspective view of a force sensor further illustrating an imaginary third plane and an imaginary fourth plane.

[0015] Figure 4 yes Figure 3A-3B An illustrative proximal cross-sectional view of an example beam showing the intersection of imaginary planes at the longitudinal center axis.

[0016] Figure 5A is a side view showing the arrangement of resistors on the first side 308 of the beam.

[0017] Figure 5B is a side view showing the placement of resistors on the second side of the beam.

[0018] Fig. 6A is an illustrative side view of an example beam showing a first example circuit layout topology of an example full Wheatstone bridge.

[0019] Figure 6B is an illustrative first schematic circuit diagram representation of a full Wheatstone bridge layout topology.

[0020] Fig. 7A is an illustrative side view of an example beam showing a second example circuit layout topology of an example full Wheatstone bridge.

[0021] Figure 7B is an illustrative first schematic circuit diagram representation of a second full Wheatstone bridge layout topology.

[0022] Fig. 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.

[0023] Figure 8B yes Fig. 8A An illustrative first schematic circuit diagram of a first and a second full-Wheatstone bridge is shown.

[0024] Fig.9A yes Figure 4 An illustrative cross-sectional end view of an example beam indicating a resistor on a first side and indicating a first planar force and a second planar force.

[0025] Fig. 9B is an illustrative force diagram indicating X-force components and Y-force components of a first planar force applied to a first proximal resistor and a first distal resistor in response to an applied force.

[0026] Fig. 9Cis an illustrative force diagram indicating an X-force component and a 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.

[0027] Fig.10 yes Figure 4 An illustrative cross-sectional end view of an example beam of indicating a resistor on a second side of the beam and indicating third and fourth planar forces.

[0028] Fig.11 is an illustrative diagram showing a metal sheet including cut-outs defining example resistors for assembly into corresponding bridge circuits on adjacent first and second sides of a beam.

[0029] Fig. 12A is a schematic diagram showing a process of wrapping first and second regions around first and second sides of a metal sheet that surrounds a beam.

[0030] Fig. 12B is an illustrative perspective view of a beam showing first and second regions of a metal sheet laid over respective first and second sides of an example beam.

[0031] Figures 13A-13B An illustrative top perspective view of an example force sensor is shown ( Fig.13A ) and bottom perspective ( Fig. 13B ), the example force sensor 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.

[0032] Fig.14A An illustrative first example half-bridge circuit layout is shown having proximal and distal tensile gauge strain resistors electrically coupled in series and having a voltage node coupled therebetween.

[0033] Fig. 14B is an illustrative first schematic circuit diagram representation of a first half-bridge circuit layout.

[0034] Fig.15A An illustrative second example half-bridge circuit layout is shown having proximal and distal compression gauge strain resistors electrically coupled in series and having a voltage node coupled therebetween.

[0035] Fig. 15B is an illustrative second schematic circuit diagram representation of a second half-bridge circuit layout.

[0036] Fig.16 is a diagram showing the first and second imaginary planes. Figures 13A-13B An illustrative near side cross-sectional view of an example beam.

[0037] Fig.17A is a side view of the beam, which shows Figures 13A-13B The first side of the beam.

[0038] Fig. 17B is a side view of the beam, which shows Figures 13A-13B on the opposite second side of the beam.

[0039] Fig.18A is an illustrative proximal cross-sectional view of an example beam indicating second and third plane strain forces applied to the second and third bridge halves.

[0040] Fig.18B is an illustrative force diagram indicating the X-force component and the Y-force component of the second plane strain force on the second half-bridge.

[0041] Fig. 18C is an illustrative force diagram indicating X-force and Y-force components of a third plane strain force applied to the third half-bridge.

[0042] Fig.19 is an illustrative proximal cross-sectional view of an example beam indicating first and fourth plane strain forces applied to first and fourth half-bridges.

[0043] Fig. 20 is an illustrative proximal cross-sectional view of an example beam indicating a first plane strain force and a second plane strain force applied to the first and second bridge halves.

[0044] Fig.21 is an illustrative proximal cross-sectional view of an example beam indicating third and fourth plane strain forces applied to the third and fourth bridge halves.

[0045] Fig. 22 An illustrative top perspective view of an example force sensor is shown that includes a rectangular beam having two tension resistor half-bridge circuits and two compression resistor half-bridge circuits located on a first side thereof.

[0046] Fig.23 yes Fig. 22 An illustrative near side cross-sectional view of an example beam.

[0047] Fig.24 yes Fig. 22 A side view of a first side of an example beam with two tension resistor half-bridges and two compression resistor half-bridges located on the example beam.

[0048] Fig.25 is an illustrative cross-sectional end view of an example beam indicating a first plane strain force and a second plane strain force applied to the first and second bridge halves.

[0049] Fig.26 is an illustrative cross-sectional end view of an example beam indicating first and second plane strain forces applied to the third and fourth bridge halves.

[0050] Fig. 27 is an illustrative cross-sectional end view of an example beam indicating first and fourth plane strain forces applied to first and fourth bridge halves.

[0051] Fig.28 is an illustrative cross-sectional end view of an example beam indicating second and third plane strain forces applied to the second and third bridge halves.

[0052] Fig.29 is an illustrative cross-sectional end view of an example beam indicating the forces applied to three example half-bridges located thereon.

[0053] Fig.30 is an illustrative diagram showing a computer system configured to monitor force sensor voltage measurements.

[0054] Fig.31 is an illustrative flow chart representing an example diagnostic process for detecting the occurrence of a faulty strain gauge resistor within a force sensor.

[0055] Figures 32A-32B An illustrative top perspective view of an example force sensor is shown ( Fig.32A ) and bottom perspective ( Fig.32B ), the example force sensor includes a rectangular beam with a Wheatstone bridge circuit on two opposite sides of the rectangular beam.

[0056] Fig.33 yes Figures 32A-32B An illustrative near side cross-sectional view of an example beam.

[0057] Fig.34A is a side view of the beam, showing a first side of the beam.

[0058] Fig.34B is a side view of the beam, showing the second side of the beam.

[0059] Fig.35A is an illustrative side view of an example beam showing a first example layout of a first full Wheatstone bridge circuit.

[0060] Fig.35B is an illustrative first schematic circuit diagram representation of the first full Wheatstone bridge layout topology.

[0061] Fig.36A is an illustrative side view of an example beam showing an alternative second example layout of the first full Wheatstone bridge circuit.

[0062] Fig.36B is an illustrative first schematic circuit diagram representation of an alternative example second layout topology for a first full Wheatstone bridge circuit.

[0063] Fig.37A is an illustrative side view of an example beam showing an example first circuit layout of a second full Wheatstone bridge circuit located on a second side of the beam.

[0064] Fig.37B is an illustrative schematic circuit diagram representation of a first example layout of a second full bridge circuit.

[0065] Fig.37C is an illustrative side view of an example beam showing an example second layout of a second example full Wheatstone bridge located on a second side of beam 3304.

[0066] Fig.37D is an illustrative schematic circuit diagram representation of a second example layout for a second full bridge circuit.

[0067] Fig.38A is an illustrative side view of an example beam showing an expanded layout of a Wheatstone bridge and illustrating the routing of the center conductor trace.

[0068] Fig.38B yes Fig.38A An illustrative first schematic circuit diagram of a first and a second full-Wheatstone bridge is shown.

[0069] Fig.39A yes Fig.33 An illustrative cross-sectional end view of an example beam indicating a resistor on a first side and indicating a first planar force and a second planar force.

[0070] Fig.39B is an illustrative force diagram indicating X-force components and Y-force components of a first planar force applied to a first proximal resistor and a first distal resistor in response to an applied force.

[0071] Fig.39C is an illustrative force diagram indicating an X-force component and a 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.

[0072] Fig.40 yes Fig.33 An illustrative proximal direction cross-sectional view of an example beam with resistors indicating X-axis force.

[0073] Fig.41 is an illustrative diagram showing a metal sheet including cutouts defining example resistors for assembly into respective first and second full Wheatstone bridges on oppositely facing first and second sides of a beam.

[0074] Fig.42A is an illustrative diagram showing a process of wrapping a metal sheet around an example 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.

[0075] Fig.42B is a schematic top perspective view of a beam with the metal sheet wrapped around three sides of the beam.

[0076] Fig.42C is an illustrative bottom perspective view of a beam with the metal sheet wrapped around three sides of the beam.

[0077] Fig.43 is an illustrative cross-sectional view of a beam. DETAILED DESCRIPTION

[0078] Extended bridge adjacent side XY force sensor

[0079] Figure 2 2 is an illustrative side view of a distal portion of an example surgical instrument 202 having an elongated shaft 204 shown in partial cutaway and a force sensor 205. 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, which may include an articulatable jaw, for example. During a surgical procedure, the end effector 208 contacts anatomical tissue, which may result in an X, Y, or Z-directed force being applied to the force sensor 206 and may result in a moment, such as a moment M about a Y-directed axis, for example. Y A force sensor 205 including a longitudinal axis 210 may be used to measure X and Y forces perpendicular to the longitudinal axis 210 .

[0080] Figure 3A is an illustrative perspective view of an example force sensor 302 that includes a rectangular beam 304 having an extended Wheatstone bridge circuit on each of its two adjacent sides. A first full Wheatstone bridge 352 (indicated by dashed lines) includes a first (R P1 ), the second (R D1 )、Third (R P2 ) and the fourth (R D2 ) resistor. The second full Wheatstone bridge 354 (indicated by the dashed line) includes a fifth (R P3 ), the sixth (R D3 ), Seventh (R P4 ) and the eighth (R D4) resistors. In the example first full Wheatstone bridge 352, the first and second resistors are coupled in the first half bridge, and 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, and the seventh and eighth resistors are coupled in the fourth half bridge. An (X, Y, Z) beam coordinate system 305 is shown to explain the force direction relative to the beam 304. The example beam 304 can have a rectangular cross-section with flat / planar sides. More specifically, the example beam can have a square cross-section. The beam 304 includes a proximal beam portion 304P and a distal beam portion 304D and includes a longitudinal center axis 306 extending between the proximal beam portion and the distal beam portion. The force sensor 302 includes an example resistor R having a matching resistor value P1 -R P4 and R D1 -R D4 .

[0081] The resistors can be placed on the beam 304 manually or using an automated machine, and can be adhered to the beam using an adhesive such as epoxy. Alternatively, the resistors can be deposited and laser etched directly onto the beam 304. In both cases, the circuit can be completed externally using wire bonding and flexible printed circuits.

[0082] First proximal strain gauge resistor ("resistor") R P1 and the second proximal resistor R P2 The first distal resistor R is located at the proximal beam portion 304P of the first side 308 of the beam 304. D1 and the second remote resistor R D2 The first set of resistors R located on the first side 308 of the beam 304 is located at the distal beam portion. As described below, the first set of resistors R located on the first side 308 of the beam P1 -R P2 and R D1 -R D2 is arranged in a first extended full Wheatstone bridge. The third proximal resistor R P3 and the fourth proximal resistor R P4 The third distal resistor R is located at the proximal beam portion 304P of the second side 310 of the beam 304. D3 and the fourth remote resistor R D4 The first side 308 of the example beam 304 is adjacent to the second side 310 of the example beam 304. As described below, the second set of resistors R P3 -R P4 and R D3 -R D4 Arranged in a second extended full Wheatstone bridge.

[0083] As explained more fully below, the first and second full bridge circuits are "spread out" in that portions of each full bridge circuit are laterally spaced apart from one another on the beam 304. For example, each full bridge may include two half bridges that are laterally spread apart from one another. One advantage of laterally spread apart half bridges is that, for example, conductor traces that couple resistors to a bias voltage or couple resistors to one another can be routed through the middle of a face of the beam 304 or proximate the neutral axis of the beam 304 on each face of the beam. Alternatively, in a circular cross-section beam (not shown), the conductor traces can advantageously be routed along the neutral axis of each half bridge. Such routing helps to reduce strain on the traces, thereby improving the accuracy of the sensor by rejecting unwanted signals. As explained more fully below, the first and second proximal resistors R located on the first side 308 of the beam 304 are located proximal to the first side 308 of the beam 304. P1 , R P2 and first and second remote resistors R D1 , R D2 The third and fourth proximal resistors R located on the second side 310 of the beam are used as Y-direction force sensor elements. P3 , R P4 and the third and fourth remote resistors R D3 , R D4 Used as an X-direction force sensor element.

[0084] Resistor R P1 -R P4 and R D1 -R D4 Each of the resistors R is a strain gauge resistor of the same type. More specifically, in the example force sensor 302 described herein, the resistors R P1 -R P4 and R D1 -R D4 is a tension type gauge resistor for measuring tensile strain. In an alternative example force sensor, the group of resistors can be a compression type gauge resistor for measuring compressive strain. As used herein, reference to a group of resistors having a "matching type" refers to a group of resistors in which all resistors are tension resistors or all resistors are compression resistors. Resistors with matching types are more likely to have similar sensitivity and performance, making the sensor more suitable for low signal-to-noise ratio situations where common mode cancellation is critical, and the effect is better. In general, although tension or compression gauge resistors can be used to determine X-direction and Y-direction forces that are orthogonal to each other, tension strain gauge resistors are generally more sensitive than compression gauge resistors.

[0085] Figure 3B Shows Figure 3AFIG. 3 is an illustrative perspective view of a force sensor 302 further illustrating an imaginary first plane P1 and an imaginary second plane P2. P1 and the first remote resistor R D1 On a first side of the beam 304 disposed within a first imaginary plane P1, the central axis 306 extends in the first imaginary plane P1, and the plane P1 defines a first lateral side axis 312 on the first side 308 of the beam 304 at a location along which the first plane P1 intersects the first side. The first lateral axis 312 and the central axis 306 extend parallel to each other. The example first lateral side axis 312 extends through the first proximal resistor R P1 and through the first remote resistor R D1 Additionally, the example first lateral side axis 312 bisects the example first proximal resistor R P1 and bisects the example first remote resistor R D1 .

[0086] Still reference Figure 3B , the second proximal resistor R P2 and the second remote resistor R D2 The example second lateral side axis 314 extends through the second proximal resistor R P2 and through the second far resistor R D2 Additionally, the example second lateral side axis 314 bisects the example second proximal resistor R P2 and bisects the example second remote resistor R D2 .

[0087] Figure 3C Shows Figure 3A FIG. 3 is an illustrative perspective view of a force sensor 302, further illustrating an imaginary third plane P3 and an imaginary fourth plane P4. P3 and the third remote resistor R D3 The example third lateral side axis 316 extends through the third proximal resistor R P3 and through the third remote resistor R D3In addition, the example third side axis bisects the example third proximal resistor R P3 and bisects the example third remote resistor R D3 .

[0088] Still reference Figure 3C , the fourth proximal resistor R P4 and the fourth remote resistor R D4 The example fourth lateral side axis 318 extends through the fourth proximal resistor R P4 and through the fourth far resistor R D4 More specifically, the example fourth lateral axis bisects the example fourth proximal resistor R P4 and bisects the example first remote resistor R D4 .

[0089] Figure 4 yes Figure 3A-3B FIG. 3 is an illustrative proximal cross-sectional view of an example beam 304 showing the intersection of imaginary planes at the longitudinal center axis 306 . Figure 5A The resistor R is shown P1 -R P2 , R D1 -R D2 A side view of an arrangement on a first side 308 of a beam 304 . Figure 5B The resistor R is shown P3 -R P4 , R D3 -R D4 A side view of the arrangement on the second side 310 of the beam 304 .

[0090] refer to Figure 4 , the proximal end view of the beam 304 shows a side view of imaginary first to fourth planes P1-P4 intersecting along the longitudinal center axis 306. An (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 spaced apart from each other by a first separation angle A1 about the central axis. The second and third imaginary planes are spaced apart from each other by a second separation angle B1. In the example force sensor 302, the first separation angle is equal to the second separation angle.

[0091] refer to Figure 5A , the first plane P1 is shown extending through the first proximal resistor RP1 and the first remote resistor R D1 , which are arranged along a first lateral side axis 312 on the first side 308 of the beam 304, and a second plane P2 is shown extending through the second proximal resistor R P2 and the second remote resistor R D2 , which are arranged along a second lateral axis 314 on the first side 308 of the beam 304. An (X, Y, Z) beam coordinate system 305 is shown to explain the direction of the forces relative to the beam 304. Note that Figure 5A , the X-axis is shown pointing toward the page. The magnitude of the first separation angle A1 corresponds to the lateral separation distance between the first side axis 312 and the second side axis 314 at the first side 308, and therefore, corresponds to the first proximal and distal resistors R P1 , R D1 The first resistor pair and the second resistor pair comprising proximal and distal resistors R P2 , R D2 In the example force sensor 302, the first lateral side axis 312 and the second lateral side axis 314 are equidistant from a neutral axis 315 of the first side 308 of the beam 304, the neutral axis 315 extending within the first side and equidistant from opposite lateral edges of the first side 308, although equidistant spacing is not required.

[0092] refer to Figure 5B , the third plane P3 is shown extending through the third proximal resistor R arranged along the third lateral side axis 316 on the second side 310 of the beam 304 P3 and the third remote resistor R D3 , and a fourth plane P4 is shown 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 the fourth remote resistor R D4 A (X, Y, Z) beam coordinate system 305 is shown to explain the direction of the forces relative to beam 304. Note that Figure 5B , the Y axis is shown as emerging from the page. The magnitude of the second separation angle B1 corresponds to the lateral separation distance between the third lateral side axis 316 and the fourth lateral side axis 318 at the second side 310, and therefore corresponds to the third proximal and distal resistors R P3 , R D3 The third resistor pair and the fourth proximal and distal resistors R arranged P4 , R D4In the example force sensor 302, the third lateral side axis 316 and the fourth lateral side axis 318 are equidistant from a neutral axis 319 of the second side 310 of the beam 304, which extends within the second side and is equidistant from opposite lateral edges of the second side 310.

[0093] Therefore, the first pair of resistors R P1 , R D1 and the second pair of resistors R P2 , R D2 The lateral extensions are separately located on the first side 308 of the beam 304. In the example beam 304, the first pair of resistors are 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 equidistantly laterally spaced from the neutral axis 315 of the first side of the beam 304 and are on opposite sides of the neutral axis 315. More specifically, the first pair of resistors are 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 The lateral extensions are separately located on the second side 310 of the beam 304. In the example 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 equidistantly laterally spaced from a 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.

[0094] In the example force sensor, the proximal and distal resistors are laterally aligned as part of the same full bridge. Additionally, in the example force sensor, the spacing between the first and second lateral axes matches the spacing between the third and fourth lateral axes. In the example force sensor, the proximal resistor R P1 -R P4 is positioned at a matching longitudinal position of the beam. In the example force sensor, the distal resistor R D1 -R D4 Positioned at matching longitudinal position of beam.

[0095] As explained below, the resistors of the first bridge 352 are laterally spaced apart to measure forces in a first direction perpendicular to the beam center axis 306 based on off-axis forces applied along the first plane P1 and the second plane P2. Similarly, the resistors of the second bridge 354 are laterally spaced apart to measure forces in a second direction perpendicular to the beam center axis 306 and perpendicular to the first direction based on measuring off-axis forces applied along the second and third planes P3, P4. Fig. 8A As 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 center axis 306 in the region of the beam 304 between the proximal resistor and the distal resistor 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 center axis 306 in the region of the beam 304 between the proximal resistor and the distal resistor of the second bridge 354.

[0096] Fig. 6A is an illustrative side view of an example beam 304 showing a first example layout topology of an example full Wheatstone bridge 602. The first example full Wheatstone bridge layout includes resistors R P1 -R P2 and R D1 -R D2 In the example force sensor 304, a resistor R located on the first side 308 of the beam 304 P1 -R P2 and R D1 -R D2 The topology of the first full Wheatstone bridge arrangement can be coupled in accordance with that of the first full Wheatstone bridge arrangement. Similarly, the resistor R P3 -R P4 and R D3 -R D4 The first full Wheatstone bridge arrangement may be coupled in accordance with the topology of the first full Wheatstone bridge arrangement. The first Wheatstone bridge arrangement is coupled to the input bias voltage conductors (EP, EN) and the output voltage conductors (Vo-, Vo+) in a first configuration. Figure 6B is a first schematic circuit diagram 604 showing an illustrative full Wheatstone bridge topology. Figure 6A-6B , the first near side resistor R P1 The second proximal resistor R is electrically coupled between the positive first DC potential (EP) and the second (also referred to as the "negative" potential) output Vo-. P2 The first remote resistor R is electrically coupled between the negative second DC potential (EN) and the second output Vo-. D1 The second remote resistor R is electrically coupled between the positive first DC potential (EP) and the first output Vo+ (also referred to as the "positive" output). D2Electrically coupled between the negative second DC potential (EN) and the first output Vo+.

[0097] Fig. 7A is an illustrative side view of an example beam 304 showing a second circuit layout topology of an example full Wheatstone bridge 702. The second example full Wheatstone bridge layout includes resistors R P1 -R P2 and R D1 -R D2 In the example force sensor 304, a resistor R located on the first side 308 of the beam 304 P1 -R P2 and R D1 -R D2 Can be coupled in accordance with the topology of the second full Wheatstone bridge layout, similarly, the resistor R located on the second side 310 of the beam 304 P3 -R P4 and R D3 -R D4 The second full Wheatstone bridge arrangement may be coupled in accordance with the topology of the second full Wheatstone bridge arrangement. The second Wheatstone bridge arrangement is coupled to the input bias voltage conductors (EP, EN) and the output voltage conductors (Vo-, Vo+) in the second configuration. Figure 7B is an illustrative first schematic circuit diagram 704 representation of a second full Wheatstone bridge topology. Figure 7A-7B , the first near side resistor R P1 The second proximal resistor R is electrically coupled between the positive first DC potential (EP) and the first output Vo+. P2 The first remote resistor R is electrically coupled between the positive first DC potential (EP) and the second output Vo-. D1 The second remote resistor R is electrically coupled between the negative second DC potential (EN) and the first output Vo+. D2 Electrically coupled between the negative second DC potential (EN) and the second output Vo-.

[0098] Generally speaking, Fig. 6A The layout in is better suited to reducing the number of traces that must span the length of the beam and can also reduce the effects of strain pickup by the traces. On the other hand, if the force sensor uses half-bridge voltage measurement, then Fig. 7A The layout in is preferred.

[0099] Fig. 8A304, showing the expanded layout of first and second full Wheatstone bridges 352, 354 and the routing of center conductor traces 356, 358 extending within the center of the bridges, between the proximal resistors and the distal resistors of the bridges. The first bridge 352 is located at a first side 304-1 of the beam 304. The second bridge 354 is located at a second side 304-2 of the beam 304. The first side 304-1 and the second side 304-2 share a side edge 303 of the beam 304.

[0100] The first full Wheatstone bridge 352 includes R P1 , R P2 and the remote resistor R D1 , R D2 , and has a first neutral axis 362, which is near the resistor R P1 , R P2 and the remote resistor R D1 , R D2 In the example first bridge, the first neutral line is parallel to R P1 and R P2 Each of the D1 and R D2 Each of the two bridges is equally spaced. The first bridge 352 is longitudinally separated, wherein the proximal resistor R P1 , R P2 With the remote resistor R D1 , R D2 The first bridge is extended horizontally, with the near side resistor R P1 , R P2 Laterally spread apart and the far resistor R D1 , R D2 The second full Wheatstone bridge 354 has a first neutral axis 364 that runs parallel to the proximal resistor R along the outer surface of the beam 304. P3 , R P4 Between and far side resistor R D3 , R D4 In the example second bridge, the second neutral line is connected to R P3 and R P4 Each of the D3 and R D4 The second bridge 354 is longitudinally separated, wherein the near side resistor R P3 , R P4 With the remote resistor R D3 , R D4 The second bridge is extended horizontally, with the near side resistor R P3 , R P4Laterally spread apart and the far resistor R D3 , R D4 Scale out separately from each other.

[0101] It should be appreciated that because the resistors of the first full Wheatstone bridge 352 are laterally spread apart, they do not occupy the first neutral axis 362. Likewise, because the resistors of the second full Wheatstone bridge 354 are laterally spread apart, they do not occupy the second neutral axis 364. Therefore, the conductor traces can be routed close to and parallel to the first and second neutral axes 362, 364, which can reduce the amount of strain applied to the traces. In addition, routing the traces along the neutral axis of the bridge circuit can be easier to produce, manufacture, or assemble.

[0102] The example first full bridge includes a first set of center conductor traces 356 along a central portion of the first bridge 352, parallel to a first neutral axis 362, along an outer surface 304-1 of the beam 304, and between a pair of proximal resistors R P1 , R P2 and a pair of remote resistors R D1 , R D2 The first set of center traces 356 includes a trace segment 356-1 coupled to a first positive output voltage VO1+. The first set of center traces 356 includes a trace segment 356-1 coupled to a first negative voltage output VO1-. The first set of center traces 356 includes a trace segment 356-3 coupled to a negative voltage potential EN.

[0103] Similarly, the example second full bridge includes a second set of center conductor traces 358 along a central portion of the second bridge 354, parallel to the second neutral axis 364, along the outer surface 304-2 of the beam 304, and between a pair of proximal resistors R P3 , R P4 and a pair of remote resistors R D3 , R D4 The second set of center traces 358 includes a trace segment 358-1 coupled to a second positive output voltage VO2+. The second set of center traces 358 includes a trace segment 358-2 coupled to a second negative voltage output VO2-. The second set of center traces 358 includes a trace segment 358-3 coupled to a negative voltage potential EN.

[0104] Figure 8B yes Fig. 8A 1 is a schematic circuit diagram of an illustrative first and second full-Wheatstone bridge. The first full-Wheatstone bridge 352 includes R coupled between EP and EN P1 and R D1To provide a first half-bridge voltage divider circuit, the first half-bridge voltage divider circuit includes a trace conductor coupled to the first positive output voltage VO1+. The first full-Wheatstone bridge 352 also includes R coupled between EP and EN P2 and R D2 To provide a second half-bridge voltage divider circuit, the second half-bridge voltage divider circuit includes a trace conductor coupled to the first negative output voltage VO1-. The second full-Wheatstone bridge 354 includes R coupled between EP and EN P3 and R D3 To provide a third half-bridge voltage divider circuit, the third half-bridge voltage divider circuit includes a trace conductor coupled to the second negative output voltage VO2-. The second full-Wheatstone bridge 354 also includes R coupled between EP and EN P4 and R D4 A fourth half-bridge voltage divider circuit is provided, the fourth half-bridge voltage divider circuit comprising a trace conductor coupled to the second positive output voltage VO2+.

[0105] Fig.9A yes Figure 4 An illustrative cross-sectional end view of an example beam 304 indicating a resistor on a first side and indicating a first in-plane force FP1 and a second in-plane force FP2. Fig. 9B is an indication of the force F applied to the first proximal resistor R in response to the applied force P1 and the first remote resistor R D1 illustrative force diagram of the orthogonal X-force component and Y-force component of the first planar force FP1. Fig. 9C is an indication of the force F applied to the second proximal resistor R in response to the applied force F. P2 and the second remote resistor R D2 illustrative force diagram of the X-force component and the Y-force component of the second planar force FP2.

[0106] In the example force sensor 302, the first pair of resistors R P1 , R D1 The resistance value of the second pair of resistors R P2 , R D2The resistor values ​​of the first and second pairs of resistors are matched. In the example force sensor 302, the first and second pairs of resistors are positioned on the example beam 304 such that an applied force F applied to the example beam 304 applies a first plane strain force FP1 to the first pair of resistors in the first plane P1 and applies a second plane strain force FP2 to the second pair of resistors in the second plane P2. It should be understood that the first plane strain force FP1 is an off-axis force because it is a force applied along the first lateral side axis 312, which 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, which is laterally offset from the neutral axis 315 of the first bridge 352. The first and second pairs of resistors are positioned on the example 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".

[0107] 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 magnitude of the off-axis force applied to the different halves of the full bridge located on the beam. In the example force sensor 302, the Y-direction force component F applied to the beam 304 by the applied force F Y The magnitude of may be determined based on the difference between the first off-axis force FP1 and the second off-axis force FP2 as follows.

[0108] Let A be the angle between P1 and P2.

[0109] Assume that the X axis bisects the angle A. Therefore, the angle between P1 and X is A / 2, and the angle between P2 and X is A / 2.

[0110] Let θ be the angle between the X-axis and the applied force F.

[0111] Force F along the X axis x =Fcosθ

[0112] The force F along the y axis y =Fsinθ

[0113] refer to Fig. 9B , force along P1 = F x cosA / 2+F y cos(90+A / 2)=FP1

[0114] refer to Fig. 9C , force along P2 = F x cosA / 2+F y cos(90-A / 2)=FP2

[0115] FP1=F x cosA / 2+F y cos(90+A / 2)

[0116] FP2=F x cosA / 2+F y cos(90-A / 2)

[0117] Use cos(θ)=-cos(180-θ)

[0118] We get

[0119] FP2=F x cosA / 2-F y cos(90+A / 2)

[0120] When we subtract FP1 and FP2

[0121] We get FP1-FP2=F x cosA / 2+F y cos(90+A / 2)

[0122] -F x cosA / 2+F y cos(90+A / 2)

[0123] Therefore, FP1-FP2=2F y cos(90+A / 2)

[0124] Therefore, FP1-FP2∝F y

[0125] Therefore, the difference between FP1 and FP2 is equal to the Y-direction force component F exerted on the beam by the applied force F. Y Directly proportional.

[0126] Furthermore, it should be understood that

[0127] F Y αV S1O+ –V S1O- ,

[0128] 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 a voltage offset generated by the first bridge circuit 352 located on the first side 308 of the beam 304 .

[0129] Fig.10 yes Figure 4304, indicating the resistors on the second side 310 of the beam 304 and indicating the third plane X-force and the fourth plane X-force. In the example force sensor 302, the third pair of resistors R P3 , R D3 The resistance value of the fourth pair of resistors R P4 , R D4 The third and fourth pairs of resistors are positioned on the example beam 304 such that an applied force applied to the example 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 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 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 example 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.

[0130] In this example, the difference between FP3 and FP4 is proportional to the X-direction force component F applied to the beam by the applied force F. X Those skilled in the art will appreciate 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.

[0131] Furthermore, it should be understood that

[0132] F X =FP3–FP4

[0133] F X αV S2O+ –V S2O- ,

[0134] Where V S2O+ is the positive output voltage, V S2O- is the negative output voltage of the second bridge 354, V S2O+ -V S2O- is the voltage offset produced by the second bridge circuit 354 on the second side 310 of the beam 304 .

[0135] Fig.11 is a schematic diagram showing a metal sheet 1102 including a defined example resistor R P1 -RP4 and R D1 -R D4 The first region 1104 of the metal sheet 1102 includes a resistor R for coupling in a first full-bridge configuration located on the first side 308 of the beam 304. P1 -R P2 and R D1 -R D2 The second region 1106 of the metal sheet 1102 includes a resistor R for coupling in a second full-bridge configuration located on the second (Y-axis) side of the example beam. P3 -R P4 and R D3 -R D4 The first and second regions are separated by a fold line 1108 .

[0136] Fig. 12A is a diagram showing folding the metal sheet 1102 at fold line 1108 to wrap the first and second regions of the metal sheet around the beam 304 to connect the first pair of resistors R P1 -R P2 and R D1 -R D2 is positioned at the first side 308 of the beam 304 and the second pair of resistors R P3 -R P4 and R D3 -R D4 Positioned at the second side 310 of the beam 304 . Fig. 12B 304, which shows the first and second regions 1104-1106 of the metal sheet 1102 laid on the corresponding first and second sides 308-310 of the example beam 304. In the example rectangular beam, the first side and the second side include adjacent sides of the beam. The metal sheet 1102 can be glued or welded to the beam 304 or a combination of both. During the attachment process, care is taken to align the metal sheet 1102 with the beam 304.

[0137] Redundant Multiple Half-Bridge XY Force Sensor

[0138] In a sensor with four half-bridges and all gauges of the same type on the first and opposite sides, subtracting the half-bridge voltages of two adjacent half-bridges provides a force measurement on an axis parallel to the plane of all gauges with two half-bridges. There are four methods to provide F x and F y Two measurement values.

[0139] Figures 13A-13B An illustrative first side perspective view of an example force sensor 2302 is shown. Fig.13A ) and the second side perspective view ( Fig. 13B ), the force sensor comprises a rectangular beam 2304, wherein two four-strain gauge resistors R P1 -R P4 , R D1 -R D4 The coupling is in two half-Wheatstone bridge circuits ("half-bridges") located on each of two opposite sides of a rectangular beam. Fig. 13B The second side 308 of the beam 2304 shown in FIG. Fig.13A 2304. The beam 2304 is shown in the figure with the first side 308 of the beam 2304 facing the opposite direction. An (X, Y, Z) beam coordinate system 2305 is provided to explain the force direction relative to the beam 2304. The example beam 2304 can have a rectangular cross-section with flat sides. More specifically, the example beam can have a square cross-section. The beam 2304 includes a proximal beam portion 2304P and a distal beam portion 2304D and includes a longitudinal center axis 306 extending between the proximal beam portion 2304P and the distal beam portion 2304D.

[0140] refer to Fig.13A , the first proximal strain gauge resistor (“resistor”) R P1 and the second proximal resistor R P2 Located at the proximal beam portion 2304P of the first side 308 of the beam 2304. The first distal resistor R D1 and the second remote resistor R D2 Located at the distal beam portion 2304D of the first side 308 of the beam 2304. Figures 14A-14B , 15A-15B, the first pair of resistors R P1 -R D1 The second pair of resistors R are electrically coupled in series and arranged in the first half bridge. P2 -R D2 are electrically coupled in series and arranged in the second half-bridge.

[0141] refer to Fig. 13B , the third proximal resistor R P3 and the fourth proximal resistor R P4 The third distal resistor R is located at the proximal beam portion 2304P of the second side 2310 (also referred to as the "opposite" side) of the beam 2304 facing in the opposite direction to the direction faced by the first side 308 of the beam 2304. D3 and the fourth remote resistor R D4 At the distal beam portion 2304D located on the opposite second side 2310 of the beam 2304. Figures 14A-14B , 15A-15B, the third pair of resistors R P3 -R D3 The fourth pair of resistors R are electrically coupled in series and arranged in the third half bridge.P4 -R D4 The first and second half bridges are electrically coupled in series and arranged in a fourth half bridge.

[0142] Fig.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 . Fig. 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.

[0143] Fig.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 . Fig. 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.

[0144] like Figures 14A-14B and Figures 15A-15B As shown, each half-bridge of the example force sensor 2302 includes a pair of strain gauge resistors having a matching type, which can be a tension type ( Figures 14A-14B ) or compressed type ( Figures 15A-15B As used herein, reference to a set of resistors having a "matched type" refers to a set of resistors where all resistors are tension resistors or all resistors are compression resistors. Although either tension or compression gauge resistors can be used to determine forces in the X and Y directions, in general, tension strain gauge resistors are more sensitive than compression gauge resistors.

[0145] Reference again Figures 13A-13B , as explained more fully below, in the first pair of resistors R P1 , R D1 The first half-bridge voltage at the first voltage node between the second pair of resistors R P2 , R D2 The voltage offset between the second half-bridge voltage at the second voltage node between can be used to measure the X-direction force applied to the beam 2304. In addition, in the third pair of resistors R P3 , R D3 The third half-bridge voltage at the third voltage node between the fourth pair of resistors R P4 , R D4 The voltage offset between the fourth half bridge voltage at the fourth voltage node between 2304 and 2305 can be used to measure the X-directed force applied to the beam 2304. Thus, the first, second, third, and fourth half bridges together provide a redundant measure of the X-directed force on the beam.

[0146] Furthermore, as explained more fully below, in the first pair of resistors R P1 , R D1 The first half-bridge voltage at the first voltage node between the fourth pair of resistors R P4 , R D4 The voltage offset between the fourth half-bridge voltage at the fourth voltage node between can be used to measure the Y-direction force applied to the beam 2304. In addition, in the second pair of resistors R P2 , R D2 The second half-bridge voltage at the second voltage node between the third pair of resistors R P3 , R D3 The offset between the third half-bridge voltage at the third voltage node between can be used to measure the Y-direction force applied to the beam 2304.

[0147] Thus, the first, second, third, and fourth half bridges together can provide a redundant measure of X-directed forces on beam 2304 and can provide a redundant measure of Y-directed forces on beam 2304. P1 -R P4 and R D1 -RD4 Failure of any one of the resistors R will result in a difference between the X-direction force measurements determined using the first and second half-bridges on the one hand and the X-direction force measurements determined using the third and fourth half-bridges on the other hand. P1 -R P4 and R D1 -R D4 Failure of any one of the two half-bridges results in a difference between the Y-direction force measurements determined using the first and fourth half-bridges on the one hand and the Y-direction force measurements determined using the second and third half-bridges on the other hand.

[0148] Still reference Fig.13A , the first near side resistor R P1 and the first remote resistor R D1 The first side 308 of the beam 2304 is arranged in a first imaginary plane P1, the central axis 306 extends in the plane P1, and the plane P1 defines a first lateral side axis 2312 on the first side 308 of the beam 2304 at a location along which the first plane P1 intersects the first side 308. The first lateral side axis 2312 and the central axis 306 extend parallel to each other. The example first lateral side axis 2312 extends through the first proximal resistor R P1 and through the first remote 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 remote resistor R D1 .

[0149] refer to Fig.13A , the second proximal resistor R P2 and the second remote resistor R D2 The example second lateral side axis 2314 extends through the second proximal resistor R P2 and through the second far 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 remote resistor R D2 .

[0150] refer to Fig. 13B , the third proximal resistor R P3 and the third remote 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 .

[0151] refer to Fig. 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 .

[0152] Fig.16 yes Figures 13A-13B An illustrative proximal cross-sectional view of an example beam 2304 showing first and second imaginary planes P1 , P2 . Fig.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. Fig. 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.

[0153] The resistors can be placed on the beam 2304 manually or using automated machinery, and can be adhered to the beam using an adhesive such as epoxy. Alternatively, the resistors can be deposited and laser etched directly onto the beam 2304. In both cases, the circuit can be completed externally using wire bonding and flexible printed circuits.

[0154] refer to Fig.16 , the 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, the central axis 306 extending in 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 extending 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 extending through the respective third and fourth half bridges HB3, HB4 also intersect the central axis 306 at the first separation angle A1.

[0155] refer to Fig.17A , the first plane P1 is shown extending through the first half bridge HB1, which includes a first proximal resistor R arranged on the first side 308 of the beam 2304 along the first lateral side axis 2312 P1 and the first remote resistor R D1 , and the second plane P2 is shown 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 the second remote resistor R D2 The magnitude of the first separation angle A1 corresponds to the lateral separation distance between the first and second lateral side axes 2312, 2314 at the first side 308, and therefore corresponds to the first proximal and distal resistors R P1 , R D1 The first half bridge HB1 and the second proximal and distal resistors R P2 , R D2 In the example force sensor 2302, the first lateral side axis 2312 and the second lateral side axis 2314 are equidistant from a 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.

[0156] refer to Fig. 17B , the first plane P1 is shown extending through the third half-bridge HB3, which includes a third proximal resistor R P3 and the third remote resistor R D3 , which are arranged on the second side 2310 of the beam 2304 along the third lateral side axis 2316, and the second plane P2 is shown extending through the fourth half bridge HB4, which includes a fourth proximal resistor R P4 and the fourth remote resistor R D4 , which are arranged on the second side 2310 of the beam 2304 along the fourth lateral side axis 2318. The magnitude of the first separation angle A1 corresponds to the lateral separation distance between the third and fourth lateral side axes 2316-2318 at the second side 2310 of the beam 2304, and therefore, corresponds to the third half-bridge HB3 including the third resistor pair including RP3, RD3 and the third half-bridge HB4 including the third resistor pair including R P4 , R D4 In the example force sensor, the third lateral axis 2316 and the fourth lateral axis 2318 are equidistant from a 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.

[0157] Half bridges HB1-HB4 are positioned laterally symmetrically about 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. In addition, in the example force sensor 2302, the spacing between the first lateral axis 2312 and the second lateral axis 2314 matches the spacing between the third lateral axis 2316 and the fourth lateral axis 2318, although equidistant spacing is not required. Half bridges HB1-HB4 are positioned longitudinally symmetrically along beam 2304. The proximal resistor R P1 -R P4 is positioned at a matching longitudinal position of the beam. In the example force sensor, the distal resistor R D1 -R D4 Positioned at matching longitudinal position of beam.

[0158] Fig.18A yes Figures 13A-13B An illustrative proximal cross-sectional view of an example beam 2304 of FIG. 2304 indicating 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 the force F applied to the beam 2304. Fig.18A In the example beam of , the second and third half-bridge HB2, HB3 only contain stretch resistors. Fig.18Bis an illustrative force diagram indicating an X-force component and a Y-force component of a second plane strain force FP2 applied to a second half-bridge HB2 in response to an applied force F, the half-bridge HB2 including a second proximal resistor R P2 and the second remote resistor R D2 . Fig. 18C is an illustrative force diagram indicating orthogonal X-force components and Y-force components of a third plane strain force FP3 applied to a third half-bridge HB3 in response to an applied force, the half-bridge HB3 including a third proximal resistor R P3 and the third remote resistor R D3 .

[0159] In the example force sensor 2302, the second pair of resistors R of the second half bridge HB2 P2 , R D2 The resistance value is the same as the third pair of resistors R of the third half bridge HB3 P3 , R D3 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 a second plane strain force FP2 to the second half bridge HB2 in the second plane P2 and applies a third plane strain force FP3 to the third half bridge HB3 in the third plane P3. 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 2314. Similarly, 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. In the example force sensor 2302, the second and third half bridges HB2, HB3 are positioned on the example beam 2304 such that the magnitude of the components of the second plane strain force FP2 matches the magnitude of the components of the third plane strain force FP3.

[0160] 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 magnitude of the off-axis force applied to the different halves of the full bridge located on the beam. In the example force sensor 2302, the Y-direction force component F applied to the beam 2304 by the applied force F Y The magnitude of may be determined based on the difference between the first off-axis force FP2 and the second off-axis force FP3 as follows.

[0161] Let A be the angle between P2 and P3.

[0162] Let the X axis bisect angle A. Therefore, the angle between P2 and X is A / 2, and the angle between P3 and X is A / 2.

[0163] Let θ be the angle between the X-axis and the applied force F.

[0164] Force F along the X axisx =Fcosθ

[0165] The force F along the y axis y =Fsinθ

[0166] refer to Fig.18B , force along P2 = F x cosA / 2+F y cos(90+A / 2)=FP2

[0167] refer to Fig. 18C , force along P3 = F x cosA / 2+F y cos(90-A / 2)=FP3

[0168] FP2=F x cosA / 2+F y cos(90+A / 2)

[0169] FP3=F x cosA / 2+F y cos(90-A / 2)

[0170] Use cos(θ)=-cos(180-θ)

[0171] We get

[0172] FP3=F x cosA / 2-F y cos(90+A / 2)

[0173] When we subtract FP1 and FP2

[0174] We get FP2–FP3=F x cosA / 2+F y cos(90+A / 2)

[0175] -F x cosA / 2+F y cos(90+A / 2)

[0176] Therefore, FP2–FP2=2F y cos(90+A / 2)

[0177] Therefore, FP2–FP3∝F y

[0178] Therefore, the difference between FP2 and FP3 is equal to the Y-direction force component F exerted on the beam by the applied force F. Y Directly proportional.

[0179] Furthermore, it should be understood that

[0180] F Y =FP2-FP2

[0181] F Y αV O2 –V O3

[0182] Where V O2 is the output voltage of HB2, V O3 is the output voltage of HB3.

[0183] Fig.19 yes Figures 13A-13B An illustrative proximal cross-sectional view of an example beam of 2304 indicating the first plane strain force FP1 and the fourth plane strain force FP4 applied to the respective first and fourth half-bridges HB1, HB4 by the force F applied to the beam 2304. Fig.19 In the example beam, the first and fourth half bridges HB1, HB4 only include stretch resistance resistors. In the example force sensor 2302, the first pair of resistors R of the first half bridge HB1 P1 , R D1 The resistance value is the same as the fourth pair of resistors R of the fourth half bridge HB4 P4 , R D4 In the example force sensor 2302, the first and fourth half bridges HB1, HB4 are positioned on the example beam 2304 so that the applied force F applied to the example beam 2304 applies the first plane strain force FP1 to the first half bridge HB1 in the first plane P1 and applies the fourth plane strain force FP4 to the fourth half bridge HB4 in the second plane P4. In the example force sensor 2302, the first and fourth half bridges HB1, HB4 are positioned on the example beam 2304 so that the magnitude of the component of the first plane strain force FP1 matches the magnitude of the component of the fourth plane strain force FP4.

[0184] In this example, the difference between FP1 and FP4 is proportional to the Y-direction force component F applied to the beam by the applied force F. Y Those skilled in the art will appreciate that the process for determining the difference between FP1 and FP4 is based on the above description of determining the difference between FP2 and FP3.

[0185] Furthermore, it should be understood that

[0186] F Y =FP1–FP4

[0187] F Y αV O1 –V O4

[0188] Where V O1is the output voltage of HB1, V O4 is the output voltage of HB4.

[0189] Fig. 20 yes Figures 13A-13B 2304, indicating 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 on the beam 2304. In the example force sensor 2302, the first pair of resistors R of the first half-bridge HB1 P1 , R D1 The resistance value of the second pair of resistors R of the second half bridge HB2 P2 , R D2 The resistance values ​​of the first and second half bridges HB1 and HB2 are matched. In the example force sensor 2302, the first and second half bridges HB1 and HB2 are positioned on the example beam 2304 so that the applied force applied to the example beam 2304 applies a first plane strain force FP1 to the first half bridge HB1 in the first plane P1 and applies a second plane strain force FP2 to the second half bridge HB2 in the second plane P2. It should be understood that the first plane 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 plane 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 and HB2 are positioned on the example beam 2304 so that the first plane strain force FP1 X The magnitude of the first plane strain force FP1 matches the magnitude of the second plane strain force FP2. X The force direction and the first plane P1 are separated from each other by a first separation angle A1.

[0190] In this example, the difference between FP1 and FP2 is proportional to the X-directed force component FX applied to the beam by the applied force F. Those skilled in the art will appreciate that the process for determining the difference between FP1 and FP2 is based on the above description of determining the difference between FP2 and FP3.

[0191] Furthermore, it should be understood that

[0192] F X =FP1-FP2

[0193] F X αV O1 –V O2

[0194] Where V O1 is the output voltage of HB1, and V O2 is the output voltage of HB2. Fig.21 yes Figures 13A-13BAn illustrative proximal cross-sectional view of an example beam 2304 is shown, indicating the force F exerted on the beam. X The third plane strain force FP3 and the fourth plane strain force FP4 applied to the respective third and fourth half bridges HB3 and HB4. In the example force sensor 2302, the third pair of resistors R of the third half bridge HB3 P3 , R D3 The resistance value is the same as the fourth pair of resistors R of the fourth half bridge HB4 P4 , R D4 The resistance values ​​of the third and fourth half bridges HB3 and HB4 are matched. In the example force sensor 2302, the third and fourth half bridges HB3 and HB4 are positioned on the example beam 2304 so that the applied force applied to the example beam 2304 applies the third plane strain force FP3 to the third half bridge HB3 in the third plane P3, and applies the fourth plane strain force FP4 to the fourth half bridge HB4 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 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 example force sensor 2302, the third and fourth half bridges HB3 and HB4 are positioned on the example beam 2304 so that Fig.21 The size is Figures 13A-13B The example of beam 2304 indicates the force F exerted on the beam. X Illustrative proximal cross-sectional view of third and fourth plane strain forces FP3, FP4 applied to respective third and fourth half-bridges HB3, HB4.

[0195] In this example, the difference between FP3 and FP4 is proportional to the X-direction force component F applied to the beam by the applied force F. X Those skilled in the art will appreciate 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.

[0196] Furthermore, it should be understood that

[0197] F X =FP3–FP4

[0198] F X αV O3 –V O4

[0199] Where V O3 is the output voltage of HB3, and V O4 is the output voltage of HB4.

[0200] Therefore, assuming that all resistors R P1 -R P4 and RD1 -R D4 Normal work,

[0201] F X αV O1 –V O2 =V O3 –V O4 and F Y αV O1 –V O4 =V O2 –V O3

[0202] Furthermore, it should be understood that F X and F Y It can be determined more generally based on each of the following four combinations of three half-bridges (HB) listed in Table 1 below.

[0203] Table 1

[0204] HB combination number <![CDATA[Suitable for determining F X and F Y HB combination]]> 1 HB1, HB2, HB3 2 HB1, HB2, HB4 3 HB3, HB4, HB2 4 HB4, HB3, HB1

[0205] Therefore, the half-bridge combination in Table 1 above can be used to X and F Y Redundancy determination is performed. Based on the above half-bridge combination, F X and F Y Comparison of the values ​​can be used to determine if the force sensor 2304 contains a faulty resistor. If even a single resistor fails, then all four combinations will produce different values ​​of Fx and Fy, indicating a fault. Since all four HBs will 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 comparisons of five or more combinations of three bridges can be used to determine which half-bridge is defective, so the measurement value from the defective half-bridge can be ignored.

[0206] Redundant Single-Sided XY Force Sensor

[0207] An example single-sided XY force sensor includes a beam including four half-bridges located on a single side thereof. Two of the half-bridges are one of a compression type, and two of the half-bridges are tension type. Since compression and tension strain gauge resistor measurements experience strains in opposite directions in response to a force applied to the beam, measurements by a combination of three half-bridges located on the same side of the beam, where one of the three half-bridges has a different strain gauge resistor type than the other two, can be used to measure X-direction forces and Y-direction forces. An 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 compression type and two of which are tension type.

[0208] In a sensor with four half bridges and all gauges of the same type on a first side and an opposite side, subtracting the half bridge voltages of two adjacent half bridges provides a force measurement on an axis parallel to the plane of all gauges with two half bridges. There are four methods that can provide two measurements of Fx and Fy.

[0209] Figures 13A-13B An illustrative first side perspective view of an example force sensor 2302 is shown. Fig.13A ) and the second side perspective view ( Fig. 13B ), the force sensor comprises a rectangular beam 2304, wherein two four-strain gauge resistors R P1 -R P4 , R D1 -R D4 The coupling is in two half-Wheatstone bridge circuits ("half-bridges") located on each of two opposite sides of the beam. Fig. 13B The second side 308 of the beam 2304 shown in FIG. Fig.13A 2304. The beam 2304 is shown in the figure with the first side 308 of the beam 2304 facing the opposite direction. An (X, Y, Z) beam coordinate system 2305 is provided to explain the force direction relative to the beam 2304. The example beam 2304 can have a rectangular cross-section with flat sides. More specifically, the example beam can have a square cross-section. The beam 2304 includes a proximal beam portion 2304P and a distal beam portion 2304D and includes a longitudinal center axis 306 extending between the proximal beam portion 2304P and the distal beam portion 2304D.

[0210] refer to Fig.13A , the first proximal strain gauge resistor (“resistor”) R P1 and the second proximal resistor R P2 Located at the proximal beam portion 2304P of the first side 308 of the beam 2304. The first distal resistor R D1 and the second remote resistor R D2 Located at the distal beam portion 2304D of the first side 308 of the beam 2304. Figures 14A-14B , 15A-15B, the first pair of resistors R P1 -R D1 The second pair of resistors R P2 -R D2 are electrically coupled in series and arranged in the second half-bridge.

[0211] refer to Fig. 13B , the third proximal resistor R P3 and the fourth proximal resistor R P4The third distal resistor R is located at the proximal beam portion 2304P of the second side 2310 (also referred to as the "opposite" side) of the beam 2304 facing in the opposite direction to the direction faced by the first side 308 of the beam 2304. D3 and the fourth remote resistor R D4 At the distal beam portion 2304D located on the opposite second side 2310 of the beam 2304. Figures 14A-14B , 15A-15B, the third pair of resistors R P3 -R D3 The fourth pair of resistors R are electrically coupled in series and arranged in the third half bridge. P4 -R D4 The first and second half bridges are electrically coupled in series and arranged in a fourth half bridge.

[0212] Fig.14A 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 RT electrically coupled in series P , RT D and having a voltage node coupled therebetween. The first example half-bridge circuit layout 2402 includes input bias voltage conductors (EP, EN) and stretched resistors RT at the proximal and distal sides. P , RT D Output voltage node (V o ). Fig. 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 electrically coupled between the positive first DC potential (EP) and the output voltage node V o Distal stretch resistor RT D electrically coupled between the 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 Figures 14A-14B Layout 2402 and circuit schematic 2404 are shown in FIG.

[0213] Fig.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 ,RCD The output voltage node (Vo) is between . Fig. 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.

[0214] like Figures 14A-14B and Figures 15A-15B As shown, each half-bridge of the example force sensor 2302 includes a pair of strain gauge resistors having a matching type, which can be a tension type ( Figures 14A-14B ) or compressed type ( Figures 15A-15B As used herein, reference to a set of resistors having a "matched type" refers to a set of resistors where all resistors are tension resistors or all resistors are compression resistors. Although either tension or compression gauge resistors can be used to determine forces in the X and Y directions, in general, tension strain gauge resistors are more sensitive than compression gauge resistors.

[0215] Reference again Figures 13A-13B , as explained more fully below, in the first pair of resistors R P1 , R D1 The first half-bridge voltage at the first voltage node between the second pair of resistors R P2 , R D2 The voltage offset between the second half-bridge voltage at the second voltage node between can be used to measure the X-direction force applied to the beam 2304. In addition, in the third pair of resistors R P3 , R D3 The third half-bridge voltage at the third voltage node between the fourth pair of resistors R P4 , R D4 The voltage offset between the fourth half bridge voltage at the fourth voltage node between 2304 and 2305 can be used to measure the X-directed force applied to the beam 2304. Thus, the first, second, third, and fourth half bridges together provide a redundant measure of the X-directed force on the beam.

[0216] Furthermore, as explained more fully below, in the first pair of resistors R P1 , R D1 The first half-bridge voltage at the first voltage node between the fourth pair of resistors R P4 , R D4The voltage offset between the fourth half-bridge voltage at the fourth voltage node between can be used to measure the Y-direction force applied to the beam 2304. In addition, in the second pair of resistors R P2 , R D2 The second half-bridge voltage at the second voltage node between the third pair of resistors R P3 , R D3 The offset between the third half-bridge voltage at the third voltage node between can be used to measure the Y-direction force applied to the beam 2304.

[0217] Thus, the first, second, third, and fourth half bridges together can provide a redundant measure of X-directed forces on beam 2304 and can provide a redundant measure of Y-directed forces on beam 2304. P1 -R P4 and R D1 -R D4 Failure of any one of the resistors R will result in a difference between the X-direction force measurements determined using the first and second half-bridges on the one hand and the X-direction force measurements determined using the third and fourth half-bridges on the other hand. P1 -R P4 and R D1 -R D4 Failure of any one of the two half-bridges results in a difference between the Y-direction force measurements determined using the first and fourth half-bridges on the one hand and the Y-direction force measurements determined using the second and third half-bridges on the other hand.

[0218] Still reference Fig.13A , the first near side resistor R P1 and the first remote resistor R D1 The first side 308 of the beam 2304 is arranged in a first imaginary plane P1, the central axis 306 extends in the plane P1, and the plane P1 defines a first lateral side axis 2312 on the first side 308 of the beam 2304 at a location along which the first plane P1 intersects the first side 308. The first lateral side axis 2312 and the central axis 306 extend parallel to each other. The example first lateral side axis 2312 extends through the first proximal resistor R P1 and through the first remote 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 remote resistor R D1 .

[0219] refer to Fig.13A , the second proximal resistor R P2 and the second remote resistor R D2The example second lateral side axis 2314 extends through the second proximal resistor R P2 and through the second far 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 remote resistor R D2 .

[0220] refer to Fig. 13B , the third proximal resistor RP3 and the third distal resistor R D3 The 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 .

[0221] refer to Fig. 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 .

[0222] Fig.16 yes Figures 13A-13BAn illustrative proximal cross-sectional view of an example beam 2304 showing first and second imaginary planes P1 , P2 . Fig.17A is a side view of beam 2304, which shows Figures 13A-13B The first side 308 of the beam includes a first resistor (R P1 ) and the second resistor (R D1 ) and includes a third resistor (R P2 ) and the fourth resistor (R D2 ). Fig. 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 resistor (R P3 ) and the sixth resistor (R D3 ), and a seventh resistor (R P4 ) and the eighth resistor (R D4 ).

[0223] The resistors can be placed on the beam 2304 manually or using automated machinery, and can be adhered to the beam using an adhesive such as epoxy. Alternatively, the resistors can be deposited and laser etched directly onto the beam 2304. In both cases, the circuit can be completed externally using wire bonding and flexible printed circuits.

[0224] refer to Fig.16 , the 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, the central axis 306 extending in 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 extending 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 extending through the respective third and fourth half bridges HB3, HB4 also intersect the central axis 306 at the first separation angle.

[0225] refer to Fig.17A , the first plane P1 is shown extending through the first half bridge HB1, which includes a first proximal resistor R arranged on the first side 308 of the beam 2304 along the first lateral side axis 2312 P1 and the first remote resistor R D1, and the second plane P2 is shown 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 the second remote resistor R D2 The magnitude of the first separation angle A1 corresponds to the lateral separation distance between the first and second lateral side axes 2312, 2314 at the first side 308, and therefore corresponds to the first proximal and distal resistors R P1 , R D1 The first half bridge HB1 and the second proximal and distal resistors R P2 , R D2 In the example force sensor 2302, the first lateral side axis 2312 and the second lateral side axis 2314 are equidistant from a 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.

[0226] refer to Fig. 17B , the first plane P1 is shown 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 the third remote resistor R D3 , and the second plane P2 is shown extending through a fourth half bridge HB4 including a fourth proximal resistor R arranged on a second side 2310 of the beam 2304 along a fourth lateral side axis 2318 P4 and the fourth remote resistor R D4 The magnitude of the first separation angle A1 corresponds to the lateral separation distance between the third and fourth lateral side axes 2316-2318 at the second side 2310 of the beam 2304, and therefore, corresponds to the lateral separation distance between the third and fourth lateral side axes 2316-2318 at the second side 2310 of the beam 2304, and thus, ... thus, corresponds to the lateral separation distance between the third and P3 , R D3 The third resistor pair of the third half bridge HB3 and includes R P4 , R D4 In the example force sensor, the third lateral axis 2316 and the fourth lateral axis 2318 are equidistant from a 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.

[0227] Half bridges HB1-HB4 are positioned laterally symmetrically about 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. In addition, in the example force sensor 2302, the spacing between the first lateral axis 2312 and the second lateral axis 2314 matches the spacing between the third lateral axis 2316 and the fourth lateral axis 2318, although equidistant spacing is not required. Half bridges HB1-HB4 are positioned longitudinally symmetrically along beam 2304. The proximal resistor R P1 -R P4 is positioned at a matching longitudinal position of the beam. In the example force sensor, the distal resistor R D1 -R D4 Positioned at matching longitudinal position of beam.

[0228] Fig.18A yes Figures 13A-13B An illustrative proximal cross-sectional view of an example beam 2304 of FIG. 2304 indicating 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 the force F applied to the beam 2304. Fig.18A In the example beam of , the second and third half-bridge HB2, HB3 only contain stretch resistors. Fig.18B is an illustrative force diagram indicating an X-force component and a Y-force component of a second plane strain force FP2 applied to a second half-bridge HB2 in response to an applied force F, the half-bridge HB2 including a second proximal resistor R P2 and the second remote resistor R D2 . Fig. 18C is an illustrative force diagram indicating orthogonal X-force components and Y-force components of a third plane strain force FP3 applied to a third half-bridge HB3 in response to an applied force, the half-bridge HB3 including a third proximal resistor R P3 and the third remote resistor R D3 .

[0229] In the example force sensor 2302, the second pair of resistors R of the second half bridge HB2 P2 , R D2 The resistance value is the same as the third pair of resistors R of the third half bridge HB3 P3 , R D3In 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 a second plane strain force FP2 to the second half bridge HB2 in the second plane P2 and applies a third plane strain force FP3 to the third half bridge HB3 in the third plane P3. 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 2314. Similarly, 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. In the example force sensor 2302, the second and third half bridges HB2, HB3 are positioned on the example beam 2304 such that the magnitude of the components of the second plane strain force FP2 matches the magnitude of the components of the third plane strain force FP3.

[0230] 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 magnitude of the off-axis force applied to the different halves of the full bridge located on the beam. In the example force sensor 2302, the Y-direction force component F applied to the beam 2304 by the applied force F Y The magnitude of may be determined based on the difference between the first off-axis force FP2 and the second off-axis force FP3 as follows.

[0231] Let A be the angle between P2 and P3.

[0232] Let the X axis bisect the angle A. Therefore, the angle between P2 and X is A / 2, and the angle between P3 and X is A / 2.

[0233] Let θ be the angle between the X-axis and the applied force F.

[0234] Force F along the X axis x =Fcosθ

[0235] The force F along the y axis y =Fsinθ

[0236] refer to Fig.18B , force along P2 = F x cosA / 2+F y cos(90+A / 2)=FP2

[0237] refer to Fig. 18C , force along P3 = F x cosA / 2+F y cos(90-A / 2)=FP3

[0238] FP2=F x cosA / 2+F y cos(90+A / 2)

[0239] FP3=F x cosA / 2+F y cos(90-A / 2)

[0240] Use cos(θ)=-cos(180-θ)

[0241] We get

[0242] FP3=F x cosA / 2-F y cos(90+A / 2)

[0243] When we subtract FP1 and FP2

[0244] We get FP2–FP3=F x cosA / 2+F y cos(90+A / 2)

[0245] -F x cosA / 2+F y cos(90+A / 2)

[0246] Therefore, FP2–FP2=2F y cos(90+A / 2)

[0247] Therefore, FP2–FP3∝F y

[0248] Therefore, the difference between FP2 and FP3 is equal to the Y-direction force component F exerted on the beam by the applied force F. Y Directly proportional.

[0249] Furthermore, it should be understood that

[0250] F Y =FP2-FP2

[0251] F Y αV O2 –V O3

[0252] Where V O2 is the output voltage of HB2, V O3 is the output voltage of HB3.

[0253] Fig.19 yes Figures 13A-13B An illustrative proximal cross-sectional view of an example beam of 2304 indicating the first plane strain force FP1 and the fourth plane strain force FP4 applied to the respective first and fourth half-bridges HB1, HB4 by the force F applied to the beam 2304. Fig.19In the example beam, the first and fourth half bridges HB1, HB4 only include stretch resistance resistors. In the example force sensor 2302, the first pair of resistors R of the first half bridge HB1 P1 , R D1 The resistance value is the same as the fourth pair of resistors R of the fourth half bridge HB4 P4 , R D4 In the example force sensor 2302, the first and fourth half bridges HB1, HB4 are positioned on the example beam 2304 so that the applied force F applied to the example beam 2304 applies the first plane strain force FP1 to the first half bridge HB1 in the first plane P1 and applies the fourth plane strain force FP4 to the fourth half bridge HB4 in the second plane P4. In the example force sensor 2302, the first and fourth half bridges HB1, HB4 are positioned on the example beam 2304 so that the magnitude of the component of the first plane strain force FP1 matches the magnitude of the component of the fourth plane strain force FP4.

[0254] In this example, the difference between FP1 and FP4 is proportional to the Y-direction force component F applied to the beam by the applied force F. Y Those skilled in the art will appreciate that the process for determining the difference between FP1 and FP4 is based on the above description of determining the difference between FP2 and FP3.

[0255] Furthermore, it should be understood that

[0256] F Y =FP1–FP4

[0257] F Y αV O1 –V O4

[0258] Where V O1 is the output voltage of HB1, V O4 is the output voltage of HB4.

[0259] Fig. 20 yes Figures 13A-13B 2304, indicating 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 on the beam 2304. In the example force sensor 2302, the first pair of resistors R of the first half-bridge HB1 P1 , R D1 The resistance value of the second pair of resistors R of the second half bridge HB2 P2 , R D2The resistance values ​​of the first and second half bridges HB1 and HB2 are matched. In the example force sensor 2302, the first and second half bridges HB1 and HB2 are positioned on the example beam 2304 so that the applied force applied to the example beam 2304 applies a first plane strain force FP1 to the first half bridge HB1 in the first plane P1 and applies a second plane strain force FP2 to the second half bridge HB2 in the second plane P2. It should be understood that the first plane 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 plane 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 and HB2 are positioned on the example beam 2304 so that the first plane strain force FP1 X The magnitude of the first plane strain force FP1 matches the magnitude of the second plane strain force FP2. X The force direction and the first plane P1 are separated from each other by a first separation angle A1.

[0260] In this example, the difference between FP1 and FP2 is proportional to the X-directed force component FX applied to the beam by the applied force F. Those skilled in the art will appreciate that the process for determining the difference between FP1 and FP2 is based on the above description of determining the difference between FP2 and FP3.

[0261] Furthermore, it should be understood that

[0262] F X =FP1-FP2

[0263] F X αV O1 –V O2

[0264] Where V O1 is the output voltage of HB1, and V O2 is the output voltage of HB2. Fig.21 yes Figures 13A-13B An illustrative proximal cross-sectional view of an example beam 2304 is shown, indicating the force F exerted on the beam. X The third plane strain force FP3 and the fourth plane strain force FP4 applied to the respective third and fourth half bridges HB3 and HB4. In the example force sensor 2302, the third pair of resistors R of the third half bridge HB3 P3 , R D3 The resistance value is the same as the fourth pair of resistors R of the fourth half bridge HB4 P4 , R D4The resistance values ​​of the third and fourth half bridges HB3 and HB4 are matched. In the example force sensor 2302, the third and fourth half bridges HB3 and HB4 are positioned on the example beam 2304 so that the applied force applied to the example beam 2304 applies the third plane strain force FP3 to the third half bridge HB3 in the third plane P3, and applies the fourth plane strain force FP4 to the fourth half bridge HB4 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 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 example force sensor 2302, the third and fourth half bridges HB3 and HB4 are positioned on the example beam 2304 so that Fig.21 The size is Figures 13A-13B The example of beam 2304 indicates the force F exerted on the beam. X Illustrative proximal cross-sectional views of third and fourth plane strain forces FP3, FP4 applied to respective third and fourth half-bridges HB3, HB4.

[0265] In this example, the difference between FP3 and FP4 is proportional to the X-direction force component F applied to the beam by the applied force F. X Those skilled in the art will appreciate 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.

[0266] Furthermore, it should be understood that

[0267] F X =FP3–FP4

[0268] F X αV O3 –V O4

[0269] Where V O3 is the output voltage of HB3, and V O4 is the output voltage of HB4.

[0270] Therefore, assuming that all resistors R P1 -R P4 and R D1 -R D4 Normal work,

[0271] F X αV O1 –V O2 =V O3 –V O4 and F Y αV O1 –V O4 =V O2 –VO3

[0272] Furthermore, it should be understood that F X and F Y It can be determined more generally based on each of the following four combinations of three half-bridges (HB) listed in Table 1 below.

[0273] Table 1

[0274] 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

[0275] Therefore, the half-bridge combination in Table 1 above can be used to X and F Y Redundancy determination is performed. Based on the above half-bridge combination, F X and F Y Comparison of the values ​​can be used to determine if the force sensor 2304 contains a faulty resistor. If even a single resistor fails, then all four combinations will produce different values ​​of Fx and Fy, indicating a fault. Since all four HBs will 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 comparisons of five or more combinations of three bridges can be used to determine which half-bridge is defective, so the measurement value from the defective half-bridge can be ignored.

[0276] Redundant Single-Sided XY Force Sensor

[0277] An example single-sided XY force sensor includes a beam including four half-bridges located on a single side thereof. Two of the half-bridges are one of a compression type and two of the half-bridges are tension type. Since compression and tension strain gauge resistor measurements experience strains in opposite directions in response to a force applied to the beam, measurements by a combination of three half-bridges located on the same side of the beam, where one of the three half-bridges has a different strain gauge resistor type than the other two, can be used to measure X-direction forces and Y-direction forces. An example single-sided XY force sensor includes four half-bridges, two of which are compression type and two of which are tension type, and the example single-sided XY force sensor can perform redundant XY measurements.

[0278] However, in general, based on any three of the four half-bridge measurements, Fx, Fy, and the temperature gradient will be measured. For a beam with four half-bridges (two tension and two compression), there are four ways to select three of the four half-bridges, so that we can obtain four measurements of Fx and Fy, providing redundancy in the measurements.

[0279] Fig. 22An example top perspective view of an example force sensor 21102 is shown, which includes a rectangular beam 21104 including two example tensile resistor half-bridges and two example compression resistor half-bridges located on an outer first side surface 21108 thereof. The example 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 example tensile half-bridges have Figures 14A-14B The first circuit layout 2402 and the first circuit schematic 2404. Two example compression half bridges have Figures 15A-15B A second circuit layout 2502 and a second circuit schematic 2504 are shown.

[0280] The first pair of tensile resistors includes a first proximal tensile resistor RT located at the proximal beam portion 21104P P1 and a first distal tensile resistor RT located at the distal beam portion 21104D D1 . The first proximal tensile resistor RT P1 and the first distal stretch resistor RT D1 The first half bridge HB1 is electrically coupled in series and arranged T The second pair of tensile resistors includes a second proximal tensile resistor (RT P2 ) and a second distal tensile resistor (RT D2 ). The second proximal tensile resistor RT P2 and the second distal stretch resistor RT D2 The second half bridge HB2 is electrically coupled in series and arranged T The first pair of compression resistors includes a first proximal compression resistor (RC P1 ) and a first distal compression resistor (RC D1 ). The first proximal compression resistor (RC P1 ) and the first distal compression resistor (RC D1 ) are electrically coupled in series and arranged in the third compression resistor half bridge HB3 C The second pair of compression resistors includes a second proximal compression resistor resistor (RC P2 ) and a second distal compression resistor resistor (RC D2 The second proximal compression resistor (RC P2 ) and the second distal compression resistor (RC D2 ) are electrically coupled in series and arranged in the fourth compression resistor half bridge HB4C middle.

[0281] As from the illustrative Figures 14A-14B and Figures 15A-15B As will be understood from the explanation of and as explained more fully below, the corresponding output voltage node is located at HB1 T The corresponding first pair of stretch resistors RT P1 , RT D1 , HB2 T The corresponding second pair of stretch resistors RT P2 , RT D2 , HB3 C The corresponding first pair of compression resistors RC P1 ,RC D1 and HB4 T The corresponding second pair of compression resistors RC P2 ,RC D2 The voltage offsets between certain combinations of these different output voltages can be used to determine a redundant measure of the X force applied to the beam. The voltage offsets between certain combinations of these different output voltages can be used to determine a redundant measure of the Y force applied to the beam. Resistor RT P1 , RT P2 , RT D1 , RT D2 ,RC P1 ,RC P2 ,RC D1 ,RC D2 Failure of any one of the resistors will result in a difference in the redundant X-direction force measurement. Similarly, failure of any one of the resistors will result in a difference in the redundant Y-direction force measurement. The difference in the redundant X-direction force measurement and / or the redundant Y-direction force measurement indicates a failure of the force sensor.

[0282] Still reference Fig. 22 , the first proximal tensile resistor RT P1 , first distal tensile resistor RT D1 , first proximal compression resistor RC P1 and the first distal compression resistor RC D1 The central axis 21108 extends on the first side 21108 of the beam 21104 in a first imaginary plane P1, and the plane P1 defines a first lateral side axis 21112 on the first side 21108 of the beam 21104 at a location along which the first plane P1 intersects the first side 21108. The first lateral side axis 21112 and the central axis 21106 extend parallel to each other. Example first lateral side axis 21112 extends through the first proximal and distal tensile resistors RT P1 -RT D1and across the first proximal and distal compression resistors RC P1 -RC D1 The example first lateral side axis 21112 bisects the example first proximal and distal tension resistors and the example first proximal and distal compression resistors.

[0283] The second proximal tensile resistor RT P2 , the second distal tensile resistor RT D2 , the second proximal compression resistor RC P2 and the second distal compression resistor RC D2 The central axis 21106 extends on the first side 21108 of the beam 21104 disposed in the second imaginary plane P2, and the plane P2 defines a second lateral side axis 21114 on the first side 21108 of the beam 21104 at a location along which 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 across 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 tension resistors and the example second proximal and distal compression resistors.

[0284] Fig.23 yes Fig. 22 21104. The proximal end view of the beam shows a side view of a first plane P1 and a second plane P2 that intersect each other along a central axis 21106, with the central axis 21106 extending within the first and second planes. The first and third half bridges HB1 T HB3 C The second and fourth half bridges HB2 are longitudinally aligned along one transverse edge of the beam 21104, and the second and fourth half bridges HB2 T HB4 C Aligned longitudinally along opposite edges of beam 21104. Extending across half bridge circuit HB1 T HB3 C A portion of the first plane and extending through the half-bridge circuit HB2 T HB4 C A portion of the second plane P2 intersects the central axis 306 at a first separation angle B1.

[0285] Fig.24 yes Fig. 22 Example of a side view of the outer surface first side 21108 of the beam 21104, two stretched resistor half bridge HB1T HB2 T and two compression resistors half bridge HB3 C HB4 C A first plane FP1 is shown extending through the first proximal and distal stretch resistors and the proximal resistor RT P1 , RT D1 The first stretch resistor half bridge HB1 T , and through the first proximal and distal compression resistors RC P1 ,RC D1 The third compression resistor half bridge HB3 C The second plane P2 is shown extending through the second proximal and distal stretch resistors and the proximal resistor RT P2 , RT D2 The second stretch resistor half bridge HB2 T , and through the second proximal and distal compression resistors RC P2 ,RC D2 The fourth compression resistor half bridge HB4 C The magnitude of the first separation angle B1 corresponds to the lateral spacing distance between the first side 21108 and the first lateral side axis 21112 and the second lateral side axis 21114, and therefore corresponds to the first stretched resistor pair R P1 , R D1 and the first compression resistor pair RC P1 ,RC D1 With the second stretch resistor on the other hand R P2 , R D2 and the second compression resistor pair RC P2 ,RC D2 In the example force sensor 21102 , the first lateral side axis 21112 and the second lateral side axis 21114 are equidistant from a neutral axis 21115 extending within a surface of the first side 21108 of the beam 21104 , parallel to the central axis 21106 and equidistant from opposite lateral edges of the first side 21108 .

[0286] The first and third half bridge HB1 T and HB3 C The resistors are staggered. RC D1 With RT D1 and RT P1 The first lateral axis 21112 is aligned between the RT P1 Along RC D1 and RC P1 The first lateral side axis 21112 is aligned between them.

[0287] The second and fourth half bridge HB2T and HB4 C The resistors are staggered. RC D4 With RT D2 and RT P2 The second lateral axis 21114 is aligned between the RT P2 Along RC D3 and RC P4 A second lateral side axis 21114 is aligned between them.

[0288] The first voltage node V O1 Coupling the first stretch resistor to RT D1 and RT P1 The second voltage node V O2 Coupled in the second stretch resistor to RT D2 and RT P2 The third voltage node V O3 Coupled in the first compression resistor pair RC D1 and RC P1 The fourth voltage node V O4 Coupled in the second compression resistor pair RC D2 and RC P2 between.

[0289] In the example force sensor, the first and second proximal stretch resistors RT P1 , RT P2 Positioned at matching longitudinal positions of beam 21104. In the example force sensor, the first and second distal stretch resistors RT D1 , RT D2 are positioned at matching longitudinal positions of beam 21104. Similarly, in the example force sensor, the first and second proximal compression resistors RC P1 ,RC P2 Positioned at matching longitudinal positions of beam 21104. In the example force sensor, the first and second distal compression resistors RC D1 ,RC D2 Positioned at matching longitudinal position of beam 21104.

[0290] Fig.25 yes Fig. 22 21104, indicating the force F exerted on the beam 21104 applied to the respective first and second stretch resistor half-bridges HB1 T HB2 T The first plane strain force FP1 and the second plane strain force FP2. In the example force sensor 21102, the first half bridge HB1 T The first pair of resistors RT P1 , RT D1The resistance value of the second half bridge HB2 T The second pair of resistors RT P2 , RT D2 The resistance values ​​of the first and second half bridges HB1 are matched. T HB2 T The example beam 21104 is positioned such that an X-direction force applied to the example beam 21104 applies a first plane strain force FP1 to the first half bridge HB1 in the first plane P1. T The second plane strain force FP2 is applied to the second half bridge HB2 in 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 planar forces.

[0291] Fig.26 yes Fig. 22 An illustrative cross-sectional end view of an example beam 21104 indicating the forces exerted on the beam 21104 to the respective third and fourth compression resistor half-bridges HB3 C HB4 C The first plane strain force FP1 and the second plane strain force FP2. In the example force sensor 21102, the third and fourth compression half bridges HB3 C HB4 C The example beam 21104 is positioned such that the applied force applied to the example beam 21104 applies a third plane strain force FP3 to the third compression half-bridge HB3 in the first plane P1. C The fourth plane strain force FP4 is applied to the fourth compression half bridge HB4 in 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 planar forces.

[0292] Fig. 27 yes Fig. 22 An illustrative cross-sectional end view of an example beam 21104 indicating that a first plane strain force FP1 and a fourth plane strain force FP2 are applied to a corresponding first stretch resistor half-bridge HB1 by a force applied on the beam 21104 T and the fourth compression resistor half bridge HB4 C In the example force sensor 21102, the first tension and fourth compression half bridges HB1 T HB4 CPositioned on the example beam 21104 such that an applied force applied to the example beam 21104 applies a first plane strain force FP1 to a first tensile half-bridge HB1 in the first plane P1 T And a fourth plane strain force FP4 is applied to the fourth compression half bridge HB4 in the second plane P2 C HB1 T and HB4 C Can be used with HB2 T or HB3 C to determine the Y component of the applied force, as shown in the following reference Fig.29 Explained.

[0293] Fig.28 yes Fig. 22 An illustrative cross-sectional end view of an example beam 21104 indicating the forces exerted on the beam 21104 to the respective second tensile and third compressive resistor half-bridges HB2 T HB3 C The second tensile and third compressive half bridges HB2 are formed by the opposite second plane strain force FP2 and the third plane strain force FP3. T HB3 C The example beam 21104 is positioned such that the applied force applied to the example beam 21104 applies a third plane strain force FP2 to the third compression half-bridge HB3 in the first plane P1. C The second plane strain force FP2 is applied to the second tensile half bridge HB2 in the second plane P2. T HB2 T and HB3 C With HB1 T or HB4 C to determine the Y component of the applied force, as shown below. Fig.29 Explained.

[0294] Determining the force component by subtracting the off-axis force component does not work for half-bridge pairs with different resistor types because the compression resistors and the stretch resistors have unmatched sensitivities. However, in the example sensor 21102 that includes a stretch resistor type half-bridge and a compression resistor type half-bridge, any combination of the three half-bridges can be used to determine the F of the applied force F. X Quantity and F Y components, which are orthogonal to each other, refer to Fig.29 The explanation is as follows.

[0295] Fig.29 is an illustrative cross-sectional end view of an example beam 21504 indicating the three example half-bridges HB applied thereto. A HBB HB C In the following explanation, two half-bridges can be of the same type (tension resistor type or compression resistor type), while the third half-bridge can be of the same type or of the opposite type. Note that, unlike the case with four half-bridges on one side, Fig. 22 Unlike beam 21102, beam 21504 has two half bridges HB A and HB B , both of which are located on the same side of the beam and have a third half bridge HB located on the opposite side of the beam C Those skilled in the art will appreciate that the force F to be applied is determined based on the force measurements using the three half-bridges. x and F Y The following process of components wherein two half-bridges have matching resistor types, which may or may not match the resistor type of the third half-bridge, independently of the circumferential position of the half-bridges on the beam and independently of the half-bridge types.

[0296] The force applied by the facility F = (F X ,F Y ).

[0297] The force,

[0298] FP 1 =F X cosθ1+F Y sinθ1 (1)

[0299] FP 2 =F X cosθ2+F Y sinθ2 (2)

[0300] FP 3 =F X cosθ3+F Y sinθ3 (3)

[0301] Assume V1, V2, V3 are HB A HB B HB C Output voltage

[0302] but,

[0303] V1=g1FP 1 +VΔT (4)

[0304] V2=g2FP 2 +VΔT (5)

[0305] V3=g3FP 3 +VΔT (6)

[0306] where VΔT is the voltage due to the temperature gradient along the half-bridge; gi is the sensitivity / gain of HB to the force along FPi.

[0307] Substituting (1), (2), and (3) into (4), (5), and (6), we obtain,

[0308] V1=g1cosθ1F X +g1sinθ1F Y +VΔT (7)

[0309] V2=g2cosθ2F X +g2sinθ2F Y +VΔT (8)

[0310] V3=g3cosθ3F X +g3sinθ3F Y +VΔT (9)

[0311] The values ​​of gi and θi are known by design or calibration, so the unknown is F X 、F Y and VΔT. We have three equations and three unknowns. This is a straightforward linear algebra problem.

[0312] F X =(V1(g3sinθ3–g2sinθ2)+V2(g1sinθ1–g3sinθ3)+V3(g2sinθ2–

[0313] g1sinθ1)) / DEN (10)

[0315] F Y =(V1(g2cosθ2–g3cosθ3)+V2(g3cosθ3-g1cosθ1)+V3(g1cosθ1–

[0316] g2cosθ2)) / DEN (11)

[0318] in:

[0319] DEN=g2g3(sinθ2cosθ3–cosθ2sinθ3)

[0320] -g1g3(sinθ1cosθ3–cosθ1sinθ3)

[0321] +g1g2(sinθ1cosθ2–cosθ1sinθ2)

[0322] HB i The gi value depends on the type of HB.

[0323] If we assume that the sensitivity of all tensile gauges HBs is g then the following is gi

[0324] If we assume that the value of gi for the tension 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.

[0325] Therefore, it is understandable that F X and F Y It can be determined based on each of the following four combinations of three half bridges (HB) listed in Table 2 below.

[0326] Table 2

[0327]

[0328]

[0329] The following are references Fig.29 Describe the process to determine Fig.26 Example of Example F X and F Y Example of force components.

[0330] This example assumes that the values ​​in Table 3 are as follows:

[0331] Table 3

[0332] 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

[0333] The value θ is Fig.26 The half angle (A / 2) between the FP1 and FP2 force planes. The g value is the sensitivity of the half bridge of the tensile gauge.

[0334] In this example, we use HB1 T HB2 T and HB3 C , using equations (10) and (11) to determine,

[0335] FX=(V1–V2) / 2gsinθ

[0336] FY=(V1(1-ρ)+V2(1+ρ)-2V3) / 2gcosθ(1+ρ)

[0337] Therefore, the half-bridge combination in Table 2 above can be used to X and F Y Redundancy determination is performed. Based on the above half-bridge combination, F X and F YComparison of the values ​​can be used to determine if force sensor 21102 contains a faulty resistor. If even a single resistor fails, all four combinations will produce different values ​​of Fx and Fy, indicating a failure. Since all four HBs will produce different results when they fail, it is impossible to determine which resistor failed.

[0338] Fig.30 21902 is an illustrative diagram of a computer system 21902 configured to monitor voltage measurements of a force sensor 2302. The example computer system 21902 includes a display screen 21904. The computer system 21902 is configured to receive a voltage measurement V on a line 21903 generated by the force sensor 2302. O1 、V O2 、V O3 and V O4 . Fig.31 22000 is an illustrative flowchart representing an example diagnostic process for detecting a faulty strain gauge resistor in a force sensor 2302 or 21102. The computer system 21902 is configured with computer readable instructions to perform the steps of the diagnostic process 22000. At block 22002, the computer system receives a voltage measurement V O1 、V O2 、V O3 and V O4 At block 22004, determine the individual F values ​​for each of the HB combinations 1-4 of Table 1. X Whether the values ​​match and the F Y More specifically, for example, computer system 21902 uses the voltage measurements from HB1, HB2, HB3, and HB4 to determine whether F X and F Y If the values ​​match, control flows back 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.

[0339] XY force sensor on the opposite side of the expansion bridge

[0340] Figures 32A-32B An exemplary top perspective view of an example force sensor 3302 is shown ( Fig.32A ) and bottom perspective ( Fig.32B ), the example force sensor 3302 includes a rectangular beam 3304 with a Wheatstone bridge circuit ("full bridge") located in two opposite sides thereof. The first full Wheatstone bridge includes a first (R P1 ), the second (R D1 )、Third (RP2 ) and the fourth (R D2 ) resistor. The second bridge includes a fifth (R P3 ), the sixth (R D3 ), Seventh (R P4 ) and the eighth (R D4 In the example first full Wheatstone bridge 3352, the first and second resistors are coupled in a first half bridge, and the third and fourth resistors are coupled in a second half bridge. Fig.32B The second side 3308 of the beam 3304 is shown facing in the same direction as Fig.32A 3304 is shown in the direction opposite to the direction facing by the first side 3308 of the beam 3304. An (X, Y, Z) beam coordinate system 3305 is shown to explain the force direction relative to the beam 3304. The example beam 3304 can have a rectangular cross-section with flat sides. More specifically, the example beam can have a square cross-section. The beam 3304 includes a proximal beam portion 3304P and a distal beam portion 3304D and includes a longitudinal center axis 3306 extending between the proximal beam portion and the distal beam portion. Fig.32A , the first proximal strain gauge resistor (“resistor”) R P1 and the second proximal resistor R P2 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 remote resistor R D2 The resistor R in the first set of resistors located on the first side 3308 of the beam 3304 is located at the distal beam portion 3304D of the first side 3308 of the beam. P1 -R P2 and R D1 -R D2 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 The first side neutral axis 3315 is positioned laterally apart from each other on opposite sides. Fig.32B , the third proximal strain gauge resistor (“resistor”) R P3 and the fourth proximal resistor R P4 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 remote resistor R D4 The resistor R of the second set of resistors is located at the distal portion of the second side of the beam. P3 -R P4 and R D3 -R D4Arranged in a second split full-Wheatstone bridge aligned with a third axis 3319 as the neutral axis of the second side of the beam.

[0341] As explained more fully below, the first and second full bridge circuits are "spread out" in that portions of each bridge circuit are laterally spaced apart from one another on the beam 3304. For example, each full bridge may include two half bridges that are laterally spread apart from one another. One advantage of laterally spread apart half bridges is that, for example, conductor traces that couple resistors to a bias voltage or couple resistors to one another may be routed through the middle of a face of the beam 3304 or near the neutral axis of the beam 3304 on each face of the beam. Alternatively, in a circular cross-section beam (not shown), the conductor traces may advantageously be routed along the neutral axis of each half bridge. Such routing helps reduce strain on the traces, thereby improving the accuracy of the sensor by rejecting unwanted signals.

[0342] The resistors can be placed on the beam 3304 manually or using automated machinery, and can be adhered to the beam using an adhesive such as epoxy. Alternatively, the resistors can be deposited and laser etched directly onto the beam 3304. In both cases, the circuits can be completed externally using wire bonding and flexible printed circuits.

[0343] As explained more fully below, the first pair of resistors R located on the first side 3304 of the beam P1 -R P2 and the second pair of resistors R D1 -R D2 , and a third pair of resistors R located on the opposite second side of the beam. P3 -R P4 and the fourth pair of resistors R D3 -R D4 Used as an X-direction force sensor element. Fig.32A , the first near side resistor R P1 and the first remote resistor R D1 On the first side 3308 of the beam 3304 disposed in a first imaginary plane P1, the longitudinal center axis 3306 extends in the plane P1 and the plane P1 defines a first lateral side axis 3312 on the first side 3308 of the beam 3304 at a location along which the first plane P1 intersects the first side 3308. The first lateral axis 3312 and the center axis 3306 extend parallel to each other and parallel to the first side neutral axis 3315. The example first lateral side axis 3312 extends through the first proximal resistor R P1 and through the first remote resistor R D1 In addition, the example first lateral side axis 3312 bisects the example first proximal resistor RP1 and bisects the example first remote resistor R D1 .

[0344] Still reference Fig.32A , the second proximal resistor R P2 and the second remote resistor R D2 The beam 3304 is disposed on an opposite first side 3308 in a second imaginary plane P2, in which the longitudinal center axis 3306 extends and the plane P2 defines a second lateral side axis 3314 on the first side 3308 of the beam 3304 at a location along which the second plane P2 intersects the first side 3308. The second lateral axis 3314 and the center axis 3306 extend parallel to each other and parallel to the first side neutral axis 3315. The example second lateral side axis 3314 extends through the second proximal resistor R P2 and through the second far resistor R D2 In addition, the example second lateral side axis 3314 bisects the example second proximal resistor R P2 and bisects the example second remote resistor R D2 .

[0345] The first pair of resistors R P1 -R D1 and the second pair of resistors R P2 -R D2 Each resistor in is a strain gauge resistor of the same type. More specifically, in the example force sensor 3302 described herein, resistor R P1 -R D1 and R P2 -R D2 are tension-type gauge resistors for measuring tensile strain. In an alternative example force sensor, the first and second pairs of resistors may be compression-type gauge resistors for measuring compressive strain. As used herein, reference to a set of resistors having a "matched type" refers to a set of resistors in which all resistors are tension resistors or all resistors are compression resistors. Resistors having a matched type are more likely to have similar sensitivity and performance, making the sensor better suited and more effective in low signal-to-noise situations where common-mode cancellation is critical. In general, although tension or compression gauge resistors can be used to determine force in the X and Y directions, in general, tension strain gauge resistors are more sensitive than compression gauge resistors.

[0346] refer to Fig.32B , the third pair of resistors R P3 -R D3 and the fourth pair of resistors R P4 -R D4The second side third axis 3319 is arranged along the second opposite side 3310 of the beam 3304. The second side third axis 3319 is a neutral axis extending within the second side, parallel to the central axis 3306, and equidistant from the lateral edge of the second side. The third and fourth pairs of resistors include non-matching type resistors. Specifically, R P3 , R P4 One of them is a tension resistor, the other is a compression resistor, and R D3 , R D4 One of the resistors is a tension resistor and the other is a compression resistor. The pitch between the tension gauge and the compression gauge is also matched.

[0347] Fig.33 yes Figures 32A-32B An illustrative proximal cross-sectional view of an example beam 3304. Fig.34A is a side view of the beam showing the first side 3308 of the beam 3304. Fig.34B is a side view of the beam showing the second side 3310 of the beam 3304.

[0348] refer to Fig.33 , the proximal end view of the beam 3304 shows a side view of a first plane P1 and a second plane P2 intersecting each other along a longitudinal center axis 3306, and the center axis 3306 extends within the first plane P1 and the second plane P2. An (X, Y, Z) beam coordinate system 3305 is shown to explain the direction of forces relative to the beam 3304. Note that in Fig.33 , the Z axis is shown as emerging from the page. The first plane P1 and the second plane P2 are spaced apart from each other about the central axis 3306 by a first separation angle A1.

[0349] refer to Fig.34A , the first lateral side axis 3312 is shown extending through the first proximal resistor R on the first side 3308 of the beam 3304 P1 and the first remote resistor R D1 . Please note that Fig.34A , the X axis extends into the page. The second lateral side axis 3314 is shown extending through the second proximal resistor R on the first side 3308 of the beam 3304. P2 and the second remote resistor R D2 The magnitude of the first separation angle A1 corresponds to the lateral separation distance between the first side axis 3312 and the second side axis 3314 at the first side 3308, and therefore corresponds to the first resistor pair R P1 , R D1 With the second resistor pair R P2 , R D2In the example 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 of the beam and is equidistant from opposing lateral edges of the first side 3308 .

[0350] refer to Fig.34B , resistor R P3 -R P4 and R D3 -R D4 The third axis 3319 is aligned along the second side of the beam 3304 and extends within the second side and is equidistant from the opposite lateral edge of the second side 3310. Fig.34A , the X axis appears from the page.

[0351] As explained below, the resistors of the first bridge circuit are laterally spaced apart to measure a force in a first direction perpendicular to the beam center axis 3306 based on an off-neutral axis force applied along the first plane P1 and the second plane P2. Fig.37A As shown, the lateral separation of the resistors of the first bridge 3352 enables routing of the first center conductor trace 3356 parallel to the beam center axis 3306 in the region of the beam 3304 between the proximal and distal resistors of the full Wheatstone bridge.

[0352] Fig.35A is an illustrative side view of an example beam 3304, which shows a resistor R P1 -R P2 and R D1 -R D2 00106] A first example layout of a first full Wheatstone bridge 3602. The first Wheatstone bridge layout is coupled to input bias voltage conductors (EP, EN) and output voltage conductors (Vo-, Vo+) in a first configuration. Fig.35B is an illustrative first schematic circuit diagram 3604 representation of a first full Wheatstone bridge topology. Figures 35A-35B , the first near side resistor R P1 The second proximal resistor R is electrically coupled between the positive first DC potential (EP) and the second (also referred to as the "negative" potential) output Vo-. P2 The first remote resistor R is electrically coupled between the negative second DC potential (EN) and the second output Vo-. D1 The second remote resistor R is electrically coupled between the positive first DC potential (EP) and the first output Vo+ (also referred to as the "positive" output). D2 Electrically coupled between the negative second DC potential (EN) and the first output Vo+.

[0353] Fig.36Ais an illustrative side view of an example beam 3304, which shows a resistor R P1 -R P2 and R D1 -R D2 An alternative second example layout of the first full Wheatstone bridge 3702. The second Wheatstone bridge layout is coupled to the input bias voltage conductors (EP, EN) and the output voltage conductors (Vo-, Vo+) in a second configuration. Fig.36B is an illustrative first schematic circuit diagram 3704 representation of a second alternative example layout of a first full Wheatstone bridge circuit. Figures 36A-36B , the first near side resistor R P1 The second proximal resistor R is electrically coupled between the positive first DC potential (EP) and the first output Vo+. P2 The first remote resistor R is electrically coupled between the positive first DC potential (EP) and the second output Vo-. D1 The second remote resistor R is electrically coupled between the negative second DC potential (EN) and the first output Vo+. D2 Electrically coupled between the negative second DC potential (EN) and the second output Vo-.

[0354] Generally speaking, Fig.35A The layout in is better suited to reducing the number of traces that must span the length of the beam and can also reduce the effects of strain pickup by the traces. On the other hand, if the force sensor uses a half-bridge voltage measurement, then Fig.36A The layout in is the preferred layout. Fig.37A is an illustrative side view of an example beam 3304 showing a resistor R disposed at a second side 3310 of the beam 3304 and including P3 -R P4 and R D3 -R D4 The second example layout of the full Wheatstone bridge 3802. The near side resistor R P3 The resistor R located near the P4 The far side resistor R D3 The resistor R located on the far side D4 The near side resistor R P3 and the remote resistor R D3 is the stretch gauge resistor, and the near side resistor R P4 and the remote resistor R D4 is a compression gauge resistor. Fig.37A In the first arrangement of the second bridge shown, the second bridge is coupled to the input bias voltage conductors (EP, EN) and to the output voltage conductors (Vo-, Vo+) in a first configuration. Fig.37B is an illustrative schematic circuit diagram 3804 representation of a first example layout of a second full bridge circuit. Figures 37A-37B , the third proximal resistor R P3 The fourth proximal resistor R is electrically coupled between the negative second DC potential (EN) and the first output Vo+. P4 The third remote resistor R is electrically coupled between the positive first DC potential (EP) and the first output Vo+. D3 The fourth remote resistor R is electrically coupled between the negative second DC potential (EN) and the second output Vo-. D4 Electrically coupled between the positive first DC potential (EP) and the second output Vo-.

[0355] Fig.37A is an illustrative side view of an example beam 3304 showing a resistor R disposed at a second side 3310 of the beam 3304 and including P3 -R P4 and R D3 -R D4 A second example layout of a second example full Wheatstone bridge 3902. The near side resistor R P3 The resistor R located near the P4 The far side resistor R D3 The resistor R located on the far side D4 The near side resistor R P3 and the remote resistor R D3 is the stretch gauge resistor, the near side resistor R P4 and the remote resistor R D4 is a compression gauge resistor. Fig.37A In the second arrangement of the second bridge shown, the second full bridge is coupled to the input bias voltage conductors (EP, EN) and to the output voltage conductors (Vo-, Vo+) in the first configuration. Fig.37B is an illustrative schematic circuit diagram 904 representation of a second example layout of a second full bridge circuit. Figures 37A-37B , the third proximal resistor R P3 The fourth proximal resistor R is electrically coupled between the positive first DC potential (EP) and the first output Vo+. P4 The third remote resistor R is electrically coupled between the positive first DC potential (EP) and the second output Vo-. D3 The fourth remote resistor R is electrically coupled between the negative second DC potential (EN) and the first output Vo+. D4 Electrically coupled between the negative second DC potential (EP) and the second output Vo-.

[0356] Fig.38A3304, showing an expanded layout of a Wheatstone bridge 3352 located on a first side 3308 of the beam 3304 and showing the routing of a center conductor trace 3356 extending within the center of the bridge between the proximal resistor and the distal resistor of the bridge. The bridge 3352 includes R P1 , R P2 and the remote resistor R D1 , R D2 , and having a first neutral axis 3362, which is near the resistor R P1 , R P2 and the remote resistor R D1 , R D2 3306. In the example bridge, the first neutral line is parallel to R P1 and R P2 Each of the D1 and R D2 Each of the two bridges is equally spaced. The first bridge 3352 is longitudinally separated, wherein the near side resistor R P1 , R P2 With the remote resistor R D1 , R D2 The first bridge is extended horizontally, with the near side resistor R P1 , R P2 Laterally spread apart and the far resistor R D1 , R D2 Scale out separately from each other.

[0357] It should be understood that because the resistors of the first full Wheatstone bridge 3352 are laterally spread apart, they do not occupy the first neutral axis 3362. Therefore, the conductor traces can be routed close to and parallel to the first neutral axis 3362, which can reduce the amount of strain applied to the traces. In addition, routing the traces along the neutral axis of the bridge circuit can be easier to produce, manufacture, or assemble.

[0358] The example first full bridge includes a first set of center conductor traces 3356 extending along a central portion of the first bridge 3352, parallel to the first neutral axis 3362, along an area of ​​the outer surface of the beam 3304, between the pair of proximal resistors R P1 , R P2 and the pair of far side resistors R D1 , R D2 The first set of center traces 3356 includes a trace segment 3356-1 coupled to a first positive output voltage VO1+. The first set of center traces 3356 includes a trace segment 3356-1 coupled to a first negative voltage output VO1-. The first set of center traces 3356 includes a trace segment 3356-3 coupled to a negative voltage potential EN.

[0359] Fig.38B yes Fig.38A 3352 includes R coupled between EP and EN. P1 and R D1 To provide a first half-bridge voltage divider circuit, the first half-bridge voltage divider circuit includes a trace conductor coupled to the first positive output voltage VO1+. The first full-Wheatstone bridge 3352 also includes R coupled between EP and EN P2 and R D2 A second half-bridge voltage divider circuit is provided, the second half-bridge voltage divider circuit comprising a trace conductor coupled to the first negative output voltage VO1-.

[0360] Fig.39A yes Fig.33 An illustrative cross-sectional end view of an example beam 3304 indicating a resistor on a first side and indicating a first planar force FP1 and a second planar force FP2. Fig.39B is an indication of the force F applied to the first proximal resistor R in response to the applied force P1 and the first remote resistor R D1 illustrative force diagram of the X-force component and the Y-force component of the first planar force FP1. Fig.39C is an indication of the force F applied to the second proximal resistor R in response to the applied force F. P2 and the second remote resistor R D2 illustrative force diagram of the X-force component and the Y-force component of the second planar force FP2.

[0361] In the example force sensor 3302, the first pair of resistors R P1 , R D1 The resistance value of the second pair of resistors R P2 , R D2In the example force sensor 3302, the first and second pairs of resistors are positioned on the example beam 3304 such that an applied force F applied to the example beam 3304 applies a first plane strain force FP1 to the first pair of resistors in the first plane P1 and applies a second plane strain force FP2 to the second pair of resistors in the second plane P2. It should be understood that the first plane strain force FP1 is an off-axis force because it is a force applied along the first lateral side axis 3312, which is laterally offset from the neutral axis 3315 of the first bridge 3352. 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 3314, which is laterally offset from the neutral axis 3315 of the first bridge 3352. The first and second pairs of resistors are positioned on the example beam 3304 such that the magnitude of the first plane strain force FP1 matches the magnitude 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 spaced apart from each other by a first separation angle “A”.

[0362] One advantage of using the same type of strain gauge resistor is that the magnitude of the force applied perpendicular to the central axis 3306 of the beam 3304 can be determined based on the difference in the magnitude of the off-axis force applied to the different halves of the full bridge located on the beam. In the example force sensor 3302, the Y-direction force component F applied to the beam 3304 by the applied force F Y The magnitude of may be determined based on the difference between the first off-axis force FP1 and the second off-axis force FP2 as follows.

[0363] Let A be the angle between P1 and P2.

[0364] Assume that the X axis bisects the angle A. Therefore, the angle between P1 and X is A / 2, and the angle between P2 and X is A / 2.

[0365] Let θ be the angle between the X-axis and the applied force F.

[0366] Force F along the X axis x =Fcosθ

[0367] The force F along the y axis y =Fsinθ

[0368] refer to Fig.37B , force along P1 = F x cosA / 2+F y cos(90+A / 2)=FP1

[0369] refer to Fig. 9C , force along P2 = F x cosA / 2+F y cos(90-A / 2)=FP2

[0370] FP1=F x cosA / 2+F y cos(90+A / 2)

[0371] FP2=F x cosA / 2+F y cos(90-A / 2)

[0372] Use cos(θ)=-cos(180-θ)

[0373] We get

[0374] FP2=F x cosA / 2-F y cos(90+A / 2)

[0375] When we subtract FP1 and FP2

[0376] We get FP1-FP2=F x cosA / 2+F y cos(90+A / 2)

[0377] -F x cosA / 2+F y cos(90+A / 2)

[0378] Therefore, FP1-FP2=2F y cos(90+A / 2)

[0379] Therefore, FP1-FP2∝F y

[0380] Therefore, the difference between FP1 and FP2 is equal to the Y-direction force component F exerted on the beam by the applied force F. Y Directly proportional.

[0381] Furthermore, it should be understood that

[0382] F Y αV S1O+ –V S1O- ,

[0383] 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 produced by the first bridge circuit 3352 located on the first side 3308 of the beam 3304.

[0384] Fig.40 yes Fig.33 An illustrative proximal cross-sectional view of an example beam 3304 of FIG. 3304 indicating the resistor R of the example second full bridge 3802 or 3902 on the second side 3310 P3 , R P4 , R D3 , R D4 , and indicates the X-axis force FX. The example second full bridge 3802 or 3902 measures the X-axis force perpendicular to the longitudinal axis 3306 and perpendicular to the third axis 3319 of the second side 3310. An example full bridge circuit including tensile resistors and compression resistors aligned longitudinally parallel to the center axis of the beam and along the neutral axis is disclosed in PCT / US2018 / 061113 filed on November 14, 2018, which is expressly incorporated herein by this reference in its entirety.

[0385] Fig.41 is a schematic diagram showing a metal sheet 31102 including a defined example resistor R P1 -R P4 and R D1 -R D4 3304 for assembly into respective first and second full Wheatstone bridges on oppositely facing first and second sides 3308, 3310 of beam 3304. The first region 31104 of metal sheet 31102 includes resistor R P1 -R P2 and R D1 -R D2 The second region 31106 of the metal sheet includes a resistor R P3 -R P4 and R D3 -R D4 3304 is coupled within a second full bridge located at a second opposite side 3310 of the example beam 3304. An intermediate third region 31108 extending between the first and second regions and sized to lay 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.

[0386] Fig.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 first, second and third 31104, 31104, 31106 regions of the metal sheet 31102 around the example beam 3304 to form the first set of resistors R P1 -R P2 and R D1 -R D2placed on the first side 3308 of the beam 3304 and the second set of resistors R P3 -R P4 and R D3 -R D4 Positioned at the second side 3310 of the beam 3304 , and the intermediate third region 31108 is positioned above the third intermediate side 3320 of the beam 3304 . Fig.42B is an illustrative top perspective view of beam 3304 with metal sheet 31102 wrapped around three sides thereof. In particular, Fig.42B A first region 31104 of the metal sheet 31102 is shown laid over a first side 3310 of the beam 3304 to position the first set of resistors at the first side. Fig.42C is an illustrative bottom perspective view of beam 3304 with metal sheet 31102 wrapped around three sides thereof. In particular, Fig.42C A second region 31106 of the metal sheet 31102 is shown laid over a second side 3310 of the beam 3304 to position a second set of resistors at the second side. In the example rectangular beam, the first side comprises a first face of the beam and the second side comprises a second side opposite the first side.

[0387] Although illustrative examples have been shown and described, extensive modifications, changes, and substitutions are contemplated in the foregoing disclosure, and in some cases, some features of the various examples may be employed without corresponding use of other features. For example, a rectangular beam is described herein. However, a beam having an alternative example beam with a circular cross-section or an octagonal cross-section may be used. More generally, an example beam having a second area moment of inertia may be used that is isotropic for all axes within 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 within a distal cross-section of a distal portion of the beam extending through a distal portion of the beam perpendicular to the central axis of the beam.

[0388] The second area moment of inertia is required to be expressed as,

[0389] I X =I Y

[0390] Among them I X represents the moment of inertia about an arbitrarily chosen X-axis lying on 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

[0391] I XY =0,

[0392] Among them I XY Represents the product moment of inertia of the cross sections of the beam.

[0393] Fig.43 is an illustrative cross-sectional view of a beam 1500 having a cross-sectional area A. For the cross-sectional area A of the beam 1500,

[0394] Let I x ,I y ,I xy The second moment of inertia

[0395] Among them I x =∫∫x 2 dA

[0396] I y =∫∫y 2 dA

[0397] I xy =∫∫xydA

[0398] For a new frame tilted at an angle θ

[0399] x 1 =xcosθ+ysinθ

[0400] y 1 =Ycosθ-xsinθ

[0401]

[0402] For I to be isotropic in all directions, the requirement is,

[0403] I x =I y and I xy =0

[0404] The second area moment of inertia is required to be expressed as,

[0405] I X =I Y

[0406] Among them I X represents the moment of inertia about an arbitrarily chosen X-axis lying on 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

[0407] I XY =0,

[0408] Among them I XY Represents the product moment of inertia of the cross sections of the beam.

[0409] Example

[0410] Example 1 may include a force sensor comprising: a rectangular beam having a proximal portion and a distal portion and having a longitudinal center 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; 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 comprising: 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 ("sixth resistor") coupled to provide a fourth voltage divider output a seventh gauge resistor ("seventh resistor") and an eighth gauge resistor ("eighth resistor"); wherein the first, second, third, fourth, fifth, sixth, seventh and eighth resistors have matching resistor types; wherein the first, second, third and fourth resistors are located on a first side of the beam so 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 parallel to a 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 so that a voltage divider 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.

[0411] Example 2 may include the subject matter of Example 1, wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors are strain gauge resistors.

[0412] Example 3 may include the subject matter of Example 1, wherein the first, third, fifth, and seventh resistors are located at a proximal portion of the beam; and wherein the second, fourth, sixth, and eighth resistors are located at a proximal portion of the beam.

[0413] Example 4 may include the subject matter of Example 3, wherein the first and third resistors have matching values, the second and fourth resistors have matching values, the fifth and seventh resistors have matching values, and the sixth and eighth resistors have matching values.

[0414] Example 5 may include the subject matter of Example 3, wherein the first and third resistors have matching longitudinal positions of the beam, the second and fourth resistors have matching longitudinal positions of the beam, the fifth and seventh resistors have matching longitudinal positions of the beam, and the sixth and eighth resistors have matching longitudinal positions of the beam.

[0415] Example 6 may include a force sensor comprising: a beam having a proximal portion and a distal portion and having a longitudinal center 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, the first gauge resistor and the second gauge resistor being arranged to extend along a first lateral axis extending along the beam parallel to the longitudinal center axis; and a third gauge resistor coupled to provide a second voltage divider output ("third resistor") and a fourth gauge resistor ("fourth resistor"), the third gauge resistor and the fourth gauge resistor being arranged to extend along a second lateral axis extending along a beam parallel to the longitudinal center axis; 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, the fifth gauge resistor and the sixth gauge resistor being arranged to extend along a third lateral axis extending along a beam parallel to the longitudinal center 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 lateral axis, the fourth lateral axis extending along a beam parallel to the longitudinal center axis; wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors are of matching resistor type; wherein the first and second resistors extending along the first lateral axis and the third and fourth resistors extending along the second lateral 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 lateral axes and parallel to the third and fourth lateral axes; and wherein the fifth and sixth resistors extending along the third lateral axis and the seventh and eighth resistors extending along the fourth lateral 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, parallel to the first and second axes, and perpendicular to the third and fourth lateral axes.

[0416] Example 7 may include the subject matter of Example 6, wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors are strain gauge resistors.

[0417] 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.

[0418] Example 9 may include the subject matter of Example 6, wherein the first, third, fifth, and seventh resistors are located at a proximal portion of the beam; and wherein the second, fourth, sixth, and eighth resistors are located at a proximal portion of the beam.

[0419] Example 10 may include the subject matter of 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.

[0420] Example 11 may include the subject matter of Example 6, wherein the first and third resistors are located in a proximal cross-sectional plane of the beam, the cross-sectional plane being perpendicular to the central axis and having a second area moment of inertia that is isotropic for all axes within the proximal cross-sectional plane passing through the longitudinal central axis; wherein the fifth and seventh resistors are located in a proximal cross-sectional plane of the beam, the cross-sectional plane being perpendicular to the central axis and having a second area moment of inertia that is isotropic for all axes within the proximal cross-sectional plane passing through the longitudinal central axis; wherein the second and fourth resistors are located in a distal cross-sectional plane of the beam, the distal cross-sectional plane being perpendicular to the central axis and having a second area moment of inertia that is isotropic for all axes within the distal cross-sectional plane passing through the longitudinal central axis; and wherein the sixth and eighth resistors are located in a distal cross-sectional plane of the beam, the distal cross-sectional plane being perpendicular to the central axis and having a second area moment of inertia that is isotropic for all axes within the distal cross-sectional plane passing through the longitudinal central axis.

[0421] Example 12 may include the subject matter described in Example 6, wherein the first side axis extends within a first plane including the longitudinal center axis; wherein the first side axis extends within a first plane including the longitudinal center 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 including the longitudinal center axis; wherein the fourth side axis extends within a fourth plane including the longitudinal center axis; and wherein the first force direction bisects a second separation angle between the third plane and the fourth plane.

[0422] Example 13 may include the subject matter of Example 12, wherein the first separation angle is equal to the second separation angle.

[0423] Example 14 may include the subject matter of Example 6, wherein the first gauge resistor, the second gauge resistor, the third gauge resistor, and the fourth gauge resistor are located at corresponding locations 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 locations of the beam having matching cross-sections.

[0424] 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 locations 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 locations of the beam having matching cross-sections.

[0425] 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 center axis extending between the proximal portion and the distal portion, the metal sheet comprising: a first cutout portion, the cutout portion being constructed to be laid over a first side 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, the cutout portion being constructed to be laid over a second side of the beam adjacent to the first side 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 a fourth gauge resistor ("fourth resistor") coupled to provide a fourth voltage divider output; Eight gauge resistors ("eighth resistor"), the seventh gauge resistor and the eighth gauge resistor are arranged to extend along a fourth lateral axis, which extends along a beam parallel to the longitudinal center axis; wherein the first, second, third, fourth, fifth, sixth, seventh and eighth resistors have matching resistance types; wherein the first, second, third and fourth resistors arranged to be laid on the first side of the beam are located at the first side of the beam so 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 be laid on the second side of the beam adjacent to the first side of the beam are located on the beam so 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.

[0426] Example 17 may include the subject matter of Example 16, wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors are strain gauge resistors.

[0427] 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.

[0428] Example 19 may include the subject matter of 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.

[0429] Example 20 may include the subject matter of Example 16, 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.

[0430] Example 21 may include a metal sheet for use with a beam having a proximal portion and a distal portion and having a longitudinal center axis extending between the proximal portion and the distal portion, the metal sheet comprising: a first cutout portion configured to be laid over the first portion of the beam, comprising: 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 be laid over the first portion of the beam and extending along a first lateral axis extending along the beam parallel to the longitudinal center axis; a third gauge resistor ("third resistor") coupled to provide a second voltage divider output The first and second cutout portions are configured to be laid over the second portion of the beam, and include: a fifth gauge resistor (the "fifth resistor") and a sixth gauge resistor (the "sixth resistor") coupled to provide a third voltage divider output, the fifth and sixth gauge resistors being arranged to be laid over the second portion of the beam and extending along a third lateral axis extending along the beam parallel to the longitudinal center axis; and a second cutout portion configured to be laid over the second portion of the beam, and including: a fifth gauge resistor (the "fifth resistor") and a sixth gauge resistor (the "sixth resistor") coupled to provide a third voltage divider output, the fifth and sixth gauge resistors being arranged to be laid over the second portion of the beam and extending along a third lateral axis extending along the beam parallel to the longitudinal center axis; and a second cutout portion configured to be laid over the second portion of the beam, and including: a fifth gauge resistor (the "fifth resistor") and a sixth gauge resistor (the "sixth resistor") coupled to provide a third voltage divider output, the fifth and sixth gauge resistors being arranged to be laid over the second portion of the beam and extending along a third lateral axis extending along the beam parallel to the longitudinal center axis; and a a seventh gauge resistor ("seventh resistor") and an eighth gauge resistor ("eighth resistor") for a fourth voltage divider output, the seventh gauge resistor and the eighth gauge resistor being arranged to be laid over the second portion of the beam and extending along a fourth lateral axis, the fourth lateral axis extending along the beam parallel to the longitudinal center axis; wherein the first, second, third, fourth, fifth, sixth, seventh and eighth resistors are of a matching resistor type; wherein the first and second resistors arranged to be laid over the first portion of the beam and extending along the first lateral axis and the third and fourth resistors arranged to be laid over the first portion of the beam and extending along the second lateral 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 lateral axes, and parallel to the third and fourth lateral axes; and wherein the fifth and sixth resistors arranged to be laid over the second portion of the beam and extending along the third lateral axis and the seventh and eighth resistors arranged to be laid over the second portion of the beam and extending along the fourth lateral axis are arranged to be positioned on the beam so 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 lateral axes.

[0431] Example 22 may include the subject matter of Example 22, wherein the first side axis extends in a first plane including the longitudinal center axis; wherein the first side axis extends in a first plane including the longitudinal center 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 in a third plane including the longitudinal center axis; wherein the fourth side axis extends in a fourth plane including the longitudinal center axis; and wherein the first force direction bisects a second separation angle between the third plane and the fourth plane.

[0432] Example 23 may include the subject matter of Example 22, wherein the first separation angle is equal to the second separation angle.

[0433] Example 24 may include a force sensor comprising: a beam having a proximal portion and a distal portion and having a longitudinal center 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 comprising: 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 center 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 center 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 comprising: a plurality of first center conductor traces extending parallel to the neutral axis in a region of the beam between the first resistor and the second resistor and between the third resistor and the fourth resistor.

[0434] Example 25 may include a force sensor comprising: a beam having a proximal portion and a distal portion and having a longitudinal center 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 comprising: a first half-bridge circuit comprising 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 center axis and coupled to provide a first voltage divider output; a second half-bridge circuit comprising a third gauge resistor ("third resistor") and a third gauge resistor ("third resistor"); Four gauge resistors ("fourth resistors"), a third gauge resistor and a fourth gauge resistor are arranged along a second lateral side axis parallel to the longitudinal center 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 are of matching resistor type; and wherein the first full-bridge circuit is arranged on the beam so that a component of a force applied in a first direction perpendicular to the longitudinal center 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.

[0435] Example 26 includes the subject matter of claim 25, further comprising: a second full-bridge circuit on the beam, the second full-bridge circuit having a second neutral axis and comprising: 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 center 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 center 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 comprising: a plurality of first center conductor traces extending parallel to the second neutral axis in a region of the beam between the fifth resistor and the sixth resistor and between the seventh resistor and the eighth resistor.

[0436] Example 27 includes the subject matter of claim 26, wherein the first, second, third and fourth resistors are of matched resistor type; wherein the first full-bridge circuit is arranged on the beam so that the component of the applied force in a first direction perpendicular to the longitudinal center 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 are of matched resistor type; and wherein the second full-bridge circuit is arranged on the beam so that the component of the applied force in a second direction perpendicular to the longitudinal center 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.

[0437] Example 28 includes a force sensor comprising: a rectangular beam having a proximal portion and a distal portion and having a longitudinal center axis extending between the proximal portion and the distal portion; a first half-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 second half-bridge circuit comprising 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 comprising 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 comprising a seventh gauge resistor ("seventh resistor") and an eighth gauge resistor ("seventh resistor") coupled to provide a fourth voltage divider output; A gauge resistor ("eighth resistor"); wherein the first, second, third, fourth, fifth, sixth, seventh and eighth resistors are of matching resistor type; wherein the first, second, third and fourth resistors are located on a first side of the beam, and the fifth, sixth, seventh and eighth resistors are located on a second side of the beam opposite to the first side of the beam, so 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; the voltage offset between the second and third voltage divider outputs represents the magnitude of the second force.

[0438] Example 29 includes the subject matter of claim 28, wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors are strain gauge resistors.

[0439] Example 29 includes the subject matter of claim 28, wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors have matched resistor values.

[0440] Example 30 includes the subject matter of claim 28, wherein the first, third, fifth, and seventh resistors are located at a proximal portion of the beam; and wherein the second, fourth, sixth, and eighth resistors are located at a distal portion of the beam.

[0441] 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.

[0442] Example 32 includes a force sensor comprising: a beam having a proximal portion and a distal portion and having a longitudinal center axis extending between the proximal portion and the distal portion; a first half-bridge circuit comprising 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 lateral axis that extends along the beam parallel to the longitudinal center axis; a second half-bridge circuit comprising 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 lateral axis A first half-bridge circuit includes a first side axis extending along a second side axis extending along a beam parallel to the longitudinal center 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 extending along a beam parallel to the longitudinal center 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 extending along a beam parallel to the longitudinal center axis; wherein, The first, second, third, fourth, fifth, sixth, seventh, and eighth resistors are of a matched resistor type; wherein the first and second resistors extending along the first lateral axis and the third and fourth resistors extending along the second lateral axis are positioned on the beam such that a voltage shift 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, second, third, and fourth lateral axes; wherein the fifth and sixth resistors extending along the third lateral axis and the seventh and eighth resistors extending along the fourth lateral axis are positioned on the beam such that a voltage shift between the third and fourth 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, second, third, and fourth lateral axes wherein the first and second resistors extending along the first lateral axis and the seventh and eighth resistors extending along the fourth lateral axis are positioned on the beam so that a voltage offset between the first 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, second, third, and fourth lateral axes; and wherein the third and fourth resistors extending along the first lateral axis and the fifth and sixth resistors extending along the third lateral axis are positioned on the beam so that a voltage offset between the second and third 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, second, third, and fourth lateral axes.

[0443] Example 33 includes the subject matter of Example 32, wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors are strain gauge resistors.

[0444] 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.

[0445] Example 35 includes the subject matter of Example 32, wherein the first, third, fifth, and seventh resistors are located at a proximal portion of the beam; and wherein the second, fourth, sixth, and eighth resistors are located at a distal portion of the beam.

[0446] 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.

[0447] Example 37 includes the subject matter of Example 35, wherein the first, third, fifth, and seventh resistors are located in a proximal cross-sectional plane of the beam, the cross-sectional plane being perpendicular to the central axis and having a second area moment of inertia that is isotropic for all axes within the proximal cross-sectional plane passing through the longitudinal central axis; and wherein the second, fourth, sixth, and eighth resistors are located in a distal cross-sectional plane of the beam, the distal cross-sectional plane being perpendicular to the central axis and having a second area moment of inertia that is isotropic for all axes within the distal cross-sectional plane passing through the longitudinal central axis.

[0448] Example 38 includes the subject matter described in Example 32, wherein the first side axis extends in a first plane including the longitudinal center 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 in a third plane including the longitudinal center axis; wherein the fourth side axis extends in a fourth plane including the longitudinal center axis; and wherein the first force direction bisects a second separation angle between the first plane and the fourth plane.

[0449] Example 39 includes the subject matter of claim 37, wherein the first and second angles are supplementary angles.

[0450] Example 40 includes a force sensor comprising: a rectangular beam having a proximal portion and a distal portion and having a longitudinal center axis extending between the proximal portion and the distal portion; a first half-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 second half-bridge circuit comprising 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 comprising 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 comprising 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 tension type and compression type, and the fifth, sixth, seventh and eighth resistors are the other of tension type and compression type.

[0451] 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 compression type resistors.

[0452] 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.

[0453] Example 43 includes the subject matter of Example 40, wherein the first, third, fifth, and seventh resistors are located at a proximal portion of the beam; and wherein the second, fourth, sixth, and eighth resistors are located at a proximal portion of the beam.

[0454] 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.

[0455] Example 45 includes a force sensor comprising: a beam having a proximal portion and a distal portion and having a longitudinal center axis extending between the proximal portion and the distal portion; a first half-bridge circuit comprising 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 lateral axis, the first lateral axis extending along the beam parallel to the longitudinal center axis; a second half-bridge circuit comprising 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 lateral axis, the second lateral axis extending along the beam parallel to the longitudinal center axis. beam extending; a third half-bridge circuit, 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 are arranged to extend along a third side axis, and the third side axis extends along a beam parallel to the longitudinal center axis; a fourth half-bridge circuit, which 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 are arranged to extend along a fourth side axis, and the fourth side axis extends along the beam parallel to the longitudinal center axis; wherein the first, second, third and fourth resistors are tensile resistors; wherein the fifth, sixth, seventh and eighth resistors are compression resistors.

[0456] Example 46 includes the subject matter of Example 45, wherein the first, second, third, and fourth resistors are stretch resistors and the fifth, sixth, seventh, and eighth resistors are compression resistors.

[0457] 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.

[0458] Example 48 includes the subject matter of Example 45, wherein the first, third, fifth, and seventh resistors are located at a proximal portion of the beam; and wherein the second, fourth, sixth, and eighth resistors are located at a proximal portion of the beam.

[0459] 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.

[0460] Example 50 includes the subject matter of Example 48, wherein the first, third, fifth, and seventh resistors are located in a proximal cross-sectional plane of the beam, the cross-sectional plane being perpendicular to the central axis and having a second area moment of inertia that is isotropic for all axes within the proximal cross-sectional plane passing through the longitudinal central axis; and wherein the second, fourth, sixth, and eighth resistors are located in a distal cross-sectional plane of the beam, the distal cross-sectional plane being perpendicular to the central axis and having a second area moment of inertia that is isotropic for all axes within the distal cross-sectional plane passing through the longitudinal central axis.

[0461] Example 51 includes the subject matter of claim 45, wherein the first side axis extends within a first plane including the longitudinal center axis; wherein the first side axis extends within a first plane including the longitudinal center 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 including the longitudinal center axis; wherein the fourth side axis extends within a fourth plane including the longitudinal center axis; and wherein the first force direction bisects a second separation angle between the third plane and the fourth plane.

[0462] Example 52 includes the subject matter of claim 51, wherein the first and second angles are supplementary angles.

[0463] Example 53 includes a force sensor comprising: a beam having a proximal portion and a distal portion and having a longitudinal center 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 ("seventh resistor") coupled to provide a fourth voltage divider output; "eighth resistor"); wherein the first, second, third and fourth resistors are of matched resistor types; wherein the fifth and sixth resistors are of one of tension and compression resistor types and the seventh and eighth resistors are of one of tension and compression resistor types; 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 to 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.

[0464] Example 54 includes the subject matter of Example 53, wherein the first, second, third, and fourth resistors are strain gauge resistors.

[0465] Example 54 includes the subject matter of Example 53, wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors have matching resistor values.

[0466] Example 55 includes the subject matter of 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.

[0467] Example 56 includes the subject matter of 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.

[0468] Example 57 includes a force sensor comprising: a beam having a proximal portion and a distal portion and having a longitudinal center 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, the first gauge resistor and the second gauge resistor being arranged to extend along a first lateral axis extending along the beam parallel to the longitudinal center axis; coupled to provide the second voltage divider output a third gauge resistor ("third resistor") and a fourth gauge resistor ("fourth resistor") coupled to provide a third voltage divider output, the third gauge resistor and the fourth gauge resistor being arranged to extend along a second lateral axis extending along a beam parallel to the longitudinal center axis; 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; and a seventh gauge resistor ("seventh resistor") coupled to provide a fourth voltage divider output and an eighth gauge resistor ("eighth resistor"), the seventh gauge resistor and the eighth gauge resistor being arranged to extend along a third lateral axis extending along a beam parallel to the longitudinal center axis; wherein the first, second, third and fourth resistors are of matching resistor type; wherein the fifth and sixth resistors are of one type of tension and compression resistor and the seventh and eighth resistors are of another type of tension and compression resistor; wherein the first and second resistors extending along the first lateral axis and the third and fourth resistors extending along the second lateral 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 lateral axes; and wherein the fifth, sixth, seventh and eighth resistors extending along the third lateral 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 lateral axes.

[0469] Example 58 includes the subject matter of Example 57, wherein the first, second, third, and fourth resistors are strain gauge resistors.

[0470] 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.

[0471] 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.

[0472] Example 61 includes the subject matter of 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.

[0473] Example 61 includes the subject matter of Example 57, wherein the first side axis extends within a first plane including the longitudinal center axis; wherein the first side axis extends within a first plane including the longitudinal center axis; wherein the second force direction bisects a first separation angle between the first plane and the second plane.

[0474] Example 62 includes a metal sheet for use with a rectangular beam having a proximal portion and a distal portion and having a longitudinal center axis extending between the proximal portion and the distal portion, the metal sheet comprising: a first cutout portion, the cutout portion being constructed to be laid over a first side of the beam, 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 cutout portion, the second cutout portion being constructed to be laid over a second side of the beam opposite to the first side of the beam, 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 ("sixth resistor") coupled to provide a fourth voltage divider output a gauge resistor ("seventh resistor") and an eighth gauge resistor ("eighth resistor"); wherein the first, second, third and fourth resistors are of matched resistor type; wherein the fifth and sixth resistors are of one of tension and compression resistor types, and the seventh and eighth resistors are of the other of tension and compression resistor types; wherein the first, second, third and fourth resistors are arranged to be laid on a first side of the beam so 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 be laid on a second side of the beam opposite to the first side of the beam so 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.

[0475] Example 63 includes the subject matter of Example 61, wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors are strain gauge resistors.

[0476] Example 64 includes the subject matter of Example 61, wherein the first, second, third, fourth, fifth, sixth, seventh, and eighth resistors have matching resistor values.

[0477] Example 65 includes the subject matter of 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.

[0478] Example 66 includes the subject matter of example 66, 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.

[0479] Example 68 includes a metal sheet for use with a beam having a proximal portion and a distal portion and having a longitudinal center axis extending between the proximal portion and the distal portion, the metal sheet comprising: a first cutout portion configured to be laid over the first portion of the beam, comprising: 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 be laid over the first portion of the beam and extending along a first lateral axis extending along the beam parallel to the longitudinal center axis; and a third gauge resistor ("third resistor") coupled to provide a second voltage divider output The third gauge resistor and the fourth gauge resistor are arranged to be laid on the first portion of the beam and extend along a second side axis extending along the beam parallel to the longitudinal center axis; and a second cutout portion, the second cutout portion is constructed to be laid on the second portion of the beam, which includes: a fifth gauge resistor (the "fifth resistor") and a sixth gauge resistor (the "sixth resistor") coupled to provide a third voltage divider output; and a seventh gauge resistor (the "seventh resistor") and an eighth gauge resistor (the "eighth resistor") coupled to provide a fourth voltage divider output, the seventh gauge resistor and the eighth gauge resistor The gauge resistors are arranged to be laid over the second portion of the beam and extend along a third side axis extending along the beam parallel to the longitudinal center axis; wherein the first, second, third and fourth resistors are of 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 be laid over the first portion of the beam and extend along the first side axis and the third and fourth resistors arranged to be laid over the first portion of the beam and extend along the second side axis are arranged to be positioned on the beam so that a voltage offset between the first and second voltage divider outputs is represented at a position perpendicular to the longitudinal axis and perpendicular to the longitudinal axis. The magnitude of a first force applied to the beam in a first force direction perpendicular to the first and second lateral axes; and wherein a fifth, sixth, seventh and eighth resistors arranged to overlie a second portion of the beam and extend along a third lateral axis are arranged to be positioned on the beam so that a 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 lateral axes; wherein the first lateral axis extends within a first plane including the longitudinal center axis; wherein the second lateral axis extends within a second plane including the longitudinal center axis; wherein the second force direction bisects a first separation angle between the first plane and the second plane.

[0480] Example 69 includes the subject matter of Example 68, wherein the first lateral axis extends within a first plane including the longitudinal center axis; wherein the first lateral axis extends within a first plane including the longitudinal center axis.

[0481] Example 70 includes a force sensor comprising: a beam comprising a proximal portion and a distal portion, a longitudinal center axis and a neutral axis extending along a surface of the beam parallel to the center axis; a first Wheatstone half-bridge ("half-bridge") comprising a stretch resistor; a second half-bridge comprising a stretch resistor; a third half-bridge comprising a compression resistor; a fourth half-bridge comprising 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 along the surface of the beam parallel to the neutral axis on opposite sides of the neutral axis and are equidistant from the neutral axis.

[0482] Example 71 includes a method for identifying a fault of the force sensor of Example 70, comprising: 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 group to produce four pairs of force measurements, the group 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 a first force component measurement of one of a pair of force measurements and a 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 a second force component measurement of one of a pair of force measurements and a second force component measurement of at least another of the pair of force measurements.

[0483] Those of ordinary skill in the art will recognize many variations, substitutions, and modifications. Therefore, the scope of the present disclosure shall 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 above 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 may be applied to other examples and applications without departing from the scope of the present invention. In the foregoing description, many details are set forth for the purpose of explanation. However, those of ordinary skill in the art will recognize that the present invention may be implemented without using these specific details. In other cases, well-known processes are shown in block diagram form so as not to obscure the description of the present invention with unnecessary details. The same figure numerals may be used to represent different views of the same or similar items in different figures. Therefore, the above description and drawings of the examples according to the present invention are merely illustrative of the principles of the present invention. Therefore, it should be understood that those skilled in the art may make various modifications to the examples without departing from the scope of the present invention, which is defined by the appended claims.

Claims

1. A force sensor, comprising: a beam, a first bridge circuit, a second bridge circuit, a third bridge circuit, and a fourth bridge circuit; wherein the beam comprises a proximal portion, a distal portion and a transverse surface; wherein a longitudinal central axis extends between said proximal portion and said distal portion; wherein the neutral axis extends along the lateral surface parallel to the central axis; wherein a first lateral side axis extends along the lateral surface parallel to the neutral axis; wherein a second lateral side axis extends along the lateral surface parallel to the neutral axis; wherein the first lateral axis and the second lateral axis are located on opposite sides of the neutral axis; wherein a first plane is defined by said central axis and said first lateral side axis; wherein a second plane is defined by said central axis and said second lateral side axis; wherein the first bridge circuit comprises a first bridge tensile strain gauge resistor arranged along the first lateral side axis; wherein the second bridge circuit comprises a second bridge tensile strain gauge resistor arranged along the second lateral side axis; wherein the third bridge circuit comprises a third bridge compression strain gauge resistor arranged along the first lateral side axis; wherein the fourth bridge circuit comprises a fourth bridge compression strain gauge resistor arranged along the second lateral side axis; wherein the strain measured by the first bridge circuit and the third bridge circuit in response to an external force applied to the beam indicates a first plane strain force in the first plane; wherein the strain measured by the second bridge circuit and the fourth bridge circuit in response to the external force applied to the beam indicates a second plane strain force in the second plane; and The combination of the first plane strain force and the second plane strain force indicates the magnitude and direction of the external force applied to the beam.

2. The force sensor according to claim 1, wherein: The first lateral side axis and the second lateral side axis are equidistant from the neutral axis.

3. The force sensor according to claim 1 or 2, wherein: The first plane is separated from the second plane by a separation angle; defining a beam coordinate system having three mutually orthogonal coordinate axes for the beam, wherein the three coordinate axes include a first coordinate axis and a second coordinate axis; The first plane strain force includes a first strain force component on the first coordinate axis and a second strain force component on the second coordinate axis; The second plane strain force includes a third strain force component on the first coordinate axis and a fourth strain force component on the second coordinate axis; The first strain force component, the second strain force component, the third strain force component, and the fourth strain force component are at least partially determined by the separation angle; as well as A combination of the first strain force component, the second strain force component, the third strain force component, and the fourth strain force component indicates the magnitude and the direction of the external force applied to the beam.

4. The force sensor according to claim 3, wherein: The first bridge circuit combination includes any three of the first bridge circuit, the second bridge circuit, the third bridge circuit and the fourth bridge circuit; A second bridge circuit combination includes any three of the first bridge circuit, the second bridge circuit, the third bridge circuit and the fourth bridge circuit, and the second bridge circuit combination is different from the first bridge circuit combination; an output of said first bridge circuit combination providing a first indication of said magnitude and said direction of said external force applied to said beam; an output of the second bridge circuit combination providing a second indication of the magnitude and the direction of the external force applied to the beam; and The first indication and the second indication are redundant.

5. The force sensor according to claim 4, wherein: A difference between the first indication and the second indication indicates a failure of the force sensor.

6. The force sensor according to claim 1 or 2, wherein: The first bridge circuit is a first half-bridge circuit; The second bridge circuit is a second half-bridge circuit; The third bridge circuit is a third half-bridge circuit; and The fourth bridge circuit is a fourth half-bridge circuit.

7. The force sensor according to claim 6, wherein: the first bridge tensile strain gauge resistor being a first proximal tensile strain gauge resistor located at the proximal portion of the beam, and the first half-bridge circuit comprising the first proximal tensile strain gauge resistor and a first distal tensile strain gauge resistor located at the distal portion of the beam; the second bridge tensile strain gauge resistor being a second proximal tensile strain gauge resistor located at the proximal portion of the beam, and the second half-bridge circuit comprising the second proximal tensile strain gauge resistor and a second distal tensile strain gauge resistor located at the distal portion of the beam; the third bridge compression strain gauge resistor being a first proximal compression strain gauge resistor located at the proximal portion of the beam, and the third half-bridge circuit comprising the first proximal compression strain gauge resistor and a first distal compression strain gauge resistor located at the distal portion of the beam; the fourth bridge compression strain gauge resistor is a second proximal compression strain gauge resistor located at the proximal portion of the beam, and the fourth half-bridge circuit includes the second proximal compression strain gauge resistor and a second distal compression strain gauge resistor located at the distal portion of the beam; the first proximal tensile strain gauge resistor, the first distal tensile strain gauge resistor, the first proximal compression strain gauge resistor, and the first distal compression strain gauge resistor being arranged along the first lateral side axis; the second proximal tensile strain gauge resistor, the second distal tensile strain gauge resistor, the second proximal compression strain gauge resistor, and the second distal compression strain gauge resistor being arranged along the second lateral side axis; one of the first proximal tensile strain gauge resistor and the first distal tensile strain gauge resistor being located between the first proximal compressive strain gauge resistor and the first distal compressive strain gauge resistor along the first lateral side axis; as well as One of the second proximal tensile strain gauge resistor and the second distal tensile strain gauge resistor is located between the second proximal compressive strain gauge resistor and the second distal compressive strain gauge resistor along the second lateral side axis.

8. The force sensor according to claim 7, wherein: one of the first proximal compression strain gauge resistor and the first distal compression strain gauge resistor being located between the first proximal tensile strain gauge resistor and the first distal tensile strain gauge resistor along the first lateral side axis; as well as One of the second proximal compression strain gauge resistor and the second distal compression strain gauge resistor is located between the second proximal tensile strain gauge resistor and the second distal tensile strain gauge resistor along the second lateral side axis.

9. The force sensor according to claim 7, wherein: the first proximal tensile strain gauge resistor and the second proximal tensile strain gauge resistor being positioned at matching longitudinal locations on the transverse surface of the beam; the first distal tensile strain gauge resistor and the second distal tensile strain gauge resistor being positioned at matching longitudinal positions on the transverse surface of the beam; the first proximal compressive strain gauge resistor and the second proximal compressive strain gauge resistor being positioned at matching longitudinal positions on the lateral surface of the beam; and The first distal compression strain gauge resistor and the second distal compression strain gauge resistor are positioned at matching longitudinal positions on the lateral surface of the beam.

10. The force sensor according to claim 1 or 2, wherein: The force sensor further comprises a metal sheet laid on the beam; and Each of the tensile strain gauge resistors and each of the compressive strain gauge resistors are coupled to the metal sheet.

11. A method for controlling an instrument, the method comprising: receiving at a computer system an input from a force sensor coupled to the instrument, wherein the force sensor comprises a beam, a first bridge circuit, a second bridge circuit, a third bridge circuit and a fourth bridge circuit, wherein the beam comprises a proximal portion, a distal portion and a transverse surface, wherein a longitudinal central axis extends between said proximal portion and said distal portion, wherein the neutral axis extends along the transverse surface parallel to the central axis, wherein a first lateral lateral axis extends along the lateral surface parallel to the neutral axis, wherein a second lateral axis extends along the lateral surface parallel to the neutral axis, wherein the first lateral axis and the second lateral axis are located on opposite sides of the neutral axis, wherein a first plane is defined by said central axis and said first lateral side axis, wherein a second plane is defined by said central axis and said second lateral side axis, wherein the first bridge circuit comprises a first bridge tensile strain gauge resistor arranged along the first lateral side axis, wherein the second bridge circuit comprises a second bridge tensile strain gauge resistor arranged along the second lateral side axis, wherein the third bridge circuit comprises a third bridge compression strain gauge resistor arranged along the first lateral side axis, wherein the fourth bridge circuit comprises a fourth bridge compression strain gauge resistor arranged along the second lateral side axis, The output of the force sensor includes at least a first bridge circuit voltage and a second bridge circuit voltage. wherein the first bridge circuit voltage comes from the first bridge circuit or the third bridge circuit, and Wherein, the second bridge circuit voltage comes from the second bridge circuit or the fourth bridge circuit; determining, via the computer system and based at least in part on the first bridge circuit voltage, a first plane strain force in the first plane; determining, via the computer system and based at least in part on the second bridge circuit voltage, a second plane strain force in the second plane; determining, via the computer system and based on the first plane strain force and the second plane strain force, one or more sensed characteristics of an external force applied to the beam, and Based at least in part on the one or more sensed characteristics of the external force applied to the beam, a display of a message is provided to an operator of the instrument.

12. The method according to claim 11, wherein: The first lateral side axis and the second lateral side axis are equidistant from the neutral axis.

13. The method according to claim 11 or 12, wherein: The first plane is separated from the second plane by a separation angle; defining a beam coordinate system having three mutually orthogonal coordinate axes for the beam, wherein the three coordinate axes include a first coordinate axis and a second coordinate axis; as well as Determining the one or more sensed characteristics of the external force applied to the beam comprises: determining, via the computer system and based at least in part on the separation angle, a first strain force component of the first plane strain force in the first coordinate axis and a second strain force component of the first plane strain force in the second coordinate axis, determining, via the computer system and based at least in part on the separation angle, a third strain force component of the second plane strain force on the first coordinate axis and a fourth strain force component of the second plane strain force on the second coordinate axis, determining, via the computer system, a sensed direction and a sensed magnitude of the external force by combining the first strain component, the second strain component, the third strain component, and the fourth strain component, and The display is based at least in part on the sensed direction and the sensed magnitude of the external force.

14. The method according to claim 13, wherein: determining the sensed direction and the sensed magnitude of the external force comprises outputting a first indication of the sensed direction and the sensed magnitude of the external force and a second indication of the sensed direction and the sensed magnitude of the external force; The first indication is an output of a first bridge circuit combination, the first bridge circuit combination including any three of the first bridge circuit, the second bridge circuit, the third bridge circuit, and the fourth bridge circuit; and The second indication is an output of a second bridge circuit combination, the second bridge circuit combination including any three of the first bridge circuit, the second bridge circuit, the third bridge circuit and the fourth bridge circuit; the second bridge circuit combination is different from the first bridge circuit combination; and The second indication is redundant with respect to the first indication.

15. The method according to claim 14, wherein: The method further includes outputting an indication of a failure of the force sensor in the event that there is a difference between the first indication and the second indication.

16. The method according to claim 11 or 12, wherein: The first bridge circuit is a first half-bridge circuit; The second bridge circuit is a second half-bridge circuit; The third bridge circuit is a third half-bridge circuit; and The fourth bridge circuit is a fourth half-bridge circuit.

17. The method of claim 16, wherein: the first bridge tensile strain gauge resistor being a first proximal tensile strain gauge resistor located at the proximal portion of the beam, and the first half-bridge circuit comprising the first proximal tensile strain gauge resistor and a first distal tensile strain gauge resistor located at the distal portion of the beam; the second bridge tensile strain gauge resistor being a second proximal tensile strain gauge resistor located at the proximal portion of the beam, and the second half-bridge circuit comprising the second proximal tensile strain gauge resistor and a second distal tensile strain gauge resistor located at the distal portion of the beam; the third bridge compression strain gauge resistor being a first proximal compression strain gauge resistor located at the proximal portion of the beam, and the third half-bridge circuit comprising the first proximal compression strain gauge resistor and a first distal compression strain gauge resistor located at the distal portion of the beam; the fourth bridge compression strain gauge resistor is a second proximal compression strain gauge resistor located at the proximal portion of the beam, and the fourth half-bridge circuit includes the second proximal compression strain gauge resistor and a second distal compression strain gauge resistor located at the distal portion of the beam; the first proximal tensile strain gauge resistor, the first distal tensile strain gauge resistor, the first proximal compression strain gauge resistor, and the first distal compression strain gauge resistor being arranged along the first lateral side axis; the second proximal tensile strain gauge resistor, the second distal tensile strain gauge resistor, the second proximal compression strain gauge resistor, and the second distal compression strain gauge resistor being arranged along the second lateral side axis; one of the first proximal tensile strain gauge resistor and the first distal tensile strain gauge resistor being located between the first proximal compressive strain gauge resistor and the first distal compressive strain gauge resistor along the first lateral side axis; as well as One of the second proximal tensile strain gauge resistor and the second distal tensile strain gauge resistor is located between the second proximal compressive strain gauge resistor and the second distal compressive strain gauge resistor along the second lateral side axis.

18. The method of claim 17, wherein: one of the first proximal compression strain gauge resistor and the first distal compression strain gauge resistor being located between the first proximal tensile strain gauge resistor and the first distal tensile strain gauge resistor along the first lateral side axis; as well as One of the second proximal compression strain gauge resistor and the second distal compression strain gauge resistor is located between the second proximal tensile strain gauge resistor and the second distal tensile strain gauge resistor along the second lateral side axis.

19. The method of claim 17, wherein: the first proximal tensile strain gauge resistor and the second proximal tensile strain gauge resistor being positioned at matching longitudinal locations on the transverse surface of the beam; the first distal tensile strain gauge resistor and the second distal tensile strain gauge resistor being positioned at matching longitudinal positions on the transverse surface of the beam; the first proximal compressive strain gauge resistor and the second proximal compressive strain gauge resistor being positioned at matching longitudinal positions on the lateral surface of the beam; and The first distal compression strain gauge resistor and the second distal compression strain gauge resistor are positioned at matching longitudinal positions on the lateral surface of the beam.

20. The method according to claim 11 or 12, wherein: The force sensor further comprises a metal sheet laid on the beam; and The metal sheet includes the tensile strain gauge resistor and the compressive strain gauge resistor.

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