MEASURING INSTRUMENT WITH ARC MOVEMENT AND CORRECTION PROCESS

Abstract

A measuring instrument includes a movable section configured to rotate in an arcuate motion about a pivot section, and an electronic position encoder configured to measure an absolute relative position between a detector section and a scale section, one of which forms a part of the movable section. A maximum range of motion of the movable encoder section and a maximum absolute measurement range are each less than 360 degrees. An offset value is determined based at least in part on detector signals received from the detector section corresponding to a radial offset (e.g., of the scale section or the detector section). The determined offset value is used to correct one or more values ​​used to determine a relative position between the detector section and the scale section (e.g.,a spatial step or another spatial value of the scale segment).

Description

GENERAL STATE OF THE ARTTechnical field

[0001] This disclosure relates to metrology and, more particularly, to measuring instruments which may include a movable member (e.g., a pin) that rotates in an arcuate motion about a pivoting portion and for which corresponding measurements are determined by an electronic position encoder, and for which some examples of such measuring instruments include test indicators, lever-type dial gauges, lever-type vernier indicators, etc. Description of related technology

[0002] Certain measuring instruments include a movable component (e.g., including a pin) that moves in an arcuate motion when in use (e.g., for determining measurements of a workpiece under inspection). As an example, U.S. Patent Publication No. 2022 / 0341733 (the '733 Publication) describes a test indicator (e.g., sometimes referred to as a lever-type dial indicator, lever-type vernier indicator, etc.) that includes a pin that rotates about a pivoting portion with a corresponding angle of rotation (e.g., in an arcuate motion). Rotation of the pin results in movement of a sector gear on an opposite side of the pivoting portion, which correspondingly rotates an encoder that detects an angle of rotation. As described, such test indicators can be used to inspect workpieces (e.g.,with the pin pressed against a surface of the workpiece), such as measuring minute displacements such as circumferential deflection, total deflection, flatness and parallelism, and for precise comparison testing such as determining a machining error of a machined workpiece, etc.

[0003] In certain implementations, it may be desirable for such measuring instruments to include encoders (e.g., for measuring such arc motions) that provide desirable combinations of features, such as combinations of compact size, high resolution, accuracy, low cost, contamination resistance, etc. Configurations of encoders that provide improved combinations of such features in such measuring instruments would be desirable. SUMMARY

[0004] This Summary is provided to introduce, in a simplified form, a selection of concepts further described below in the Detailed Description. This Summary is neither intended to identify key features of the claimed subject matter nor to be used as an aid in determining the scope of the claimed subject matter.

[0005] According to one aspect, a measuring instrument is provided that includes a movable portion and an electronic position encoder. The movable portion is configured to rotate in an arcuate motion about a pivot portion and includes a movable encoder portion MEP.

[0006] The electronic position encoder is configured to measure an absolute relative position between a detector portion and a scale portion, for example, along an arcuate movement direction. The movable encoder portion MEP of the movable portion includes one of the detector portion or the scale portion. The scale portion extends along a scale direction and includes a first scale element portion comprising first signal-modulating scale elements; and a second scale element portion comprising second signal-modulating scale elements. The detector portion is configured to be proximate to the scale portion during a relative movement between the detector portion and the scale portion resulting from the arcuate movement of the movable encoder portion MEP.The detector section includes a field-generating section configured to generate a changing magnetic flux in response to drive signals; and a sensing section. The sensing section includes a first sensing element section comprising a first set of first sensing elements and arranged in a first track section with the first scale element section; and a second sensing element section comprising a first set of second sensing elements and arranged in a second track section with the second scale element section.

[0007] In various implementations, a maximum range of motion of the arcuate movement of the movable encoder portion is less than 360 degrees and the first scale element portion is arranged with a central reference point at a first radial distance RD1 from the pivoting portion and the second scale element portion is arranged with a central reference point at a second radial distance RD2 from the pivoting portion, wherein the ratio of RD1 / RD2 is at least 1.4.

[0008] According to another aspect, a method of operating the measuring instrument including the movable portion and the electronic position encoder is provided. The method generally includes two steps. The first step includes providing drive signals to cause the field-generating portion to generate a changing magnetic flux. The second step includes receiving detector signals from the detector portion, the detector signals including: detector signals from the first set of first sensing elements cooperating with first signal-modulating scale elements; and detector signals from the first set of second sensing elements cooperating with second signal-modulating scale elements.

[0009] In various implementations, the measuring instrument further includes a signal processing configuration configured to: provide drive signals to cause the field-generating portion of the detector portion to generate a changing magnetic flux; receive detector signals from the detector portion, the detector signals comprising: detector signals from the first set of first sensing elements cooperating with first signal-modulating scale elements; and detector signals from the first set of second sensing elements cooperating with second signal-modulating scale elements; determine an offset value corresponding to a radial offset of at least one of the scale portion or the detector portion based at least in part on the received detector signals;and using the determined offset value to correct one or more values ​​used to determine a relative position between the detector portion and the scale portion;

[0010] According to another aspect, a method of operating the measuring instrument including the movable section and an electronic position encoder is provided. The method generally includes four steps. The first step includes providing drive signals to cause the field-generating section to generate a changing magnetic flux. The second step includes receiving detector signals from the detector section, the detector signals comprising: detector signals from the first set of first sensing elements cooperating with first signal-modulating scale elements; and detector signals from the first set of second sensing elements cooperating with second signal-modulating scale elements.The third step includes determining an offset value corresponding to a radial offset of at least one of the scale portion or the detector portion based at least in part on the received detector signals. The fourth step includes using the determined offset value to correct one or more values ​​used to determine a relative position between the detector portion and the scale portion.

[0011] According to another aspect, the electronic position sensor is provided, which is configured to measure an absolute relative position between the detector section and the scale section, for example, along an arcuate motion direction. The electronic position sensor is configured to be used in the measuring instrument comprising the movable section configured to rotate in an arcuate motion around a pivot section. BRIEF DESCRIPTION OF THE DRAWINGS Fig. 1 is a diagram of a measuring instrument including an electronic position sensor with a transducer including a detector section and a scale section. Fig. 2 is a diagram showing a further detail of an implementation of a measuring instrument, such as that of the Fig. 1, illustrated. Fig. 3A is a diagram of an implementation of a portion of a transducer configured to be used with an arcuate motion between a detector portion and a scale portion included in the measuring instrument of the Fig. 2 can be used and has a first large separation of the scale tracks. Fig. 3B is an explanatory list of the Fig. 3A used reference symbols. Fig. 4 is a diagram showing certain dimensions and characteristics of the measuring instrument of the Fig. 2 and the converter of the Fig. 3A illustrates. Fig. Figure 5 is a diagram illustrating certain signals resulting from the operation of the converter of the Fig. 3A and Fig. 4 with arc movement between the detector section and the scale section. Fig. Figure 6 is a diagram of an implementation of a portion of a transducer configured to be used with an arcuate motion between a detector portion and a scale portion used in the measuring instrument of the Fig. 2 can be used and a relatively smaller separation of the scale tracks compared to the implementation of the Fig. 3A. Fig. 7 is a diagram showing certain dimensions and characteristics of the measuring instrument of the Fig. 2 and the converter of the Fig. 6 illustrates. Fig. 8A-8B are diagrams showing an offset with respect to certain features of the Fig. 6 and Fig. 7 illustrate. Fig. 9A-9C are graphs of curves illustrating certain data resulting from the operations and a correction process of the converter of the Fig. 6 and Fig. 7, with an offset as shown in the Fig. 8A-8B. Fig. 10A-10B are diagrams showing an offset with respect to certain features of the Fig. 3A and Fig. 4 illustrate. Fig. 11A-11C are graphs of waveforms illustrating certain data resulting from the operations and a correction process of the converter of the Fig. 3A and Fig. 4, with an offset as shown in the Fig. 10A-10B. Fig. 12 is a diagram showing certain dimensions and characteristics of the measuring instrument of the Fig. 2 and a portion of a transducer configured to be used with an arcuate movement between a detector portion and a scale portion included in the measuring instrument of the Fig. 2 and has a second large separation of the scale tracks. Fig. 13A-13B are diagrams showing an offset with respect to certain features of the Fig. 12 illustrate. Fig. 14A-14C are graphs of waveforms illustrating certain data resulting from the operations and a correction process of the converter of the Fig. 12, with an offset as shown in the Fig. 13A-13B. Fig. 15 is a diagram showing certain dimensions and characteristics of the measuring instrument of the Fig. 2 and a portion of a transducer configured to be used with an arcuate movement between a detector portion and a scale portion included in the measuring instrument of the Fig. 2 can be used and has a third large separation of the scale tracks. Fig. 16A-16B are diagrams illustrating an offset in a first direction with respect to certain features of the Fig. 15 illustrate. Fig. 17A-17B are graphs of waveforms illustrating certain data resulting from the operations and a correction process of the converter of the Fig. 15, with an offset in the first direction as shown in the Fig. 16A-16B. Fig. 18A-18B are diagrams illustrating an offset in a second direction with respect to certain features of the Fig. 15 illustrate. Fig. 19A-19B are graphs of curves illustrating certain data resulting from the operations and a correction process of the converter of the Fig. 15, with an offset in the second direction, as shown in the Fig. 18A-18B. Fig. 20 is a flowchart illustrating a method of operating an arc-motion measuring instrument to determine a relative position between a detector portion and a scale portion. Fig. 21 is a flowchart illustrating a method for a correction process for a measuring instrument with arc movement. Fig. Figure 22 is a schematic plan view diagram illustrating certain features of a representative prior art electronic position encoder configured to be used with linear movement between a detector portion and a scale portion, presented as background information relevant to various principles described herein. DETAILED DESCRIPTION

[0012] Fig. 1 is a block diagram of exemplary components of a measuring instrument 100 (e.g., a test indicator) having an electronic absolute position encoder 101. In various implementations, the electronic absolute position encoder 101 includes a scale portion 170 and a detector portion 167, which together form a transducer (TDR). As described in more detail below, the encoder 101, as used herein, is an absolute (ABS) position encoder that utilizes two or more encoder tracks to provide absolute positioning (i.e., each position within the absolute range of the encoder 101 has a unique combination of signals). In general, the ABS encoder may be more robust than the incremental (INC) encoder (e.g., which counts increments while moving) and may therefore be more desirable for certain implementations (e.g., may tolerate one power cycle without loss of position, etc.).The measuring instrument 100 includes suitable user interface features, such as a display 138 and / or user-operable controls 136 (e.g., switches, buttons, etc.). The measuring instrument 100 may additionally include a power supply 165.

[0013] All of these elements of the measuring instrument 100 and / or the transmitter 101 are coupled to a signal processing configuration 166 (e.g., including one or more signal processors), which in various implementations may be implemented as signal processing and display electronics in an integrated circuit (IC) chip(s). The signal processing configuration 166 receives detector signals from the detector portion 167 and processes the detector signals to determine an absolute position of the detector portion 167 along the scale portion 170. It should be understood that the signal processing configuration 166 may include any combination of signal processing and physical circuitry. In various implementations, the signal processing configuration 166 and the detector portion 167 may be included as part of an electronic assembly 160 (e.g., as disposed on a substrate, etc.).

[0014] Fig. Figure 2 is a diagram showing a further detail of an implementation of a measuring instrument 100 such as that in Fig. 1. As will be described in more detail below, the measuring instrument 100 includes an electronic position sensor 101 which includes a transducer TDR. In the example of Fig. 2, the measuring instrument 100 is a test indicator (e.g., sometimes referred to as a lever indicator, lever-shaped dial gauge, lever-shaped vernier indicator, etc.). In various implementations, certain aspects of the mechanical design and operation of the measuring instrument 100 may be similar to certain prior test indicators, such as those described in the previously incorporated '733 publication.

[0015] As in Fig. 2, a contact section CPN (e.g., a pin) is coupled to a pivoting section PPN and rotates around it (e.g., rotates around a pivot point PPT of the pivoting section PPN) at a corresponding angle (e.g., in an arcuate motion). The contact section CPN includes at one end a contact point CPT, such as can be used to contact workpieces for performing measuring operations (e.g., for measuring displacements and / or dimensions, etc. of the workpiece). A measurement can be displayed on a digital display (e.g., display 138 of the Fig. 1) which may be mounted on a measuring instrument body MIB or another location of the measuring instrument 100. Certain operating elements (e.g. operating elements 136 of the Fig. 1) be provided on the measuring instrument 100.

[0016] A movable portion MPN of the measuring instrument 100 includes the contact portion CPN on a first side of the pivoting portion PPN and a movable encoder portion support member MEPSM supporting a movable encoder portion MEP on a second side of the pivoting portion PPN. The movable portion MPN is configured such that a workpiece measuring operation (e.g., for measuring a workpiece) that causes the contact portion CPN to rotate relative to the pivoting portion PPN (e.g., resulting from the contact point CPT touching or moving along a surface of a workpiece) correspondingly causes the support member MEPSM and the movable encoder portion MEP to rotate in an arcuate motion ARCM (e.g., in an arcuate motion direction ARCD). In the measuring instrument 100, a maximum angular motion range θ is MAXthe arcuate movement ARCM of the movable encoder section MEP is less than 360 degrees (and may, for example, and in some implementations, be less than 90 degrees, or 45 degrees, or 15 degrees, etc.). Such relatively smaller angular movement ranges are typical for certain types of measuring instruments, particularly for applications where only relatively small deflections of the contact section CPM (e.g., a pin) are used to measure a workpiece.

[0017] In various implementations, the movable encoder portion MEP may include one of the detector portion 167 or the scale portion 170 (e.g., as described above with respect to Fig. 1 and as described below with respect to Fig. 3A). The other of the detector portion 167 or the scale portion 170, which is not included in the movable encoder portion MEP, is included in a fixed encoder portion FEP (not shown, but may be fixed, for example, to the measuring instrument body MIB) at a location near the movable encoder portion MEP. In a specific illustrative example, the movable encoder portion MEP may be arranged parallel to and facing the fixed encoder portion FEP, and a front side of the movable encoder portion MEP facing the fixed encoder portion FEP may be separated from the fixed encoder portion FEP by a gap (e.g., on the order of 0.1 mm-0.2 mm) along the z-axis direction. Regardless of whether the detector portion 167 is included in the movable encoder portion MEP or the fixed encoder portion FEP, the front side of the detector portion 167 (e.g.,including its conductor components) must be covered by an insulating coating.

[0018] In the orientation of the Fig. 2, the fixed encoder section FEP can be located directly below the movable encoder section MEP (and is thus in Fig. 2 not visible). The fixed encoder section FEP and the movable encoder section MEP (which include, for example, the detector section 167 and the scale section 170) respectively form the transducer TDR. As described above, the relative movement between the movable encoder section MEP and the fixed encoder section FEP (i.e., corresponding to a relative movement between the detector section 167 and the scale section 170) results from a movement of the movable encoder section MEP in the arcuate direction of travel ARCD, as a consequence of movements of the contact section CPN (e.g., as part of workpiece measuring operations).

[0019] As in Fig. 2, a first and a second movement limit indicator ML1 and ML2 are illustrated as dashed lines, which represent a maximum movement range of the arc movement ARCM (e.g., including the movable encoder section MEP) and as the maximum angular movement range θ MAX The electronic position encoder 101 is an absolute position encoder that has two or more encoder tracks (e.g. see Fig. 3A) to provide absolute positioning (i.e. for which each position has a unique combination of signals) corresponding to an absolute angle measurement range θ ABS which is described in more detail below. In the example of the Fig. 2 is the absolute angle measuring range θ ABS as approximately equal to the maximum angular movement range θ MAX stated, although it is understood that in alternative implementations the absolute angle measuring range θ ABSand the maximum angular movement range θ MAX may be different (e.g. in most such implementations where the absolute angle measuring range θ ABS larger than the maximum angle measuring range θ MAX and in all cases where the absolute angle measuring range θ ABS less than 360 degrees). It should be noted that for certain implementations the absolute angle measuring range θ ABS and the maximum angular movement range θ MAX in the example of Fig. 2 are shown for illustrative purposes and may not be to scale.

[0020] An end point ENDPT at the end of the movable encoder section support member MEPSM also corresponds to an end point of the movable section MPN. The end point ENDPT is located at an opposite end of the movable section MPN relative to the contact point CPT at the end of the contact section CPN. As mentioned herein, the contact section CPN and the contact point CPT are located on a first side of the pivoting section PPN, and the support member MEPSM, the movable encoder section MEP, and the end point ENDPT are located on a second side of the pivoting section PPN.

[0021] It is understood that the measuring instrument of the Fig. 1 and Fig. 2 is one of several applications that typically implement an electronic position encoder that has been developed over several years to provide a relatively optimized combination of compact size, economical operation (e.g., for long battery life), high resolution and high measurement accuracy, low cost, robustness to contamination, etc. Even small improvements in any one of these factors in any one of these applications are highly desirable but difficult to achieve, particularly given the design constraints imposed to achieve commercial success in the various applications. The principles disclosed herein provide improvements in certain of these factors for various applications.

[0022] Fig. 22 is a plan view diagram schematically illustrating certain features of a representative prior art inductive electronic position sensor shown in U.S. Patent No. 6,011,389 (the '389 patent), which is hereby incorporated by reference in its entirety and is presented as background information relevant to various principles disclosed elsewhere herein. Fig. 22 further includes reference number annotations to show the comparable reference numbers or symbols used to designate comparable elements in other figures included herein. In the following abbreviated description, which is based on the disclosure of the '389 patent, some of the comparable reference numbers or symbols in other figures of the present disclosure are shown in parentheses next to the original reference numbers from the '389 patent. A complete description of Fig. 22 of the prior art is found in the '389 patent. Therefore, only an abbreviated description (e.g., including certain teachings from the '389 patent relevant to the present disclosure) is included here.

[0023] As disclosed in the '389 patent, a converter such as that shown in Fig. 22, at least two substantially coplanar paths of wire or windings. A transmitter winding 102 (PRTFGE''') forms one large planar loop. In this example, the transmitter winding 102 forms an entire field generating section PRTFGE'''. A receiver winding 104 (PRTSEN''', SETSEN''') lying substantially in the same plane as the transmitter winding 102 is wound in one direction, as indicated by the arrows, in a zigzag or sinusoidal pattern and then in a reverse direction, as indicated by the arrows, such that the winding crosses itself to form alternating loops 106 (SEN+''') and 108 (SEN-''') interposed therebetween, as shown. As a result, each of the alternating loops 106 (SEN+''') and 108 (SEN-''') of the receiver winding 104 (PRTSEN''', SETSEN''') has a different winding direction compared to adjacent loops.By applying a varying (changing) current to the transmitter winding 102 (PRTFGE'''), the transmitter winding generates a time-varying magnetic field (a changing magnetic flux) that extends through the loops 106 (SEN+''') and 108 (SEN-''') of the receiver winding 104 (PRTSEN''', SETSEN'''). In various implementations, the loops 106 (SEN+''') and 108 (SEN-''') may be referred to as a set of sensing elements (SETSEN''') of a sensing section (PRTSEN''').

[0024] If a scale section (170") or scale pattern 112 (180''') (one segment of which is in Fig. 22 by alternating long dashed lines and short dashed lines), including a conductive object (e.g., a signal modulating element such as a conductive plate 114 (SME'''), some of which are indicated using short dashed lines on the scale pattern 112 in Fig. 22), is moved close (proximal) to the detector section (167'''), the varying magnetic field generated by the transmitter winding 102 (PRTFGE''') induces eddy currents in the conductive object, which in turn builds up a magnetic field from the object that opposes the varying transmitter magnetic field (the changing magnetic flux). This changes or perturbs the magnetic flux received by the receiver winding 104 (PRTSEN'''), causing the receiver winding to output a non-zero EMF signal (a voltage) at the output terminals V+ and V- of the receiver winding 104, which changes polarity as the conductive object moves between the "+" and "-" loops 106 (SEN+'') and 108 (SEN-''').

[0025] The distance between the location of two loops of the same polarity (e.g., between the location of one loop 106 (SEN+''') to the location of the next loop 106 (SEN+''')) is defined as a linear spatial step (which may also be referred to, for example, as a pitch or wavelength) 110 (WSEN''') of the set of sensing elements (SETSEN''') and, in certain implementations, may be equal to a linear spatial step (which may also be referred to, for example, as a pitch or wavelength) 110 (WSME''') of the scale pattern (180''') of the scale section (170''') as arranged along the scale direction SCD''' and / or the measurement axis direction MA'''. It can be seen that each loop 106 (SEN+''') and / or 108 (SEN-''') along the measuring axis direction (MA'''), which can also be referred to as the scale direction SCD''', has a length or maximum dimension of 0.5* (WSEN'''). If the conductive object described above (e.g.a conductive plate 114 (SME''')) is located near the receiver winding 104 (PRTSEN''') and is continuously changed in position along a measuring axis 300 (MA''), the AC amplitude of the signal emitted by the receiver winding (PRTSEN''') varies continuously and periodically with the linear spatial step (which may also be referred to as pitch or wavelength, for example) 110 (WSME''') due to the periodic variation of the loops 106 (SEN+''') and 108 (SEN-''') and local disturbance of the transmitted magnetic field caused by the conductive object (e.g., a conductive plate 114 (SME''')). The signal emitted by the receiver winding (PRTSEN''') can thus be used (e.g., processed) to indicate a relative position between the detector section (167''') and the scale section (170'''). It is understood that the signal emitted by the receiver winding (PRTSEN''') can be used (e.g., processed) to indicate a relative position between the detector section (167''') and the scale section (170'''). Fig. 22 and described above, transmitter winding 102 (PRTFGE''') and receiver winding 104 (PRTSEN''') are an example of an implementation of prior art elements referred to as detector section (167''').

[0026] Fig. Figure 3A is a diagram of an implementation of a portion of a transducer TDR configured to be used with an arcuate movement ARCM between a detector portion 167 and a scale portion 170 incorporated in the electronic position encoder 101 of the measuring instrument 100 of the Fig. 1 and Fig. 2 can be used. The TDR converter uses two track sections TR1 and TR2, as shown in Fig. 3A illustrates. Fig. 3B is an explanatory list of the Fig. 3A used reference symbols.

[0027] It will be understood that certain aspects of the field generating elements and sensing elements of a detector section (e.g., detector section 167, etc.) as described herein are based at least in part on principles as described above with respect to Fig. 22 described, worked and understood. In the implementation of the Fig. 3A, the scale section 170, the detector section 167 and a signal processing configuration 166 (e.g., the Fig. 1 and Fig. 2) together to provide the electronic position encoder 101, which is usable to determine a relative position between two elements (e.g., between the detector portion 167 and the scale portion 170 and / or elements attached thereto), such as along an arcuate movement direction. In various implementations, the detector portion 167 is formed on a detector substrate and the scale portion 170, including the periodic scale pattern 180, is formed on a scale substrate, and wherein measurement operations involve relative movements between the two substrates (which may, for example, be relatively planar and parallel to each other). In various implementations, the detector portion 167 and the scale portion 170 may generally lie in respective planes extending along the x-axis direction and the y-axis direction, with a z-axis direction orthogonal to the planes.

[0028] In various implementations, the scale section 170 extends along the scale direction SCD and includes a first scale element section PRTSC1 including first signal modulating elements SME1 and a second scale element section PRTSC2 including a second signal modulating element SME2. The first signal modulating elements SME1 are arranged along the scale direction SCD according to and form a first signal modulating element pattern PATSME1. The second signal modulating elements SME2 are arranged along the scale direction SCD according to and form a second signal modulating element pattern PATSME2. The first signal modulating element pattern PATSME1 and the second signal modulating element pattern PATSME2 are each part of a periodic scale pattern 180 of the scale section 170. In various implementations, the periodic scale pattern 180 may alternatively be referred to as a signal modulating pattern 180.In various implementations, the first and / or second signal modulating elements SME1 and SME2 (i.e., as included in the first and second scale element portions PRTSC1 and PRTSC2) may be fabricated on a scale substrate (e.g., using known printed circuit board fabrication techniques).

[0029] The relative movement between the detector portion 167 and the scale portion 170 (e.g., in an arcuate direction of travel) may indicate relative positions and / or measurements (e.g., with respect to the relative positions between the detector portion 167 and the scale portion 170). As discussed above with respect to the Fig. 1 and Fig. 2, a measured relative position or dimension may be displayed on a display 138 (e.g., a digital display). In various implementations, controls 136, such as a power switch and other optional control buttons, may be included.

[0030] As in Fig. As shown in Figure 3A, the detector section 167 may include a field-generating section PRTFGE and a sensing section PRTSEN arranged along the scale direction SCD. In various implementations, with respect to the sensing section PRTSEN, the scale direction SCD may also or alternatively be referred to as the sensing section direction SPD. The field-generating section PRTFGE includes a first field-generating element section PRTFGE1 and a second field-generating element section PRTFGE2. The sensing section PRTSEN includes a first sensing element section PRTSEN1 and a second sensing element section PRTSEN2.As described in more detail below, the first sensing element section PRTSEN1 is configured to cooperate with the first field generating element section PRTFGE1 and the first scale element section PRTSC1 as part of a first track section TR1, and the second sensing element section PRTSEN2 is configured to cooperate with the second field generating element section PRTFGE2 and the second scale element section PRTSC2 as part of a second track section TR2.

[0031] In various implementations, the field-generating section PRTFGE may include a number of elongated sections ELP and end sections EDP. The elongated sections may extend generally along the scale direction SCD and thus run parallel thereto, while the end sections may run generally transverse (e.g., perpendicular) to the scale direction SCD. The elongated sections ELP and the end sections EDP may, in combination, form regions (in which, for example, a changing magnetic flux may be generated by current flow through the elongated sections and end sections resulting from drive signals), and wherein the regions may include certain of the sensing elements.

[0032] In various implementations, the field-generating section PRTFGE may include first and second field-generating element sections PRTFGE1 and PRTFGE2. The first field-generating element section PRTFGE1 is configured to cooperate with the first sensing element section PRTSEN1 and with first signal-modulating elements SME1 of the first scale element section PRTSC1. The first field-generating element section PRTFGE1 includes elongated sections ELP1A, ELP1B, ELP1C, ELP1D and end sections EDP1A, EDP1B, EDP1C, EDP1D (which in some implementations may be considered, for example, as forming two field-generating element loops, as in a configuration of Fig. 8, and / or otherwise as a single field-generating element loop forming two loops in such a configuration to form two interior regions). More specifically, the elongated sections ELP1A and ELP1B and the end sections EDP1A and EDP1D can be considered as a first half-loop FGE1FHL of a first field-generating element having an interior region FGE1FHIA. The interior region FGE1FHIA of the first half of the first field-generating element is configured to be aligned with the pattern section FHPP1 of a first half of the first scale element section PRTSC1. The elongated sections ELP1C and ELP1D and the end sections EDP1C and EDP1B can be considered as forming a second half-loop FGE1SHL of the first field-generating element having an interior space FGE1SHIA.The inner region FGE1SHIA of the second half of the first field generating element is configured to be aligned with the pattern section SHPP1 of a second half of the first scale element section PRTSC1.

[0033] In various implementations, an end portion EDP (e.g., or another part of the first field-generating element portion PRTFGE1) may include a port or other connection configuration. For example, the end portion EDP1B may be split in two, such as with two provided contact points. The contact points may be used to receive drive signals and may be provided at locations where signal lines / circuit traces from the processing portion 166 may connect, etc. In various implementations, such a port may be representative of a general connection configuration, such as being coupled to field-generating drive electronics. Such field-generating drive electronics may, in various implementations, include electronic components such as capacitors, transistors, etc., and may be at least partially or fully included in or coupled to the processing section 166 to provide the drive signals to cause the first field generating element section PRTFGE1 to generate a changing magnetic flux.

[0034] During operation, alternating current may be provided, although for the sake of simplicity of the following description, only one current direction is described (e.g., for the purposes of an example of one direction and / or as may occur in configurations where diodes or other components / configurations are provided to limit current flow to one direction). For example, current (as provided by drive signals) may flow through the following sequence of sections (e.g., in the following order for current in one direction), including: end section EDP1D; elongated section ELP1A; end section EDP1A; elongated section ELP1B; and end section EDP1B; elongated section ELP1C; end section EDP1C; and elongated section ELP1D. According to this example of current flow, it is understood that the current flows in the same direction (e.g., from left to right in the illustration of the Fig. 3A) passes through the elongated sections (i.e., the elongated sections ELP1A and ELP1C) at the outer limits of the configuration and in the same direction (i.e., from right to left in the illustration of the Fig. 3A) passes through the elongated sections (i.e., the elongated sections ELP1B and ELP1D) in the center of the configuration. This also corresponds to a counterclockwise current flow around the first half-loop FGE1FHL of the first field-generating element and a clockwise current flow around the first half-loop FGE1SHL of the first field-generating element (i.e., the directions of current flow through the respective loops are referred to as opposite, with corresponding opposite polarities of the resulting magnetic flux from each respective loop).

[0035] Such directions / orientations / polarities of the current flow and the corresponding magnetic flux may be advantageous for certain configurations, such as resulting in generated signals in first sensing elements SEN1 (e.g., such as at least partially aligned with the interior regions FGE1FHIA and FGE1SHIA of the first field-generating element section PRTFGE1). In one aspect, it should be noted that with respect to the opposite current flow directions and corresponding opposite polarities of the magnetic flux generated by the respective loops FGE1FHL and FGE1SHL of the first and second half pattern sections FHPP1 and SHPP1, which are spatially offset, result in detector signals (i.e., from the first sensing element section PRTSEN1) indicating the position of the first sensing element section PRTSEN1 relative to the first scale element section PRTSC1.

[0036] The second field-generating element section PRTFGE2 is configured to cooperate with the second sensing element section PRTSEN2 and with second signal-modulating elements SME2 of the second scale element section PRTSC2. The second field-generating element section PRTFGE2 includes elongated sections ELP2A, ELP2B, ELP2C, ELP2D and end sections EDP2A, EDP2B, EDP2C, EDP2D (which in some implementations may be considered, for example, as forming two field-generating element loops, as in a configuration of Fig. 8, and / or otherwise as a single field-generating element loop forming two loops in such a configuration to form two interior regions). More specifically, the elongated sections ELP2A and ELP2B and the end sections EDP2A and EDP2D can be considered as a first half-loop FGE2FHL of a second field-generating element having an interior region FGE2FHIA. The interior region FGE2FHIA of the first half of the second field-generating element is configured to be aligned with the pattern section FHPP2 of the first half of the second scale element section PRTSC2. The elongated sections ELP2C and ELP2D and the end sections EDP2C and EDP2B can be considered as forming a second half-loop FGE2SHL of the second field-generating element having an interior space FGE2SHIA.The inner region FGE2SHIA of the second half of the second field generating element is configured to be aligned with the pattern portion SHPP2 of the second half of the second scale element portion PRTSC2.

[0037] In various implementations, an end portion EDP (e.g., or another part of the second field-generating element portion PRTFGE2) may include a port or other connection configuration. For example, the end portion EDP2B may be split in two, such as with two contact points provided. The contact points may be used to receive drive signals and may be provided at locations where signal lines / circuit traces from the processing portion 266 may connect, etc. In various implementations, such a port may be representative of a general connection configuration, such as being coupled to field-generating drive electronics. Such field-generating drive electronics may, in various implementations, include electronic components such as capacitors, transistors, etc., and may be at least partially or completely included in or coupled to the processing section 266 to provide the drive signals to cause the second field generating element section PRTFGE2 to generate a changing magnetic flux.

[0038] During operation, alternating current may be provided, although for the sake of simplicity of the following description, only one current direction is described (e.g., for the purposes of an example of one direction and / or as may occur in configurations where diodes or other components / configurations are provided to limit current flow to one direction). For example, current (as provided by drive signals) may flow through the following sequence of sections (e.g., in the following order for current in one direction), including: end section EDP2D; elongated section ELP2A; end section EDP2A; elongated section ELP2B; and end section EDP2B; elongated section ELP2C; end section EDP2C; and elongated section ELP2D. According to this example of current flow, it is understood that the current flows in the same direction (e.g., from left to right in the illustration of the Fig. 3A) passes through the elongated sections (i.e., the elongated sections ELP2A and ELP2C) at the outer limits of the configuration and in the same direction (i.e., from right to left in the illustration of the Fig. 3A) passes through the elongated sections (i.e., the elongated sections ELP2B and ELP2D) in the center of the configuration. This also corresponds to a counterclockwise current flow around the first half-loop FGE2FHL of the second field-generating element and a clockwise current flow around the first half-loop FGE2SHL of the second field-generating element (i.e., for which the directions of current flow through the respective loops are said to be opposite, with corresponding opposite polarities of the resulting magnetic flux from each respective loop).

[0039] Such directions / orientations / polarities of the current flow and the corresponding magnetic flux may be advantageous for certain configurations, such as resulting in generated signals in second sensing elements SEN2 (e.g., such as at least partially aligned with the interior regions FGE2FHIA and FGE2SHIA of the second field-generating element section PRTFGE2). In one aspect, it should be noted that with respect to the opposite current flow directions and corresponding opposite polarities of the magnetic flux generated by the respective loops FGE2FHL and FGE2SHL, the first and second half pattern sections FHPP2 and SHPP2, which are spatially offset, result in detector signals (i.e., from the second sensing element section PRTSEN2) indicating the position of the second sensing element section PRTSEN2 relative to the second scale element section PRTSC2.

[0040] As noted above, the sensing section PRTSEN includes the first and second sensing element sections PRTSEN1 and PRTSEN2 (e.g., each including respective sensing elements SEN1 and SEN2). In the illustrated implementation, the sensing elements SEN1 and SEN2 comprise sensing loop elements (alternatively referred to as sensing coil elements or sensing winding elements) connected in series and extending generally transversely (e.g., nominally perpendicular) relative to the scale direction SCD. The first sensing element section PRTSEN1 includes a first set of first sensing elements SET1SEN1 and a second set of first sensing elements SET2SEN1. The second sensing element section PRTSEN2 includes a first set of second sensing elements SET1SEN2 and a second set of second sensing elements SET2SEN2. In the illustrated implementation, adjacent loop elements (e.g.,conductive loops) in each respective set of sensing elements are connected by a configuration of conductors on different layers of a PCB (e.g., connected by vias, which in some implementations may include conductors passing through microvias, which may also be referred to as blind vias or buried vias) according to known methods. For example, the adjacent sensing elements SEN1 in each set of the first sensing element section PRTSEN1 and the adjacent sensing elements SEN2 in each set of the second sensing element section PRTSEN2 may have opposite winding polarities (e.g., with the sensing elements in each respective set alternating between SEN+ and SEN-, as described above with respect to . Fig. 22). Thus, if a first loop corresponding to a sensing element responds to a changing magnetic field with a positive polarity detector signal contribution, then the adjacent loops corresponding to adjacent sensing elements respond with a negative polarity detector signal contribution. Loops with a positive polarity detector signal contribution may be referred to herein as SEN+ sensing elements, and loops with a negative polarity detector signal contribution may be referred to herein as SEN sensing elements in various contexts. In various implementations, the sensing elements in each respective set are connected in series such that their detector signals or signal contributions per set are summed, and a "summed" detector signal is provided to detector signal output connections (e.g.,at the connections for each of the signals SIG1A and SIG1B and SIG2A and SIG2B) to a signal processing configuration 166 (e.g., the . Fig. 1) is issued.

[0041] In the illustrated implementation, the first set of first sensing elements SET1SEN1 includes sixteen first sensing elements SEN1 (i.e., including first sensing elements SEN1-A1 to SEN1-A12), and the second set of first sensing elements SET2SEN1 includes sixteen first sensing elements SEN1 (i.e., including first sensing elements SEN1-B1 to SEN1-B12). For ease of illustration, only the first two (i.e., A1-A2 and B1-B2) and the last two (i.e., A15-A16 and B15-B16) sensing elements of each set are labeled, although the sensing elements (i.e., A3-A14 and B3-B14) are similarly understood to correspond to the remaining sensing elements, as shown. In the illustrated implementation, the first set of second sensing elements SET1SEN2 includes eight second sensing elements SEN2 (i.e.,including second sensing elements SEN2-A1 to SEN2-A8) and the second set of second sensing elements SET2SEN2 includes eight second sensing elements SEN2 (i.e., including second sensing elements SEN2-B1 to SEN2-B6). For ease of illustration, only the first two (i.e., A1-A2 and B1-B2) and the last two (i.e., A7-A8 and B7-B8) sensing elements of each set are labeled, although the sensing elements (i.e., A3-A6 and B3-B6) are similarly understood to correspond to the remaining sensing elements as shown.

[0042] It will be appreciated that in various implementations, it is advantageous to configure the detector (e.g., in each of the first and second sensing element sections PRTSEN1 and PRTSEN2) to provide two or more sets of sensing elements at different spatial phase positions (e.g., to provide or otherwise correspond to quadrature signals, etc.), as will be understood by one of ordinary skill in the art. Thus, for example, the first set of first sensing elements SET1SEN1 and the second set of first sensing elements SET2SEN1 are located at different spatial phase positions. Likewise, the first set of second sensing elements SET1SEN2 and the second set of second sensing elements SET2SEN2 are located at different spatial phase positions. It will be understood, however, that the sensing element configurations described herein are intended to be exemplary only and not limiting.As an example, in some implementations, individual sensing element loops may output individual signals to a corresponding signal processing configuration, such as disclosed in U.S. Patent 9,958,294, which is hereby incorporated by reference in its entirety. More generally, various known sensing element configurations may be used in combination with the principles described herein for use in combination with various scale pattern and signal processing schemes, etc.

[0043] In the illustrated implementation of the scale portion 170 and the scale pattern 180, the first signal-modulating element pattern PATSME1 in the first scale element portion PRTSC1 in the first track portion TR1 includes a first-half pattern portion FHPP1 and a second-half pattern portion SHPP2, each half-pattern portion including a row of first signal-modulating elements SME1. Similarly, the second signal-modulating element pattern PATSME2 in the second scale element portion PRTSC2 in the second track portion TR2 includes a first-half pattern portion FHPP2 and a second-half pattern portion SHPP2, each half-pattern portion including a row of second signal-modulating elements SME2.

[0044] In various embodiments, the signal modulating elements SME1 and / or SME2 may comprise conductive plates (such as formed by regions fabricated on a printed circuit board, or as formed by raised regions extending from a conductive substrate, or as fabricated on a glass substrate, or according to other manufacturing techniques, etc.). The scale pattern 180 is generally implemented on the scale portion 170. It will be appreciated that, in operation, there is relative movement between the scale pattern 180 and the detector portion 167 (e.g., along an arcuate direction of travel). The scale pattern 180 has spatial properties that change depending on position to provide position-dependent detector signals arising in the sensing elements SEN1 and SEN2 of the sensing portion PRTSEN in the detector portion 167.In various implementations, the field generating section PRTFGE and the sensing section PRTSEN of the detector section 167 may be configured according to many different alternative configurations used in combination with many different corresponding signal processing schemes, as will be understood by those skilled in the art.

[0045] In a specific illustrative example, the detector portion 167 may be arranged parallel to and facing the scale portion 170, and a front side of the detector portion 167 facing the scale portion 170 may be separated from the scale portion 170 (and / or the scale pattern 180) by a gap distance (e.g., on the order of 0.1 mm-0.2 mm) along the z-axis direction. The front side of the detector portion 167 (e.g., including its conductive components) may be covered by an insulating coating.

[0046] It is understood that different elements may be located on different manufacturing layers located in different planes along the z-axis direction, as needed, to provide different working gaps and / or insulation layers, as will be apparent to one of ordinary skill in the art based on the described implementations and the incorporated references. It is understood that the illustrated dimensions of the x-axis, y-axis, and / or z-axis of one or more elements in all figures of this disclosure may be exaggerated for clarity, but it is understood that they are not intended to contradict the various design principles and relationships described herein.

[0047] The transducer TDR includes a first transducer section PRTTDR1 and a second transducer section PRTTDR2. The first transducer section PRTTDR1 includes the first sensing element section PRTSEN1, the first field-generating element section PRTFGE1, and the first scale element section PRTSC1. The second transducer section PRTTDR2 includes the second sensing element section PRTSEN2, the second field-generating element section PRTFGE2, and the second scale element section PRTSC2. The first and second track sections TR1 and TR2 include the first transducer section PRTTDR1 and the second transducer section PRTTDR2, respectively. As described herein, operations of the first transducer section PRTTDR1 of the first track section TR1 generate detector signals SIG1A and SIG1B, and operations of the second transducer section PRTTDR2 of the second track section TR2 generate detector signals SIG2A and SIG2B. The processing of the signals (e.g.,by the signal processing configuration 166) enables an absolute relative position between the detector section 167 and the scale section 170 to be determined.

[0048] The first transducer section PRTTDR1 of the first track section TR1 and the second transducer section PRTTDR2 of the second track section TR2 can be operated according to first and second drive operations, respectively, which, in various implementations, can be performed simultaneously or at different times. As part of a first drive operation, the first field-generating element section PRTFGE1 generates a changing magnetic flux in response to a coil drive signal (such as provided by a signal processing configuration 166). The first sensing elements SEN1 of the first sensing element section PRTSEN1 are configured to provide detector signals (e.g., SIG1A, SIG1B) that respond to a local effect on the changing magnetic flux generated by first signal-modulating elements SME1 (e.g.,including first signal modulating elements SME1 that are relatively adjacent to or otherwise aligned with sensing elements SEN1 along the z-axis direction) of the first scale element section PRTSC1. As part of a second drive operation, the second field generating element section PRTFGE2 generates a changing magnetic flux in response to a coil drive signal (such as provided by a signal processing configuration 166). The second sensing elements SEN2 of the second sensing element section PRTSEN2 are configured to provide detector signals (e.g., SIG2A, SIG2B) that are responsive to a local effect on the changing magnetic flux produced by second signal modulating elements SME2 (e.g.,including second signal modulating elements SME2 relatively adjacent to or otherwise aligned with sensing elements SEN2 along the z-axis direction) of the second scale element portion PRTSC2.

[0049] A signal processing configuration (e.g., the signal processing configuration 166 of the Fig. 1, etc.) may be configured to determine a position of the sensing portion PRTSEN (e.g., including the first and second sensing element portions PRTSEN1 and PRTSEN2) of the detector portion 167 relative to the scale portion 170 based on the detector signals input from the detector portion 167. For example, the first sensing element portion PRTSEN1 may provide detector signals SIG1A and SIG1B, and the second sensing element portion PRTSEN2 may provide detector signals SIG2A and SIG2B. In various implementations, the detector signals may also or alternatively be referred to as sensing signals. The signals from the detector portion 167 may be input to the signal processing configuration 166 and used to determine the measurement / position of the detector portion 167 relative to the scale portion 170.In general, the sensing element sections and field generating element sections may operate at least partially according to known principles (e.g., for inductive sensors), such as those described above with respect to . Fig. 22, and which are described at least in part in U.S. Patent Nos. 5,841,274; 5,886,519; 5,894,678; 6,124,708; 10,520,335; 10,612,943 and 10,775,199, which are hereby incorporated by reference in their entirety.

[0050] Fig. Figure 4 is a diagram illustrating certain dimensions and aspects of the measuring instrument 100 including the transducer TDR. In Fig. 4, certain elements (e.g., the centerline CL1 of the first scale element section PRTSC1, the centerline CL2 of the second scale element section PRTSC2, the movable encoder section support member MEPSM, etc.) are each shown as lines (where, for example, the positions may correspond to those of centerlines or other representations of the corresponding components). Representations of the pivot section PPN, including the pivot point PPT, as part of the movable section MPN, are illustrated (e.g., the contact section CPN is shown in Fig. 4, but is to be understood as being located below the pivot section PPN, as in Fig. 2 illustrates).

[0051] The movable encoder section support member MEPSM is illustrated as rotating about the pivot section PPN in an arcuate motion direction. The support member MEPSM can move between first and second motion limit indicators ML1 and ML2 as part of the movement over a maximum angular motion range θ MAX In certain implementations, the maximum angular movement range θ MAX the absolute angle measuring range θ ABS In various alternative implementations, the absolute angle measuring range θ ABS and the maximum angular movement range θ MAX may vary. As above with regard to Fig. 2, an end point ENDPT corresponds to one end of the movable encoder section support member MEPSM and also corresponds to one end of the movable section MPN, and moves accordingly in the arc movement along the arc movement direction.

[0052] In some implementations, the first and second scale element portions PRTSC1 and PRTSC2 of the scale portion 170 may be attached to the movable encoder portion support member MEPSM (e.g., in implementations where the movable encoder portion MEP includes the scale portion 170), in which case the first and second scale element portions PRTSC1 and PRTSC2 move relative to the detector portion 167 according to the arcuate movement ARCM along the arcuate movement direction ARCD. Alternatively, if the movable encoder portion MEP includes the detector portion 167, then the detector portion 167 may be attached to the movable encoder portion support member MEPSM and move relative to the first and second scale element portions PRTSC1 and PRTSC2 of the scale portion 170 according to the arcuate movement ARCM in the arcuate movement direction ARCD.

[0053] As in the Fig. 3A and Fig. 4, the first scale element portion PRTSC1 and / or the first sensing element portion PRTSEN1 has / have a first central reference point REF1 (e.g., located at a central x- and / or y-axis position, such as at a centerline CL1, of the first scale element portion PRTSC1 and / or the first sensing element portion PRTSEN1) that is located a first radial distance RD1 from the pivot portion PPN (e.g., from the pivot point PPT of the pivot portion PPN). The second scale element portion PRTSC2 and / or the second sensing element portion PRTSEN2 has / have a second central reference point REF2 (e.g. located at a central x- and / or y-axis position, such as at a centerline CL2, of the second scale element portion PRTSC2 and / or the second sensing element portion PRTSEN2) which is located at a second radial distance RD2 from the pivot portion PPN (e.g.from the pivot point PPT of the pivot section PPN).

[0054] As in the Fig. 3A and Fig. 4, the first and second scale element sections PRTSC1 and PRTSC2 of the first and second track sections TR1 and TR2 are arcuate and parallel to each other (e.g., forming concentric arcs). The second track section TR2 is closer to the pivot section PPN than the first track section TR1 (e.g., such that a radial distance RD2 of a second central reference point REF2 of the second track section TR2 is smaller than a radial distance RD1 of a first central reference point REF1 of the first track section TR1). As shown in Fig. As illustrated in Figure 3A, the first signal-modulating scale elements SME1 are arranged according to an angular spatial step θ WSME1a first signal modulating element along the first scale element section PRTSC1 and the second signal modulating scale elements SME2 are arranged according to an angular spatial step θ WSME2 a second signal modulating element which differs from the angular spatial step θ WSME1 of the first signal modulating element, along the second scale element section PRTSC2. As described in more detail below, in certain implementations, at least one of the angular spatial step θ WSME1 or θ WSME2 of the first or second signal modulating element is not uniform in 360 degrees.

[0055] As in Fig. 4, the first scale element section PRTSC1 has a first angular range θ RG1 and a corresponding arc length ARC1 and the second scale element section PRTSC2 has a second angular range θRG2 and a corresponding arc length ARC2. The angular ranges θ RG1 and θ RG2 are stated as nominally equal and are shown in the example of Fig. 3A and Fig. 4 as nominally equal to the absolute angle measuring range θ ABS and the maximum angular movement range θ MAX As described in more detail below, the angular spatial steps θ WSME1 and θ WSME2 of the first and second signal-modulating element to the absolute angle measuring range θ ABS The arrangement of the first scale element section PRTSC1 with the first angular range θ RG1 and the arc length ARC1 and the second scale element section PRTSC2 with the second angular range θ RG2 and the arc length ARC2 enables operations which, in combination, cover the absolute angle measuring range θ ABS to reach.

[0056] A scale direction SCD (which is used, for example, in the implementation of the Fig. 3A and Fig. 4 may lie in an arc direction) is indicated (along which, for example, the signal modulating elements SME of the first and second scale sections PRTSC1 and PRTSC2 may be arranged, such as according to the respective angular spatial steps θ WSME1 and θ WSME2 , such as in Fig. 3A). In various implementations, the first scale element portion PRTSC1 (which is, for example, arcuate) is arranged at the first radial distance RD1 from the pivot portion PPN, and the second scale element portion PRTSC2 (which is, for example, arcuate) is arranged at the second radial distance RD2 from the pivot portion PPN, wherein the first radial distance RD1 is greater than the second radial distance RD2. In various implementations, the first and second scale element portions PRTSC1 and PRTSC2 define a respective absolute angle measurement range θ ABS(where, for example, any relative position between the detector section 167 and the scale section 170 within the absolute angle measuring range θ ABS a unique combination of detector signals is generated by the detector section 167).

[0057] In different implementations, the ratio of the angular spatial steps θ WSME2 / θ WSME1 of the signal-modulating elements can be expressed so that it is equal to at least one of the following EQUATIONS 1-4, for which n and m are positive integers in each of the equations. In certain implementations, m is a positive integer that is at least 2 (e.g., in certain implementations, m can be 2, 3, 4, or 5, etc.). It should be noted that for a configuration in which m is 2 or greater, such relationships correspond to a relatively large difference between the angular spatial steps θ WSME1 and θ WSME2of the signal-modulating elements (where, for example, the angular spatial step θ WSME2 close to an integer multiple (e.g. m = 2 or larger) of the angular spatial step θ WSME1 In implementations where m=1, the equations turn out to be reducible to a simpler form (in which, for example, the nm factor is reduced to n). With regard to these equations, it should be noted that a technique for encoding an absolute angle measurement range θ ABS into an encoder using an arc motion consists in using two scale element sections with angular spatial steps of the signal modulating elements that satisfy certain relationships. For example, the following equations illustrate certain relationships that describe the angular spatial steps θ WSME1 and θ WSME2of the signal modulating elements of the scale element sections PRTSC1 and PRTSC2 of the track sections TR1 and TR2. θWSME2 / θWSME1=(nm / (n−1)) θWSME2 / θWSME1=(nm / (n+1)) θWSME2 / θWSME1=((nm+1) / n) θWSME2 / θWSME1=((nm−1) / n)

[0058] In various implementations, the absolute angle measuring range θ ABS equal to one of nθ WSME1 or nθ WSME2 For example, in certain implementations, a configuration conforming to EQUATION 1 or 2 may satisfy an additional condition where the absolute angle measurement range θ ABS =nθ WSME1 and a configuration corresponding to EQUATION 3 or 4 can satisfy an additional condition where the absolute angle measuring range θ ABS =nθ WSME2 In various implementations, a configuration corresponding to EQUATION 1 can satisfy an additional condition where the absolute angle measuring range θABS =((n-1) / m)θ WSME2 , a configuration corresponding to EQUATION 2 can satisfy an additional condition where the absolute angle measuring range θ ABS =((n+1) / m)θ WSME2 , a configuration corresponding to EQUATION 3 can satisfy an additional condition where the absolute angle measuring range θ ABS =(nm+1)θ WSME1 and a configuration corresponding to EQUATION 4 can satisfy an additional condition where the absolute angle measuring range θ ABS =(nm-1)θ WSME1 According to such relationships, it is understood that one method for choosing the two angular spatial steps of the signal modulating elements is to select an integer number n of angular spatial steps (e.g., for either θ WSME1 or θ WSME2 ) that fall within the absolute angle measuring range θ ABSare to be recorded, and wherein the other angular spatial step of the signal modulating elements (e.g. either θ WSME2 or θ WSME1 ) can be determined according to a relationship such as the one given above.

[0059] In various implementations, the first scale element portion PRTSC1 has an arc length ARC1 and is arranged at a first radial distance RD1 from the pivot portion PPN, and the second scale element portion PRTSC2 has an arc length ARC2 and is arranged at a second radial distance RD2 from the pivot portion PPN (such as in Fig. 4), where ARC2 / ARC1 =RD2 / RD1. In various implementations, the angular spatial step θ WSME2 of the second signal modulating element is greater than the angular spatial step θ WSME1of the first signal-modulating element (e.g., in configurations where m is 2 or larger, the angular spatial step θ WSME2 close to a corresponding integer multiple of the angular spatial step θ WSME1 lay).

[0060] As noted above, the first signal-modulating element pattern PATSME1 in the first scale element section PRTSC1 in the first track section TR1 includes a first-half pattern section FHPP1 and a second-half pattern section SHPP1, each half-pattern section including a row of first signal-modulating elements SME1. In each scale row, the first signal-modulating elements SME1 are arranged according to an angular spatial step θ WSME1of the first signal-modulating element (e.g., spaced / spatially positioned). For the two adjacent scale rows in the half-pattern sections, the spatial phase of the scale row in the second half-pattern section is 1 / 2 of the angular spatial step θ WSME1 of the first signal-modulating element is offset from the spatial phase of the adjacent scale row in the first half-pattern section. Thus, in this example, the spatial phase offset of the signal-modulating element is 1 / 2 of the angular spatial step θ WSME1 of the first signal-modulating element (which may, for example, correspond to a spatial phase shift / difference between the adjacent scale rows of 180 degrees).

[0061] As noted above, the second signal-modulating element pattern PATSME2 in the second scale element section PRTSC2 in the second track section TR2 includes a first-half pattern section FHPP2 and a second-half pattern section SHPP2, each half-pattern section including a row of second signal-modulating elements SME2. In each scale row, the second signal-modulating elements SME2 are arranged according to an angular spatial step θ WSME2 of the second signal-modulating element (e.g., spaced apart / spatially positioned). For the two adjacent scale rows in the half-pattern sections, the spatial phase of the scale row in the second half-pattern section is 1 / 2 of the angular spatial step θ WSME2of the second signal-modulating element is offset from the spatial phase of the adjacent scale row in the first half-pattern section. Thus, in this example, the spatial phase offset of the signal-modulating element is 1 / 2 of the angular spatial step θ WSME2 of the second signal-modulating element (which may, for example, correspond to a spatial phase shift / difference between the adjacent scale rows of 180 degrees).

[0062] In various implementations, the first and second sets of first sensing elements SET1SEN1 and SET2SEN1 in the first sensing element section PRTSEN1 are located at different angular spatial phase positions, as separated by an angular spatial phase offset of the first sensing element. In various implementations, an angular spatial step θ WSEN1of the first sensing element of the first sensing element section PRTSEN1 (e.g., each of the sets of first sensing elements SET1SEN1 and SET2SEN1) to the angular spatial step θ WSME1 of the first signal modulating element of the first scale element section PRTSC1 (e.g., be equal). In various implementations, the angular spatial phase offset of the first sensing element may be approximately equal to 1 / 4 of the angular spatial step θ WSEN1 of the first sensing element (e.g., according to a quadrature configuration, as understood by one skilled in the art).

[0063] Likewise, in various implementations, the first and second sets of second sensing elements SET1SEN2 and SET2SEN2 in the second sensing element section PRTSEN2 are located at different angular spatial phase positions, as separated by an angular spatial phase offset of the second sensing element. In various implementations, an angular spatial step θ WSEN2 of the second sensing element of the second sensing element section PRTSEN2 (e.g., each of the sets of second sensing elements SET1SEN2 and SET2SEN2) to the angular spatial step θ WSME2 of the second signal modulating element of the second scale element section PRTSC2 (e.g., be equal). In various implementations, the angular spatial phase offset of the second sensing element may be approximately equal to 1 / 4 of the angular spatial step θ WSEN2of the second sensing element (e.g., according to a quadrature configuration, as understood by one skilled in the art).

[0064] In an exemplary implementation, θ WSME1 = 0.0300 radians and θ WSME2 = 0.625 radians. With respect to these values ​​and according to EQUATION 1, θ WSME2 / θ WSME1 = (nm / (n-1)) = (50 / 24) = 0.0625 radians / 0.0300 radians = 3.58 degrees / 1.72 degrees. In addition, in various implementations, θ ABS according to θ ABS = nθ WSME1 = 25(0.0300 radians) = 0.75 radians or 25(1.72 degrees) = 43 degrees, and with θ ABS = ((n-1) / m)θ WSME2 = ((25-1) / 2)(0.0625 radians) = 0.75 radians or ((25-1) / 2)(3.58 degrees) = 43 degrees. According to these relationships, within the absolute angle measuring range θ ABS 25 θ WSME1 (corresponding to 25 SME1) and 12 θ WSME2(corresponding to 12 SME2). It should be noted that the relationships of this configuration can alternatively be written as EQUATION 3, where θ WSME2 / θ WSME1 = ((nm+1) / n) = 25 / 12 = 0.0625 radians / 0.0300 radians or 3.58 degrees / 1.72 degrees when n=12 and m=2. In addition, θ ABS =nθ WSME2 = 12(0.0625 radians) = 0.75 radians or 12(3.58 degrees) = 43 degrees and θ ABS =(nm+1)θ WSME1 = (24+1)(0.0300 radians) = 0.75 radians or (24+1)1.72 degrees = 43 degrees.

[0065] As a further example, it should be noted that in an alternative arrangement where the absolute angle measuring range θ ABS (still at 0.75 radians = 43 degrees) 25 θ WSME1 (corresponding to 25 SME1), where θ WSME1 remains at 0.0300 radians = 1.72 degrees, and 13 θ WSME2 (corresponding to 13 SME2) if θ WSME2= 0.75 radians / 13 = 0.0577 radians or 43 degrees / 13 = 3.31 degrees, the relationships could be expressed as EQUATION 2 or 4. More precisely, θ WSME2 / θ WSME1 = (nm / (n+1)) = 50 / 26 = 0.0577 radians / 0.0300 radians = 3.31 degrees / 1.72 degrees at n=25 and m=2 according to EQUATION 2. At θ ABS = nθ WSME1 = ((n+1) / m)θ WSME2 are in the absolute angle measuring range 25 θ WSME1 (corresponding to 25 SME1) and 13 θ WSME2 (corresponding to 13 SME2). Alternatively, θ WSME2 / θ WSME1 = ((nm-1) / n) = 25 / 13 = 0.0577 radians / 0.0300 radians = 3.31 degrees / 1.72 degrees at n=13 and m=2 according to EQUATION 4. At θ ABS = nθ WSME2 = (nm-1)θ WSME1 are in the absolute angle measuring range 13 θ WSME2 (corresponding to 13 SME2) and 25 θ WSME1 (corresponding to 25 SME1). In yet another alternative example, θ WSME2 / θ WSME1= ((nm-1) / n) = 23 / 12 = 0.0625 radians / 0.0326 radians = 3.58 degrees / 1.87 degrees at n=12 and m=2 according to EQUATION 4. At θ ABS = nθ WSME2 = (nm-1)θ WSME1 are in the absolute angle measuring range 12 θ WSME2 (corresponding to 12 SME2) and 23 θ WSME1 (corresponding to 23 SME1).

[0066] The converter of the Fig. 3A and Fig. 4, the first scale element section PRTSC1 is located within a first scale track ST1 with a first scale track width STW1 (where, for example, the upper and lower edges of the first scale element section PRTSC1 can correspond to the upper and lower limits of the first scale track ST1). The second scale element section PRTSC2 is located within a second scale track ST2 with a second scale track width STW2 (where, for example, the upper and lower edges of the second scale element section PRTSC2 can correspond to the upper and lower limits of the second scale track ST2). A separation distance SEP12 is illustrated as a radial distance between the first and second scale tracks ST1 and ST2. A separation area SEPA is illustrated between the first and second scale tracks ST1 and ST2 (which, for example,has a radial width defined by the separation distance SEP12, as defined by the lower boundary of the first scale track ST1 and the upper boundary of the second scale track ST2). Note that the separation area SEPA is illustrated empty (e.g., does not include a scale element portion as disposed in an encoder track portion with a sensing element portion). A differential distance D12 is indicated as the difference in distance between the center reference points REF1 and REF2 and, correspondingly, also as the difference between the first radial distance RD1 and the second radial distance RD2. As some specific example dimensions, in one implementation, the first scale track width STW1 may be 4.0 mm, the second scale track width STW2 may be 2.75 mm, the separation distance SEP12 may be 8.25 mm, the first radial distance RD1 may be 37.125 mm, the second radial distance 25.5 mm, and the differential distance D12 may be 11.625 mm.In various implementations, such dimensions may result in certain desirable operating characteristics, as described in more detail below.

[0067] Fig. Figure 5 is a diagram illustrating certain signals 500 resulting from the operation of the converter TDR of the Fig. 3A with arc movement between the detector section 167 and the scale section 170. As in Fig. 5, a trace 510A illustrates SEN1 signals as a function of angular position. In various implementations, the signals of trace 510A may correspond to the detector signals SIG1A and SIG1B of the transducer section PRTTDR1 of the first track section TR1. A trace 520A similarly illustrates SEN2 signals as a function of angular position. In various implementations, the signals of trace 520A may correspond to the detector signals SIG2A and SIG2B of the transducer section PRTTDR2 of the second track section TR2. Traces 510B and 520B illustrate phase signals for the SEN1 and SEN2 signals of traces 510A and 520A, respectively (i.e., from the calculation of arctan(SIGxB / SIGxA), such as arctan(SIG1B / SIG1A) and arctan(SIG2B / SIG2A)).

[0068] Trace 530 illustrates an absolute ABS phase signal (e.g., resulting from a combination of the other signals, such as including those of traces 510B and 520B). In various implementations, the absolute ABS phase signal may be represented as follows: ΦABS=ΦSIG1−mΦSIG2

[0069] As indicated in curve 530, the absolute angle measuring range θ ABSover a range of -21.5 degrees to +21.5 degrees (i.e. from -0.375 radians to +0.375 radians), which corresponds to an absolute angular range of 43 degrees (i.e. 0.75 radians). Accordingly, in the curves 510A and 510B, within the angular range of -21.5 degrees to +21.5 degrees (i.e., -0.375 radians to +0.375 radians), 25 cycles / periods (e.g., corresponding to 25 SME1 in the first scale element section PRTSC1 of the first track section TR1) are illustrated, and in the curves 520A and 520B, within the angular range of -21.5 degrees to +21.5 degrees (i.e., -0.375 radians to +0.375 radians), 12 cycles / periods (e.g., corresponding to 12 SME2 in the second scale element section PRTSC2 of the second track section TR2) are illustrated.

[0070] It is understood that according to the principles described herein, an absolute angle measuring range θ ABS for a specific maximum angular movement range θ MAXcan be adjusted / configured for a specific application. The specific numerical examples above illustrate an arrangement that is suitable for an absolute angle measuring range θ ABS of 43 degrees (i.e., 0.75 radians), although it is understood that other arrangements may be configured for larger or smaller absolute angle measurement ranges according to the principles described above. In some implementations, smaller absolute angle measurement ranges may be used for specific applications (e.g., ranges smaller than 15 degrees, 10 degrees, or 5 degrees).

[0071] It is understood that the possibility of changing the absolute angle measuring range θ ABSfor a specific application, can have certain advantages. For example, a design for a longer absolute angle measurement range for a multi-track transducer generally requires a certain level of resolution and precision to achieve the longer range (e.g., with suitable and unambiguous signal levels over the entire range, such as a high level of information accuracy required for each increment, particularly with regard to the relationships between the multiple track sections (e.g., TR1 and TR2), to make each increment distinguishable over the entire range). In contrast, with a relatively shorter absolute angle measurement range in a multi-track transducer (such as may be designed according to the principles described herein), over the shorter range (e.g.,using smaller and / or otherwise different increments / spatial steps between the multiple traces, which might otherwise be too fine and / or have other problems for a larger area), a higher level of resolution can be achieved, and / or sufficient accuracy can be achieved over the smaller area using an implementation with lower complexity / cost / performance requirements, etc.

[0072] In some implementations, a comparison can be made with absolute rotary encoders, which have an integer number of angular spatial steps in each track section around an absolute range of a full 360 degrees (e.g., to function effectively for continuous measurement of angular position in implementations where full 360-degree rotations and beyond can be performed). According to such principles, if a section of such an encoder is used in an arc motion application (e.g., if 1 / 4 or 1 / 8 of such an encoder is used for a measurement range of 90 degrees or 45 degrees), the angular spatial steps in each track section will continue to divide equally into 360 degrees, respectively.For example, if a section of such a rotary encoder is used, for each track section in the transducer, 360 degrees divided by the given angular spatial step of the track section will be an integer number.

[0073] Such implementations utilizing a portion of a rotary encoder have certain disadvantages (e.g., as noted above, a design for a relatively longer measurement range, such as the full 360-degree angle measurement range, generally requires a certain level of resolution and precision to achieve the full 360-degree range, particularly with regard to the relationships between the track portions to make each increment distinguishable). In contrast, as noted above, an arcuate motion encoder according to the principles described herein can be designed with a relatively smaller absolute angle measurement range (i.e., less than 360 degrees, and in some implementations, smaller such as less than 45 degrees, or 15 degrees, or 5 degrees) and have certain advantages such as those noted above.

[0074] Fig. Figure 6 is a diagram of an implementation of a portion of a transducer TDR'''' configured to be used with an arcuate motion between a detector portion 167'''' and a scale portion 170'''' incorporated in the measuring instrument of the Fig. 2 can be used and a relatively smaller separation of the scale tracks ST1 and ST2'''' compared to the implementation of the Fig. 3A. Fig. Figure 7 is a diagram showing certain dimensions and characteristics of the measuring instrument of the Fig. 2 and the converter of the Fig. 6. The implementation of the Fig. 6 and Fig. 7 is in some respects similar to the implementation of the Fig. 3A and Fig. 4, as further described below.

[0075] It should be noted that the first encoder track section TR1 is used in the implementation of the Fig. 6 and Fig. 7 is identical to the first encoder track section TR1 of the implementation of the Fig. 3A and Fig. 4 and can be understood from the above description of the first encoder track section TR1. The second encoder track section TR2'''' of the Fig. 6 and Fig. 7 is configured to generate similar signals as the second encoder track section TR2 of the Fig. 3A and Fig. 4, and where Fig. 5 is representative of signals resulting from the operation of the implementation of the Fig. 6 and Fig. 7, as well as representative of signals resulting from the operation of the implementation of the Fig. 3A and Fig. 4. In this respect, the signals SIG2A'''' and SIG2B''''' can be used to implement the Fig. 6 during operation be similar to the signals SIG2A and SIG2B of the implementation of the Fig. 3A.

[0076] In addition, it is understood that each of the components of the second encoder track section TR2 of the Fig. 3A a corresponding component in the second encoder track section TR2'''' of the Fig. 6 (which may be designated, for example, by a quadruple prime '''). Thus, the components of the transducer TDR''' will be understood by those skilled in the art based on the corresponding components of the transducer TDR, unless otherwise described below. A complete description of the components of the transducer TDR''' is therefore not provided herein, although a brief description is provided below for convenience. This numbering scheme (e.g., including use of different numbers with prime designations, such as XX, XX', XX'', etc.) to indicate elements of analogous designation and / or function is also applied in the other figures as described herein.

[0077] In general, the components in the second encoder track section TR2'''' of the Fig. 6 along the arc movement direction ARCD be larger than the corresponding components of the second encoder track section TR2 of the Fig. 3A. In various implementations, the larger sizes of the components correspond to the larger radial distance RD2'''' compared to the radial distance RD2 and the corresponding larger arc length ARC2'''' compared to the arc length ARC2, as required to generate similar signals, as will be understood by one skilled in the art. To generate the similar signals, it is noted that the angular spatial step θ WSME2 '''' of the second signal modulating element of the second scale element section PRTSC2'''' with the angular spatial step θ WSME2 of the second signal modulating element of the second scale element section PRTSC2 can be identical and that the angular spatial step θ WSE2 '''' of the second detection element with the angular spatial step θ WSEN2 of the second detection element can be identical.

[0078] Similar to the implementation of the Fig. 3A and Fig. 4, the first scale element section PRTSC1 is in the implementation of the Fig. 6 and Fig. 7 within a first scale track ST1 with a first scale track width STW1 (where, for example, the upper and lower edges of the first scale element section PRTSC1 can correspond to the upper and lower limits of the first scale track ST1). The second scale element section PRTSC2'''' is located within a second scale track ST2'''' with a second scale track width STW2'''' (where, for example, the upper and lower edges of the second scale element section PRTSC2'''' can correspond to the upper and lower limits of the second scale track ST2''''). A separation distance SEP12'''' is illustrated as a radial distance between the first and second scale tracks ST1 and ST2''''. A separation area SEPA'''' is illustrated between the first and second scale tracks ST1 and ST2'''' (which, for example,has a radial width defined by the separation distance SEP12'''', as defined by the lower boundary of the first scale track ST1 and the upper boundary of the second scale track ST2''''). It should be noted that the separation area SEPA'''' is empty (e.g., does not include a scale element section, as arranged in an encoder track section with a sensing element section).

[0079] As in Fig. 7, the first and second scale element portions PRTSC1 and PRTSC2'''' of the first and second track portions TR1 and TR2'''' are arcuate and parallel to each other (e.g., forming concentric arcs). The second track portion TR2'''' is closer to the pivot portion PPN than the first track portion TR1 (e.g., such that a radial distance RD2'''' of a second central reference point REF2'''' of the second track portion TR2'''' is smaller than a radial distance RD1 of a first central reference point REF1 of the first track portion TR1). In various implementations, the reference point REF1 may lie on the centerline CL1, and the reference point REF2'''' may lie on the centerline CL2''''. A differential distance D12'''' is indicated as the difference in the distance between the central reference points REF1 and REF2'''', and correspondingly also as the difference between the first radial distance RD1 and the second radial distance RD2''''.

[0080] The first scale element section PRTSC1 has a first angular range θ RG1 and a corresponding arc length ARC1 and the second scale element section PRTSC2'''' has a second angular range θ RC2 and a corresponding arc length ARC2''''. The angular ranges θ RG1 and θ RG2 are stated as nominally equal and are shown in the example of Fig. 6 and Fig. 7 as nominally equal to the absolute angle measuring range θ ABS and the maximum angular movement range θ MAX specified.

[0081] As some specific example dimensions, in one implementation, the first scale track width STW1 may be 4.0 mm, the second scale track width STW2 may be 2.75 mm, the separation distance SEP12 may be 1.25 mm, the first radial distance RD1 may be 37.125 mm, the second radial distance RD2 may be 32.5 mm, and the differential distance D12 may be 4.625 mm. In various implementations, such dimensions may result in certain less desirable operating characteristics (e.g., compared to those of the implementations of the Fig. 3A and Fig. 4), as described in more detail below.

[0082] It should be noted that the implementation of the Fig. 6 and Fig. 7 leads to a smaller overall size of the corresponding converter TDR'''' compared to the implementation of the Fig. 3A and Fig. 4 with the relatively larger overall size of the corresponding transducer TDR. This is a major reason why prior art encoders are typically designed with a relatively small gap between the encoder tracks to limit the corresponding overall size. According to these prior art design principles, it may have been considered illogical and / or surprising that an implementation such as that of Fig. 3A and Fig. 4 (i.e., with the relatively larger separation of the encoder / scale tracks) would result in certain more desirable operating characteristics, as described in more detail below.

[0083] In general, it should be noted that for transducers that utilize arcuate motion, the signal periodicity depends on the spatial steps in the scale track sections and also on the radial distance of the scale section and / or detector section from the pivoting section. This is in contrast to standard transducers that use only linear motion, where the signal periodicity depends only on the spatial steps in the scale track sections. The dependence of arcuate motion transducers on the radial distance of the scale section and / or detector section from the pivoting section can lead to certain problems in the event of offset / misalignment. For example, a transducer may be designed to ideally operate with the scale section and detector section centered and aligned relative to each other along a radial direction, which can result in a designed signal periodicity.However, if there is a radial offset / misalignment (e.g., of the scale portion relative to the detector portion) due to the dependence on the radial distance, the signal periodicity may differ from the design, which may result in certain positions having a linear error due to the operation of the transducer (e.g., the error may increase linearly with further arc movement of the transducer as the measured position moves further away from a reference point).

[0084] As an example of how radial offset / misalignment can occur, during the manufacture / assembly of a measuring instrument, such as that of the Fig. 2, the movable encoder section MEP (e.g., consisting of a printed circuit board with the scale section or detector section fabricated thereon) is coupled (e.g., attached, fixed, etc.) to the carrier component MEPSM. During such manufacturing / assembly, a certain degree of radial offset / misalignment of the movable encoder section MEP may occur (e.g., due to manufacturing tolerances, etc., such as for the positioning of the movable encoder section MEP on the carrier component MEPSM). The resulting radial offset / misalignment of the movable encoder section MEP (i.e., as coupled to the carrier component MEPSM) may correspond to a radial offset / misalignment of the scale section (e.g., relative to the detector section). As noted above, such radial offset / misalignment may result in errors in a particular position of the transducer.As described in more detail below, to address these problems, in accordance with the principles described herein, an offset value corresponding to such radial offset may be determined based at least in part on signals from the transducer, and the determined offset value may be used to correct one or more values ​​used to determine a relative position between the detector portion and the scale portion.

[0085] In various implementations, the following concepts may relate to determining an offset value based at least in part on signals from the converter. With respect to the signals from the Fig. 5 correspond to the SEN1 signal and the SEN1 phase (e.g. corresponding to the signal phase Φ SIG1 ) the angular spatial step θ WSME1of the first signal-modulating element of the first scale element section PRTSC1 of the first scale track ST1. Similarly, the SEN2 signal and the SEN2 phase (e.g., corresponding to the signal phase Φ SIG2 ) the angular spatial step θ WSME2 of the second signal modulating element of the second scale element section PRTSC2 of the second scale track ST2. As described above, the angular spatial step θ WSME1 of the first signal-modulating element is smaller than the angular spatial step θ WSME2 of the second signal modulating element, and therefore the angular spatial step θ WSME1 of the first signal-modulating element can be characterized as a finer or fine spatial step (e.g. the fine track ST1), while the angular spatial step θ WSME2of the second signal-modulating element can be characterized as a coarser spatial step (e.g. the sub-track ST2).

[0086] As illustrated and described, the spatial step of the first scale element section PRTSC1 of the first scale track ST1 can provide the finest measurement resolution and can thus be referenced and used as part of the determination of a highly accurate absolute measurement position. However, as part of the determination of an overall absolute measurement position, a determination must be made as to which cycle / period of the SEN1 phase (i.e., corresponding to the signal phase Φ SIG1 ) a current absolute measurement position lies or otherwise corresponds to it (such as an integer number of occurring spatial steps, and to which the SEN1 phase / signal phase Φ SIG1 specified position can be added). For example, in the illustration of the Fig. 5 25 periods / cycles of the SEN1 phase (ie corresponding to the signal phase Φ SIG1 ) corresponding to the 25 signal modulating elements SME1 (in the first scale element section PRTSC1 of the first track section TR1 of the Fig. 6) and corresponding to 25 spatial steps within the absolute range (ie within the absolute range θ ABS , as indicated for the absolute ABS phase). It should also be noted that there are 12 periods / cycles of the SEN2 phase (i.e., corresponding to the signal phase Φ SIG2 ), corresponding to the 12 signal modulating elements SME2 and corresponding to 12 spatial steps within the absolute range. With further reference to Fig. 5, the absolute ABS phase (ie corresponding to the signal phase (Φ ABS) in various implementations have sufficient accuracy to be used to determine which cycle / period a current absolute measurement position corresponds to. In various implementations, such a process may be referred to as a phase unpacking process, a chaindown process, etc.

[0087] In certain implementations, the absolute ABS phase (ie corresponding to the signal phase Φ ABS ) can be considered sufficiently accurate to be used to determine which cycle / period (e.g. of the 25 cycles / periods in the example of the Fig. 5) the SEN1 phase (ie corresponding to the signal phase Φ S1G1) corresponds to a current absolute measurement position. Such a corresponding process can be referred to as a direct chaindown process (i.e., for which only a single chaindown step is performed). Alternatively, as part of a more robust process (e.g., more robust against certain types of encoder errors or other accuracy problems), the absolute ABS phase (i.e., corresponding to the signal phase Φ ABS ) to determine which cycle / period (e.g. of the 12 cycles / periods in the example of the Fig. 5) the SEN2 phase (ie corresponding to the signal phase Φ SIG2 ) corresponds to a current absolute measurement position, and for which the results of such a first determination can then be used to determine which cycle / period (e.g. of the 25 cycles / periods in the example of the Fig. 5) the SEN1 phase (ie corresponding to the signal phase Φ SIG1) corresponds to a current absolute measurement position. Such a corresponding process can be referred to as a double chaindown process (i.e., for which the two chaindown steps are performed).

[0088] As part of such a chaindown process, a rounding process can be performed (e.g. with respect to the absolute ABS phase / signal phase Φ ABS, as in the direct chaindown process or in the first step of the double chaindown process). The rounded-off amounts (e.g., between -0.5 and +0.5) can be referred to as chaindown values ​​and can represent a difference in the accumulated position values. In a perfect configuration (e.g., with no radial offset, etc.), chaindown values ​​can be close to or equal to zero. However, in actual, practical configurations (e.g., as manufactured and assembled, with certain manufacturing / assembly tolerances, etc.), some degree of radial offset can occur (which can, for example, result in certain chaindown values). As described in more detail below, in various implementations, a chaindown slope (i.e., corresponding to a chaindown curve of the chaindown values) can be determined and can be related to and / or used to determine an offset value (e.g.,corresponding to a radial offset of the scale portion, such as with respect to the detector portion, or corresponding to a radial offset of the detector portion, such as with respect to the scale portion. In various implementations, the determined offset value may be used to correct one or more values ​​(e.g., a spatial step or other spatial dimension) used to determine a relative position between the detector portion and the scale portion.

[0089] As part of the chaindown processes described below, the absolute phase Φ ABS in the range [0, 1] and the signal phases Φ SIG1 and Φ SIG2 in the range of [-0.5, +0.5] and can be expressed as follows: ΦSIG1=(1 / 2π)arctan(SIG1B / SIG1A) ΦSIG2=(1 / 2π)arctan(SIG2B / SIG2A)

[0090] A relationship for the absolute phase Φ ABScan be expressed as follows: ΦABS=(ΦSIG1−mΦSIG2+Φ0)%1 where Φ0 is a buffer ABS signal phase, included in some implementations to avoid a jump in the ABS spatial space / step, and %1 indicates a modulo / modulus operation that returns the remainder or signed remainder of a division after the number has been divided by the designated divisor, which in this case is 1, so the result is generally not an integer value (e.g., for a value of 1.2, the operation performed would return 0.2, etc.).

[0091] For a direct chaindown process, a next determination can be as follows: nAWSME1=round((ΦABS(θABS / θWSME1)−ΦSIG1+Φ1) where n AWSME1is an integer number of spatial steps of the first signal-modulating element for determining the absolute measuring distance, “round” indicates a rounding operation (e.g., for determining an integer number for n AWSME1 ) and Φ1 is included in some implementations to minimize the values ​​of the first chaindown and thus avoid a spatial step jump of θ WSME1 to avoid. It should be noted that θ ABS / θ WSME1 the number of angular spatial steps θ WSME1 of the first signal-modulating element in the absolute angle measuring range θ ABS results (e.g. in an example like the one described above, where if θ ABS = 0.75 radians and θ WSME1 = 0.03 radians, then θ ABS / θ WSME1 = 25). After an integer number of spatial steps n AWSME1of the first signal modulating element, the absolute measurement can be determined according to EQUATION 12, as described in more detail below.

[0092] As an alternative to the direct chaindown process, for a double chaindown process as part of a first chaindown step, a next determination according to EQUATION 8 can be as follows: nAWSME2=round((ΦABS(θABS / θWSME2)−ΦSIG2+Φ1) where n AWSME2 is an integer number of spatial steps of the second signal-modulating element for determining the absolute measuring distance, “round” indicates a rounding operation (e.g., for determining an integer number for n AWSME2 ) and Φ1 is included in some implementations to minimize the values ​​of the first chaindown and thus avoid a spatial step jump of θ WSME2 to avoid. It should be noted that θ ABS / θ WSME2 the number of angular spatial steps θ WSME2of the second signal-modulating element in the absolute angle measuring range θ ABS results (e.g. in an example like the one described above, where if θ ABS = 0.75 radians and θ WSME2 = 0.0625 radians, then θ ABS / θ WSME2 = 12). As a further part of the double chaindown process, a second / next chaindown step can be as follows: nAWSME1=round(((nAWSME2+ΦSIG2)(θWSME2 / θWSME1))−ΦSIG1+Φ2) where n AWSME1 is an integer number of spatial steps of the first signal-modulating element for determining the absolute measuring distance, “round” indicates a rounding operation (e.g., for determining an integer number for n AWSME1 ), Φ2 is included in some implementations to minimize the values ​​of the second chaindown and thus avoid a spatial step jump of θ WSME1 to avoid, and θ WSME2 / θ WSME1is a ratio value (where, for example, the above exemplary values ​​correspond to 0.0625 / 0.03 = 2.0833).

[0093] After an integer number of spatial steps n AWSME1 of the first signal-modulating element according to EQUATION 9 (e.g., as part of a direct chaindown process) or according to EQUATION 11 (e.g., as part of a double chaindown process), the absolute measurement can be determined as follows: MEASANG=θWSME1(nAWSME1+ΦSIG1)−θ0 where MEAS ANG is the absolute angle measurement (e.g., in radians) and θ0 is the angular origin position. In certain implementations, the absolute measurement can be expressed in terms of an arc distance, which is related to the angular spatial steps θ WSME1 of the first signal-modulating element and the radial distance RD1 of the first scale element section PRTSC1 of the first scale track ST1 can be represented as follows: MEASARC=(MEASANG)RD1

[0094] This corresponds to one arc distance along the first scale track ST1. As described above, the rounded-off amounts (e.g., in either the direct or double chaindown process) can be referred to as chaindown values. With respect to the direct chaindown process and EQUATION 9, the chaindown values ​​can be expressed as follows: Chaindown value=(ΦABS(θABS / θWSME1)−ΦSIG1+Φ1)−nAWSME1

[0095] Regarding the double chaindown process and EQUATION 10, the chaindown values ​​can be expressed as follows: Chaindown value=(ΦABS(θABS / θWSME2)−ΦSIG2+Φ1)−nAWSME2

[0096] In various implementations, such chaindown values ​​may be included in a chaindown trace and / or otherwise used to determine a chaindown slope, which may be used to correct a linear error, as described in more detail below. Briefly, regarding EQUATION 12 (and certain other equations above), if (e.g., due to a radial offset of the scale section or the detector section) the signal periodicity of the first scale element section PRTSC1 of the first scale track ST1 does not coincide with θ WSME1(or e.g., its arc pitch equivalent), the determined measurement accumulates the error. A determined chaindown tilt can be used to determine an offset value corresponding to a radial offset of the scale section or the detector section (e.g., with respect to each other), where the determined offset value can be used to correct a value (e.g., determining a corrected value θ WSME1C ), which can be used to determine the relative position between the detector section and the scale section (as used, for example, in EQUATION 12).

[0097] Generally speaking, transducers that utilize arcuate motion are generally sensitive to radial offset / misalignment (e.g., of the scale portion with respect to the sensing portion), with such radial offset / misalignment causing a long-range linear error (LRE) (e.g., with a slope in some implementations approximately equal to the radial offset divided by the radial distance of the scale track). One method for correcting such an LRE would be to calibrate a known standard (e.g., a reference encoder or calibration blocks), although in some implementations such processes may be excessively laborious, difficult, expensive, etc. Alternatively, and in accordance with certain principles described herein, a dual-track arc encoder (i.e., with a transducer that utilizes arcuate motion) may be configured to "self-correct" such problems (e.g.,at least in part by utilizing the known separation of the first and second scale tracks as a reference and / or otherwise for correcting values). In other words, in implementations such as those described herein, where the first and second scale track portions have different radial distances from the pivot portion, a radial offset, if present, causes a slope of the chaindown progression of the chaindown values ​​(i.e., a chaindown slope) that can be measured (e.g., without requiring an external reference standard) and used to correct values ​​(e.g., to correct the linear error). As described in more detail below, in various implementations, a relatively large separation / difference in the radial separations of the two scale tracks may enable a more accurate / sufficiently accurate determination of an offset value (e.g., corresponding to the radial offset) that can be used to correct values ​​(e.g.,to correct the linear error).

[0098] According to the above principles, the following equations give certain corresponding relationships. LRE tilt=OFF / (RD−OFF)≈OFF / RD where OFF is the radial offset and RD is the radial distance of the corresponding scale track / scale element section. Note that the radial offset OFF is typically sufficiently small relative to the radial distance RD that RD-OFF can be adequately approximated by RD. For a direct chaindown process, the chaindown slope can be characterized as follows: CDSLOPEDIR≈−OFF((1 / RD2)−(1 / RD1))(n) where CDSLOPE DIRis the chaindown slope for the direct chaindown process, and RD1 and RD2 are the radial distances of the first and second scale element sections and the first and second scale tracks, respectively. In certain implementations, EQUATION 17 can be modified to be further defined as follows: CDSLOPEDIR≈−OFF((1 / RD2)−(1 / RD1))(n−1)

[0099] For a double chaindown process, the chaindown propensity can be characterized as follows: CDSLOPEDBL≈−OFF((1 / RD2)−(1 / RD1))(n / m) where CDSLOPE DBL is the chaindown slope for the double chaindown process. Note that EQUATION 19 can be used to calculate the offset according to: -OFF ≈ CDSLOPE DBL / (1 / RD2)-(1 / RD1))(n / m)). In certain implementations, EQUATION 19 can be modified to be further defined as follows: CDSLOPEDBL≈−OFF((1 / RD2)−(1 / RD1))((n−1) / m)

[0100] It should be noted that EQUATION 20 can be used to calculate the offset according to: -OFF ≈ CDSLOPE DBL / (((1 / RD2)-(1 / RD1))((n-1) / / m)). In various implementations, a self-correction / correction process can be characterized as follows: θWSME1C=θWSME1(1−(OFFD / RD1)) where θ WSME1C the corrected value for θ WSME1 is and OFF D is the specific radial offset (e.g., as determined based on the chaindown slope CDSLOPE). The above principles and certain related examples (e.g., with respect to the above equations, etc.) are explained below using the Fig. 8A-21 is described in more detail.

[0101] Fig. 8A-8B are diagrams illustrating an offset (e.g., a radial offset of the scale section or the detector section) with respect to certain features of the Fig. 6 and Fig. 7 illustrate. Fig. Figure 8A can be seen with a representation of sections of the vertical centerline of the Fig. 7 and generally corresponds to it. In the illustration of the Fig. 8A (which may, for example, correspond to a zero radial offset condition in various implementations), the first central reference point REF1z (e.g., located at a central x- and / or y-axis position, such as at a centerline CL1, of the first scale element section PRTSC1 of the first scale track ST1 and / or the first sensing element section PRTSEN1) is at a radial distance RD1 Z from the pivot section PPN. The second central reference point REF2 Z '''' (e.g. located at a central x- and / or y-axis position, such as at a centerline CL2'''', of the second scale element section PRTSC2'''' of the second scale track ST2'''' and / or the second sensing element section PRTSEN2'''') is located at a radial distance RD2 Z'''' from the swivel section PPN.

[0102] A differential distance D12'''' is defined as the difference of the distance between the central reference points REF1z and REF2 z '''' and accordingly also as the difference between the first radial distance RD1 z and the second radial distance RD2 z ''''. Some specific numerical examples are given in the illustrations in Fig. 8A indicates that the first radial distance RD1 z 37.125 mm, the second radial distance RD2 z '''' 32.5 mm (e.g. corresponding to a value calculated above using the Fig. 6 and Fig. 7 described numerical example) and accordingly the difference distance D12''''' can be 4.625 mm. As noted above, the numerical examples in the illustration of the Fig. 7 further include that the first scale track width STW1 may be 4.0 mm, the second scale track width STW2'''' may be 2.75 mm and the separation distance SEP12'''' may be 1.25 mm.

[0103] Fig. Figure 8B illustrates a condition with an offset OFF P (e.g. a radial offset of the scale section or the detector section). In the illustration of the Fig. 8B (which, for example, in various implementations of a condition of a positive radial offset OFF P can correspond) a first central reference point REF1 P (e.g. the first scale element section PRTSC1 of the first scale track ST1) by the offset OFF P shifted upwards so that it is at a radial distance RD1 P from the pivot section PPN. Accordingly, the second central reference point REF2 P '''' (e.g. of the second scale element section PRTSC2''''' of the second scale track ST2'''') by the offset OFFP shifted upwards (e.g. by having the first and second scale element sections and corresponding scale tracks on a single printed circuit board that is connected to the MEPSM carrier component of the Fig. 2 can be coupled so that the scale section has a total radial offset OFF P may have) in order to be at a radial distance RD2 P '''' from the pivoting section PPN. It should be noted that the difference distance D12'''' in Fig. 8B as identical to the one in Fig. 8A (for which, for example, in certain implementations, the constant known differential distance D12'''' and / or corresponding properties can be considered as an internal reference for performing the self-correction described herein).

[0104] It should also be noted that while in this example the scale section may have a radial offset as indicated, the detector section including the sensing section with central reference points REF1 Z and REF2 z '''' can remain in positions as in Fig. 8A. Thus, in some implementations, the radial offset of the scale portion may be referenced with respect to the detector portion including the sensing portion (e.g., and in some implementations, the detector portion including the sensing portion may also or alternatively be referenced as radially offset with respect to the scale portion). In an alternative example, the described positions may be interchanged, with the scale portion being aligned with the central reference points REF1 Z and REF2 z '''' in positions as in Fig. 8A and the detection section with the central reference points REF1 P and REF2 P '''' in positions as in Fig. 8B (where, for example, the sensing portion may be shown to have a radial offset with respect to the scale portion, and / or the scale portion may be shown to have a radial offset with respect to the sensing portion). As some specific numerical examples, the illustrations in Fig. 8B indicates that the first radial distance RD1 P 37.225 mm, the second radial distance RD2 P '''' 32.6 mm (e.g. corresponding to the positive radial offset OFF P , which can be 0.1 mm). The constant differential distance D12'''' can still be 4.625 mm.

[0105] The Fig. 9A-9C are diagrams of traces 910-930 illustrating certain data resulting from the operations and a correction process of the converter of the Fig. 6 and Fig. 7, with an offset as shown in the Fig. 8A-8B. The x-axis of the curves 910-930 is located with respect to the arc distance along the first scale track TR1 (where, for example, in various implementations, EQUATION 13 or a similar calculation can be used to convert an angle value into an arc distance or vice versa, such as according to known formulas for such calculations concerning angle values ​​into arc distances, etc.). With respect to the plotted curve values ​​in millimeters in the Fig. 9A and Fig. 9C, in various implementations, an equation regarding chaindown values ​​in millimeters can be as follows: Chaindown (in millimeters) = Chaindown * θWSME1 * RD1

[0106] It should be noted that the term θ WSME1 * RD1 applies to both axes and cancels out when calculating the inclination. This convention, as used for the Fig. 9A and Fig. 9B also applies to the Fig. 11A, Fig. 11B, Fig. 14A, Fig. 14B, Fig. 17A and Fig. 19A. In addition, it should be noted that some or all of the curves of the Fig. 9A-9C, 11A-11C, 14A-14C, 17A-17B and 19A-19B and corresponding calculations described below can be made according to a -OFF convention, and that in an alternative +OFF convention the traces / curve traces can be horizontally inverse and the signs of the calculated values ​​can be reversed.

[0107] Fig. 9A is a trace 910 of a chaindown curve 911 of chaindown values ​​for a direct chaindown process. Fig. Figure 9B is a plot 920 of a chaindown curve 921 of chaindown values ​​for a double chaindown process. It is understood (as indicated, for example, by EQUATIONS 17-20) that the chaindown slope in Fig. 9B (ie for the double chaindown process) 1 / 2 of the chaindown slope in Fig. 9A (i.e., for the direct chaindown process) according to the inclusion of the m variable (e.g., equal to 2 in the current examples) in the denominator of the chaindown propensity equations for the double chaindown process.

[0108] Fig. 9C is a trace 930 illustrating long-range error traces 931 and 933, where long-range error trace 931 represents data before a correction process and long-range error trace 933 represents data after a correction process has been performed according to principles described herein (e.g., according to EQUATION 21 and / or other processes). More specifically, in various implementations, a chaindown bias may be determined based on data, such as indicated in trace 910 or 920. For example, in a specific implementation, determining the chaindown bias may involve applying a linear least squares fit to the data.

[0109] The determined chaindown tilt can be used to determine an offset value (e.g., corresponding to a radial offset of the scale portion or the detector portion), such as according to an equation (e.g., one of EQUATIONS 17-20) or another calculation or method that enables determination of an offset value based on a determined chaindown tilt or otherwise based on chaindown data. The determined offset value can be used to correct one or more values ​​used to determine a relative position between the detector portion and the scale portion. For example, the determined offset value can be used according to EQUATION 21 or another calculation to correct a spatial step value or other spatial value of the scale portion, which is then used in one or more equations (e.g.,EQUATION 12) or other calculation to determine a measurement (i.e., corresponding to a relative position between the detector section and the scale section).

[0110] As noted above, the long-range error trace 933 represents data after such a correction process has been performed. Trace 933 with the correction (i.e., with a remaining slope of approximately -0.67 μm of error per mm of measurement) indicates some improvement relative to the original error trace 931 (i.e., with a slope of approximately -2.67 μm of error per mm of measurement). However, the remaining error (i.e., -0.67 μm per mm) may be too high for certain practical applications. In various implementations, this may be characterized as resulting, at least in part, from the difficulty of accurately determining the chaindown slope from data such as that indicated in trace 910 or 920.

[0111] For example, the accuracy of determining the chaindown tilt may be compromised due to the nature of such data in practical applications, such as when the data may exhibit a certain degree of variance / fluctuation due to various factors (e.g., noise, amplitude deviations, misalignments, etc.), as indicated by the variances / oscillations in traces 911 and 921. Such limited accuracy in determining the chaindown tilt may result in limited accuracy in determining the offset value (corresponding, for example, to the radial offset of the scale portion or the detector portion) and, accordingly, the correction process resulting in the error trace 933 indicating the remaining error. Such properties may arise, at least in part, from certain dimensional relationships in the implementation of the Fig. 6 and Fig. 7, whereas the implementation of the Fig. 3A and Fig. 4 may result in improved properties that provide sufficient accuracy for certain practical applications, as described in more detail below.

[0112] The Fig. 10A to 10B are diagrams illustrating an offset (e.g., a radial offset of the scale portion or the detector portion) with respect to certain features of the Fig. 3A and Fig. 4. The Fig. 10A and Fig. 10B show certain similarities to the Fig. 8A and Fig. 8B. Fig. 10A can be seen with a representation of sections of the vertical centerline of the Fig. 4 and generally corresponds to it. In the illustration of the Fig. 10A (which, for example, in various implementations may correspond to a condition of a radial offset of zero), the first central reference point REF1 Z(e.g., located at a central x- and / or y-axis position, such as at a center line CL1, of the first scale element section PRTSC1 of the first scale track ST1 and / or the first sensing element section PRTSEN1) at a radial distance RD1 z from the pivot section PPN. The second central reference point REF2 Z (e.g. located at a central x- and / or y-axis position, such as at a center line CL2, of the second scale element section PRTSC2 of the second scale track ST2 and / or the second sensing element section PRTSEN2) is located at a radial distance RD2 Z from the swivel section PPN.

[0113] A difference distance D12 is defined as the difference of the distance between the central reference points REF1 Z and REF2 Z and accordingly also as the difference between the first radial distance RD1 Z and the second radial distance RD2 ZAs some specific numerical examples, the illustrations in Fig. 10A indicates that the first radial distance RD1 Z 37.125 mm, the second radial distance RD2z 25.5 mm (e.g. corresponding to a value determined above using the Fig. 3A and Fig. 4 described numerical example) and accordingly the difference distance D12 can be 11.625 mm. As noted above, the numerical examples in the illustration of the Fig. 4 further include that the first scale track width STW1 can be 4.0 mm, the second scale track width STW2 can be 2.75 mm and the separation distance SEP12 can be 8.25 mm.

[0114] Fig. 10B illustrates a condition with an offset OFF P (e.g. a radial offset of the scale section or the detector section). In the illustration of the Fig. 10B (which, for example, in various implementations of a condition of a positive radial offset OFF Pcan correspond) a first central reference point REF1 P (e.g. the first scale element section PRTSC1 of the first scale track ST1) by the offset OFF P shifted upwards so that it is at a radial distance RD1 P from the pivot section PPN. Accordingly, the second central reference point REF2 P (e.g. the second scale element section PRTSC2 of the second scale track ST2) by the offset OFF P shifted upwards (e.g. by having the first and second scale element sections and corresponding scale tracks on a single printed circuit board that is connected to the MEPSM carrier component of the Fig. 2 can be coupled so that the scale section has a total radial offset OFF P may have) in order to be at a radial distance RD2 P from the pivoting section PPN. It should be noted that the differential distance D12 in Fig. 10B as identical to the one in Fig. 10A (for which, for example, in certain implementations, the constant known differential distance D12 and / or corresponding properties can be considered as an internal reference for performing the self-correction described herein).

[0115] It should also be noted that while in this example the scale portion may have a radial offset as indicated, the detector portion including the sensing portion with central reference points REF1z and REF2z may remain at positions as in Fig. 10A. Thus, in some implementations, the radial offset of the scale portion may be referenced with respect to the detector portion including the sensing portion (e.g., and in some implementations, the detector portion including the sensing portion may also be referenced as radially offset with respect to the scale portion). In an alternative example, the described positions may be interchanged, with the scale portion having the central reference points REF1z and REF2z at positions as shown in Fig. 10A and the detection section with the central reference points REF1 P and REF2 P in positions such as Fig. 10B (where, for example, the sensing portion may be shown to have a radial offset with respect to the scale portion, and / or the scale portion may be shown to have a radial offset with respect to the sensing portion). As some specific numerical examples, the illustrations in Fig. 10B indicates that the first radial distance RD1 P 37.225 mm, the second radial distance RD2 P 25.6 mm (e.g. corresponding to the positive radial offset OFF P , which can be 0.1 mm). The constant differential distance D12 can still be 11.625 mm.

[0116] The Fig. 11A-11C are diagrams of traces 1110-1130 illustrating certain data resulting from the operations and a correction process of the converter of the Fig. 3A and Fig. 4, with an offset as shown in the Fig. 10A-10B. The x-axis of curves 1110-1130 lies along the first scale track TR1 with respect to the arc spacing. The curves 1110-1130 show certain similarities to the curves 910-930 of Fig. 9A-9C and are based at least in part on the descriptions of the Fig. 9A-9C unless otherwise stated below.

[0117] Fig. 11A is a trace 1110 of a chaindown curve 1111 of chaindown values ​​for a direct chaindown process. Fig. Figure 11B is a plot 1120 of a chaindown curve 1121 of chaindown values ​​for a double chaindown process. It is understood (as indicated by EQUATIONS 17-20) that the chaindown slope in Fig. 11 B (ie for the double chaindown process) 1 / 2 of the chaindown slope in Fig. 11A (i.e., for the direct chaindown process) according to the inclusion of the m variable (e.g., equal to 2 in the current examples) in the denominator of the chaindown slope equations for the double chaindown process. As a specific numerical example with respect to EQUATION 17, if an offset OFF to be determined is approximately 0.1 mm and if RD1=37.125 mm, RD2=25.5 mm, and n=25, EQUATION 17 indicates that CDSLOPE DIR ≈ 0.03, which corresponds approximately to the chaindown slope observed in the chaindown curve 1111, and could therefore be used to approximately determine the offset OFF.

[0118] Fig. 11C is a trace 1130 illustrating long-range error traces 1131 and 1133, where long-range error trace 1131 represents data before a correction process and long-range error trace 1133 represents data after a correction process has been performed according to principles described herein (e.g., according to EQUATION 21 and / or other processes). More specifically, in various implementations, the chaindown bias may be determined based on data, such as indicated in trace 1110 or 1120. For example, in a specific implementation, determining the chaindown bias may involve applying a linear least squares fit to the data.

[0119] The determined chaindown tilt can be used to determine an offset value OFF (e.g., corresponding to a radial offset of the scale portion or the detector portion), such as according to an equation (e.g., one of EQUATIONS 17-20) or another calculation or method that allows for the determination of an offset value based on a determined chaindown tilt or otherwise based on chaindown data. The determined offset value can be used to correct one or more values ​​used to determine a relative position between the detector portion and the scale portion. For example, the determined offset value can be used according to EQUATION 21 or another calculation to correct a spatial step value or other spatial value of the scale portion, which is then used in one or more equations (e.g.,EQUATION 12) or other calculation to determine a measurement (i.e., corresponding to a relative position between the detector section and the scale section).

[0120] As noted above, the long-range error curve 1133 represents data after such a correction process has been performed. The curve 1133 with the correction (i.e., with a remaining slope of approximately -0.2 µm error per mm measurement) indicates a significant improvement relative to the original error curve 1131 (i.e., with a slope of approximately -2.67 µm error per mm measurement). This may be more than sufficient for certain practical applications (e.g., in contrast to the Fig. 9A-9C, where significantly higher error levels remained after the correction process). Such improved properties of the Fig. 11A-11C may differ, at least in part, due to certain dimensional relationships in the implementation of the Fig. 3A and Fig. 4 compared to the implementation of the Fig. 6 and Fig. 7 result.

[0121] As noted above, a key aspect of the implementation of the Fig. 3A and Fig. 4 the large separation of the scale traces. With regard to certain relationships (e.g., as given by EQUATIONS 17-20), the large separation of the scale traces can be represented in certain examples by the relationship (1 / RD2)-(1 / RD1). For the exemplary values ​​of the implementation of the Fig. 3A and Fig. 4 of RD2=25.5 mm and RD1=37.125 mm, (1 / RD2)-(1 / RD1) = 0.01228 mm -1 , which corresponds to the desired results of the Fig. 11A-11C. This is in line with the implementation of Fig. 6 and Fig. 7, for which the exemplary values ​​RD2=32.5 mm and RD1=37.125 mm (1 / RD2)-(1 / RD1) = 0.00383 mm -1It should be noted that the factor 0.01228 mm -1 for the correction process is approximately 3.2x better than the factor 0.00383 mm -1 In certain implementations it may be desirable that the factor (1 / RD2)-(1 / RD1) is at least 0.01 mm -1 amounts.

[0122] Another way to represent / characterize the large separation of the scale tracks is the ratio RD1 / RD2. In the implementation of the Fig. 3A and Fig. 4, RD1 / RD2 = 1.456. This is in contrast to the implementation of the Fig. 6 and Fig. 7, where RD1 / RD2 = 1.142. In certain implementations, it may be desirable for the ratio of RD1 / RD2 to be at least 1.4.

[0123] Another way to represent / characterize the large separation of the scale tracks is to consider the separation distance SEP12 between the first and second scale tracks, such as in relation to the width of the first and / or second scale tracks. Fig. 6 and Fig. 7, it should be noted that the separation distance SEP12 is 1.25 mm, which is smaller than the width of the first and second scale tracks of 4.0 mm and 2.75 mm, respectively. In contrast, in the implementation of the Fig. 3A and Fig. 4 the separation distance SEP12 is 8.25 mm, which is greater than the width of the first and / or second scale track. In various implementations, it may be desirable for the separation distance SEP12 to be greater than the width of the first scale track and greater than the width of the second scale track. In various implementations, it may be desirable for the separation distance SEP12 to be greater than the width of the first and second scale tracks combined. In various implementations, it may be desirable for the separation distance SEP12 to be greater than a multiple of the width of the second scale track, such as greater than 2 times the width of the second scale track. In various implementations, it may further be desirable for a separation region between the first and second scale tracks to have a width defined by the separation distance SEP12 and for which the separation region is relatively empty (e.g., includesno scale element section arranged in a track section with a detection element section).

[0124] Fig. 12 is a diagram showing certain dimensions and characteristics of the measuring instrument of the Fig. 2 and a portion of a transducer TDR' configured to be used with an arcuate movement between a detector portion and a scale portion included in the measuring instrument of the Fig. 2 and has a second large separation of the scale tracks. The converter TDR' of the Fig. 12 is configured to generate signals similar to the TDR converter of the Fig. 3A and Fig. 4, and where Fig. 5 is representative of signals resulting from the operation of the implementation of the Fig. 12, as well as representative of signals resulting from the operation of the implementation of the Fig. 3A and Fig. 4. In this respect, the signals of the implementation of the Fig. 12 during operation be similar to the signals SIG1A, SIG1B, SIG2A and SIG2B of the implementation of the Fig. 3A.

[0125] It is therefore understood that each of the components of the TDR converter of the Fig. 3A a corresponding component in the converter TDR' of the Fig. 12 (which may be designated, for example, by a prime '). Thus, the components of the transducer TDR' will be understood by those skilled in the art based on the corresponding components of the transducer TDR, unless otherwise described below. A complete description of the components of the transducer TDR' is thus not provided herein. A primary difference between the transducer TDR' and the transducer TDR are certain dimensional relationships, some of which are described in more detail below.

[0126] The converter of the Fig. 12, the first scale element section PRTSC1' is located within a first scale track ST1' with a first scale track width STW1' (where, for example, the upper and lower edges of the first scale element section PRTSC1' can correspond to the upper and lower limits of the first scale track ST1'). The second scale element section PRTSC2' is located within a second scale track ST2' with a second scale track width STW2' (where, for example, the upper and lower edges of the second scale element section PRTSC2' can correspond to the upper and lower limits of the second scale track ST2'). A separation distance SEP12' is illustrated as a radial distance between the first and second scale tracks ST1' and ST2'. A separation area SEPA' is illustrated between the first and second scale tracks ST1' and ST2' (which, for example,has a radial width defined by the separation distance SEP12', as defined by the lower boundary of the first scale track ST1' and the upper boundary of the second scale track ST2'). The separation area SEPA' is empty (e.g., does not include a scale element section, as arranged in an encoder track section with a sensing element section).

[0127] The second scale element portion PRTSC2' of the second scale track ST2', as included as part of a second encoder track portion, is closer to the pivot portion PPN than the first scale element portion PRTSC1' of the first scale track ST1', as included as part of a first encoder track portion (e.g., such that a radial distance RD2' of a second central reference point REF2' of the second scale element portion PRTSC2' of the second scale track ST2' of the second encoder track portion is smaller than a radial distance RD1' of a first central reference point REF1' of the first scale element portion PRTSC1' of the first scale track ST1' of the first encoder track portion). In various implementations, the reference point REF1' may lie on the center line CL1' and the reference point REF2' may lie on the center line CL2'.A differential distance D12' is specified as the difference in distance between the central reference points REF1' and REF2' and accordingly also as the difference between the first radial distance RD1' and the second radial distance RD2'.

[0128] The first scale element section PRTSC1' has a first angular range θ RG1 and a corresponding arc length ARC1' and the second scale element section PRTSC2'' has a second angular range θ RG2 and a corresponding arc length ARC2'. The angular ranges θ RG1 and θ RG2 are stated as nominally equal and are shown in the example of Fig. 12 as nominally equal to the absolute angle measuring range θ ABS and the maximum angular movement range θ MAX In these examples, the arc lengths can be determined according to a standard arc length equation, such as ARC1' = RD1'(θ ABS ) and ARC2' = RD2'(θ ABS ) (where e.g. θABS has a value in radians). As some specific example dimensions, in one implementation, the first scale track width STW1' may be 4.0 mm, the second scale track width STW2' may be 2.75 mm, the separation distance SEP12' may be 13.85 mm, the first radial distance RD1' may be 38.725 mm, the second radial distance RD2' may be 21.5 mm, and the differential distance D12' may be 17.225 mm. In various implementations, such dimensions may result in certain desirable operating characteristics, as described in more detail below.

[0129] The Fig. 13A-13B are diagrams illustrating an offset (e.g., a radial offset of the scale portion or the detector portion) with respect to certain features of the Fig. 12. The Fig. 13A and Fig. 13B are the Fig. 10A and Fig. 10B and are based on the description of the Fig. 10A and Fig. 10B unless otherwise noted below. The main difference between the Fig. 13A and Fig. 13B are the numerical examples of the dimensions, which are described in more detail below. In the illustration of the Fig. 13A (which, for example, in various implementations may correspond to a condition of zero radial offset), the first central reference point REF1z' lies at a radial distance RD1z' from the pivot section PPN. The second central reference point REF2 Z ' is located at a radial distance RD2z' from the pivoting section PPN.

[0130] As some specific numerical examples, the illustrations in Fig. 13A indicates that the first radial distance RD1 Z ' 38.725 mm, the second radial distance RD2 Z ' 21.5 mm (e.g. corresponding to a value calculated above using the Fig. 12 described numerical example) and accordingly the difference distance D12' can be 17.225 mm. As noted above, the numerical examples in the illustration of the Fig. 12 further include that the first scale track width STW1' may be 4.0 mm, the second scale track width STW2' may be 2.75 mm and the separation distance SEP12' may be 13.85 mm.

[0131] In the illustration of the Fig. 13B (which, for example, in various implementations of a condition of a positive radial offset OFF P can correspond) a first central reference point REF1 P ' (e.g. the first scale element section PRTSC1' of the first scale track ST1') by the offset OFF P shifted upwards so that it is at a radial distance RD1 P ' from the pivot section PPN. Accordingly, the second central reference point REF2 P' (e.g. the second scale element section PRTSC2' of the second scale track ST2') by the offset OFF P shifted upwards so that it is at a radial distance RD2 P ' from the pivot section PPN. It should be noted that the difference distance D12' in Fig. 13B as identical to the one in Fig. 13A (for which, for example, in certain implementations, the constant known differential distance D12' and / or corresponding properties may be considered as an internal reference for performing the self-correction described herein).

[0132] It should also be noted that while in this example the scale section may have a radial offset as indicated, the detector section including the sensing section with central reference points REF1 Z ' and REF2 Z ' can remain in positions as in Fig. 13A. Thus, in some implementations, the radial offset of the scale portion may be referenced with respect to the detector portion including the sensing portion (e.g., and in some implementations, the detector portion including the sensing portion may also be referenced as radially offset with respect to the scale portion). In an alternative example, the described positions may be interchanged, with the scale portion being aligned with the central reference points REF1 Z ' and REF2 Z ' in positions like Fig. 13A and the detection section with the central reference points REF1 P ' and REF2 P ' in positions like Fig. 13B (where, for example, the sensing portion may be shown to have a radial offset with respect to the scale portion, and / or the scale portion may be shown to have a radial offset with respect to the sensing portion). As some specific numerical examples, the illustrations in Fig. 13B indicates that the first radial distance RD1 P ' 38.825 mm, the second radial distance RD2 P ' 21.6 mm (e.g. corresponding to the positive radial offset OFF P , which can be 0.1 mm). The constant differential distance D12' can still be 17.225 mm.

[0133] The Fig. 14A-14C are diagrams of traces 1410-1430 illustrating certain data resulting from the operations and a correction process of the converter of the Fig. 12, with an offset as shown in the Fig. 13A-13B. The x-axis of curves 1410-1430 lies along the first scale track TR1 with respect to the arc spacing. The curves 1410-1430 show certain similarities to the curves 1110-1130 of Fig. 11A-11C and are based at least in part on the descriptions of the Fig. 11A-11C unless otherwise stated below.

[0134] Fig. 14A is a trace 1410 of a chaindown curve 1411 of chaindown values ​​for a direct chaindown process. Fig. Figure 14B is a chaindown curve 1420 of chaindown values ​​for a double chaindown process. As a specific numerical example with respect to Equation 17, when an offset OFF to be determined is approximately 0.1 mm and when RD1=38.725 mm, RD2=21.5 mm, and n=25, Equation 17 indicates that CDSLOPE DIR≈ 0.05, which corresponds approximately to the chaindown slope observed in the chaindown curve 1411, and could therefore be used to approximately determine the offset OFF.

[0135] Fig. 14C is a trace 1430 illustrating long-range error traces 1431 and 1433, where long-range error trace 1431 represents data before a correction process and long-range error trace 1433 represents data after a correction process has been performed according to principles described herein (e.g., according to EQUATION 21 and / or other processes). More specifically, in various implementations, the chaindown bias may be determined based on data, such as indicated in trace 1410 or 1420. For example, in a specific implementation, determining the chaindown bias may involve applying a linear least squares fit to the data.

[0136] The determined chaindown tilt can be used to determine an offset value OFF (e.g., corresponding to a radial offset of the scale portion or the detector portion), such as according to an equation (e.g., one of EQUATIONS 17-20) or another calculation or method that allows for the determination of an offset value based on a determined chaindown tilt or otherwise based on chaindown data. The determined offset value can be used to correct one or more values ​​used to determine a relative position between the detector portion and the scale portion. For example, the determined offset value can be used according to EQUATION 21 or another calculation to correct a spatial step value or other spatial value of the scale portion, which is then used in one or more equations (e.g.,EQUATION 12) or other calculation to determine a measurement (i.e., corresponding to a relative position between the detector section and the scale section).

[0137] As noted above, the long-range error curve 1433 represents data after such a correction process has been performed. The curve 1433 with the correction (i.e., with a remaining slope of approximately -0.1 µm error per mm measurement) indicates a significant improvement relative to the original error curve 1431 (i.e., with a slope of approximately -2.67 µm error per mm measurement). This may be more than sufficient for certain practical applications (e.g., in contrast to the Fig. 9A-9C, where significantly higher error levels remained after the correction process). Such improved properties of the Fig. 14A-14C may differ, at least in part, due to certain size relationships in the implementation of the Fig. 12-13B compared to the implementation of the Fig. 6 and Fig. 7 result.

[0138] An essential aspect of the implementation of the Fig. 12-13B is the large separation of the scale traces according to the principles described herein. With regard to certain relationships (e.g., as given by EQUATIONS 17-20), the large separation of the scale traces can be represented in certain examples by the relationship (1 / RD2)-(1 / RD1). For the exemplary values ​​of the implementation of the Fig. 12-13B of RD2=21.5 mm and RD1=38.725 mm, (1 / RD2)-(1 / RD1) = 0.02069 mm -1 , which corresponds to the desired results of the Fig. 14A-14C. This is in line with the implementation of the Fig. 6 and Fig. 7, for which the exemplary values ​​RD2=32.5 mm and RD1=37.125 mm (1 / RD2)-(1 / RD1) = 0.00383 mm -1In certain implementations, it may be desirable that the factor (1 / RD2)-(1 / RD1) is at least 0.01 mm -1 or at least 0.015 mm -1 amounts.

[0139] Another way to represent / characterize the large separation of the scale tracks is the ratio RD1 / RD2. In the implementation of the Fig. 12-13B, RD1 / RD2 = 1.801. This is in contrast to the implementation of the Fig. 6 and Fig. 7, where RD1 / RD2 = 1.142. In certain implementations, it may be desirable for the ratio of RD1 / RD2 to be at least 1.4 or at least 1.5.

[0140] Another way to represent / characterize the large separation of the scale tracks is to consider the separation distance SEP12 between the first and second scale tracks, such as in relation to the width of the first and / or second scale tracks. Fig. 6 and Fig. 7, it should be noted that the separation distance SEP12 is 1.25 mm, which is smaller than the width of the first and second scale tracks of 4.0 mm and 2.75 mm, respectively. In contrast, in the implementation of the Fig. 12-13B, the separation distance SEP12 is 13.85 mm, which is greater than the width of the first and / or second scale track. In various implementations, it may be desirable for the separation distance SEP12 to be greater than the width of the first scale track and greater than the width of the second scale track. In various implementations, it may be desirable for the separation distance SEP12 to be greater than the width of the first and second scale tracks combined. In various implementations, it may be desirable for the separation distance SEP12 to be greater than a multiple of the width of the second scale track, such as greater than 2 times the width of the second scale track or greater than 3 times the width of the second scale track.

[0141] Fig. 15 is a diagram showing certain dimensions and characteristics of the measuring instrument of the Fig. 2 and a portion of a transducer TDR'' configured to be used with an arcuate movement between a detector portion and a scale portion included in the measuring instrument of the Fig. 2 and has a second large separation of the scale tracks. The converter TDR'' of the Fig. 15 may have certain different design features (e.g., n=60 and m=2 and corresponding spatial step relationships according to EQUATION 1), but may otherwise be configured to operate substantially similarly to the transducer TDR of Fig. 3A and Fig. 4. Thus, the components of the TDR converter will be understood by those skilled in the art based on the corresponding components of the TDR converter, unless otherwise described below. A complete description of the components of the TDR converter is therefore not provided herein. Certain differences of the TDR converter compared to the TDR converter are certain dimensional relationships, some of which are described in more detail below.

[0142] The converter of the Fig. 15, the first scale element section PRTSC1'' is located within a first scale track ST1'' with a first scale track width STW1'' (where, for example, the upper and lower edges of the first scale element section PRTSC1'' can correspond to the upper and lower limits of the first scale track ST1''). The second scale element section PRTSC2'' is located within a second scale track ST2'' with a second scale track width STW2'' (where, for example, the upper and lower edges of the second scale element section PRTSC2'' can correspond to the upper and lower limits of the second scale track ST2''). A separation distance SEP12'' is illustrated as a radial distance between the first and second scale tracks ST1'' and ST2''. A separation area SEPA'' is illustrated between the first and second scale tracks ST1'' and ST2'' (which, for example,has a radial width defined by the separation distance SEP12'', as defined by the lower boundary of the first scale track ST1'' and the upper boundary of the second scale track ST2''). The separation area SEPA'' is empty (e.g., does not include a scale element section, as arranged in a sensor track section with a sensing element section).

[0143] The second scale element portion PRTSC2'' of the second scale track ST2'', as included as part of a second encoder track portion, is closer to the pivot portion PPN than the first scale element portion PRTSC1'' of the first scale track ST1'', as included as part of a first encoder track portion (e.g., such that a radial distance RD2'' of a second central reference point REF2'' of the second scale element portion PRTSC2'' of the second scale track ST2'' of the second encoder track portion is smaller than a radial distance RD1'' of a first central reference point REF1'' of the first scale element portion PRTSC1'' of the first scale track ST1'' of the first encoder track portion). In various implementations, the reference point REF1'' may lie on the centerline CL1'' and the reference point REF2'' may lie on the centerline CL2''.A differential distance D12'' is specified as the difference in distance between the central reference points REF1'' and REF2'' and accordingly also as the difference between the first radial distance RD1'' and the second radial distance RD2''.

[0144] The first scale element section PRTSC1'' has a first angular range θ RG1 and a corresponding arc length ARC1'' and the second scale element section PRTSC2'''' has a second angular range θ RG2 and a corresponding arc length ARC2''. The angular ranges θ RG1 and θ RG2 are stated as nominally equal and are shown in the example of Fig. 15 as nominally equal to the absolute angle measuring range θ ABS and the maximum angular movement range θ MAX In these examples, the arc lengths can be determined according to a standard arc length equation, such as ARC1'' = RD1''(θ ABS ) and ARC2'' = RD2''(θ ABS) (where e.g. θ ABS has a value in radians). As some specific example dimensions, in one implementation, the first scale track width STW1'' may be 4.0 mm, the second scale track width STW2'' may be 2.75 mm, the separation distance SEP12'' may be 16.625 mm, the first radial distance RD1'' may be 40 mm, the second radial distance RD2'' may be 20 mm, and the differential distance D12'' may be 20 mm. In various implementations, such dimensions may result in certain desirable operating characteristics, as described in more detail below.

[0145] The Fig. 16A-16B are diagrams illustrating an offset (e.g., a radial offset of the scale portion) in a first direction (e.g., in a positive direction) with respect to certain features of the Fig. 15. The Fig. 16A and Fig. 16B are the Fig. 10A and Fig. 10B and are based on the description of the Fig. 10A and Fig. 10B unless otherwise noted below. The main difference between the Fig. 16A and Fig. 16B are the numerical examples of the dimensions, which are described in more detail below. In the illustration of the Fig. 16A (which, for example, in various implementations may correspond to a condition of a radial offset of zero) the first central reference point REF1 Z '' at a radial distance RD1 Z '' from the pivot section PPN. The second central reference point REF2 Z '' is located at a radial distance RD2 Z '' from the swivel section PPN.

[0146] As some specific numerical examples, the illustrations in Fig. 16A indicates that the first radial distance RD1 Z '' 40 mm, the second radial distance RD2 Z '' 20 mm (e.g. corresponding to a value calculated above using the Fig. 15 described numerical example) and accordingly the difference distance D12'' can be 20 mm. As noted above, the numerical examples in the illustration of the Fig. 15 further include that the first scale track width STW1'' may be 4.0 mm, the second scale track width STW2'' may be 2.75 mm and the separation distance SEP12'' may be 16.625 mm.

[0147] In the illustration of the Fig. 16B (which, for example, in various implementations of a condition of a positive radial offset OFF P can correspond) a first central reference point REF1 P '' (e.g. the first scale element section PRTSC1'' of the first scale track ST1'') by the offset OFF P shifted upwards so that it is at a radial distance RD1 P '' from the pivot section PPN. Accordingly, the second central reference point REF2 P'' (e.g. the second scale element section PRTSC2'' of the second scale track ST2'') by the offset OFF P shifted upwards so that it is at a radial distance RD2 P '' from the pivot section PPN. It should be noted that the difference distance D12'' in Fig. 16B as identical to the one in Fig. 16A (for which, for example, in certain implementations, the constant known differential distance D12'' and / or corresponding properties may be considered as an internal reference for performing the self-correction described herein).

[0148] It should also be noted that while in this example the scale section may have a radial offset as indicated, the detector section including the sensing section with central reference points REF1 Z '' and REF2 Z '' can remain in positions as in Fig. 16A. Thus, in some implementations, the radial offset of the scale portion may be referenced with respect to the detector portion including the sensing portion (e.g., and in some implementations, the detector portion including the sensing portion may also be referenced as radially offset with respect to the scale portion). In an alternative example, the described positions may be interchanged, with the scale portion being aligned with the central reference points REF1 Z '' and REF2 Z '' in positions like Fig. 16A and the detection section with the central reference points REF1 P '' and REF2 P '' in positions like Fig. 16B (where, for example, the sensing portion may be shown to have a radial offset with respect to the scale portion, and / or the scale portion may be shown to have a radial offset with respect to the sensing portion). As some specific numerical examples, the illustrations in Fig. 16B indicates that the first radial distance RD1 P '' 40.1 mm, the second radial distance RD2 P '' 20.1 mm (e.g. corresponding to the positive radial offset OFF P , which can be 0.1 mm). The constant differential distance D12'' can still be 20 mm.

[0149] The Fig. 17A and Fig. 17B are diagrams of traces 1720 and 1730, respectively, illustrating certain data resulting from the operations and a correction process of the converter of the Fig. 15, with an offset as shown in the Fig. 16A-16B. The x-axis of curves 1720 and 1730 lies along the first scale track TR1 with respect to the arc spacing. Curves 1720 and 1730 show certain similarities to curves 1120 and 1130 of Fig. 11B and Fig. 11C and are based at least in part on the descriptions of the Fig. 11B and Fig. 11C, unless otherwise stated below.

[0150] Fig. Figure 17A is a chaindown curve 1720 of chaindown values ​​for a double chaindown process. As a specific numerical example with respect to Equation 19, when an offset OFF to be determined is approximately 0.1 mm and when RD1=40 mm, RD2=20 mm, n=60, and m=2, Equation 19 indicates that CDSLOPE DIR≈ 0.075, which corresponds approximately to the chaindown slope observed in the chaindown curve 1721, and could therefore be used to approximately determine the offset OFF.

[0151] Fig. 17B is a trace 1730 illustrating long-range error traces 1731, 1732, and 1733, where long-range error trace 1731 represents data from the first scale trace before a correction process, long-range error trace 1732 represents data from the second scale trace before a correction process, and long-range error trace 1733 represents data after a correction process has been performed according to principles described herein (e.g., according to EQUATION 21 and / or other processes). More specifically, in various implementations, the chaindown bias may be determined based on data, such as indicated in trace 1720. For example, in a specific implementation, determining the chaindown bias may involve applying a linear least squares fit to the data.

[0152] The determined chaindown tilt can be used to determine an offset value OFF (e.g., corresponding to a radial offset of the scale portion or the detector portion), such as according to an equation (e.g., one of EQUATIONS 19-20) or another calculation or method that allows for the determination of an offset value based on a determined chaindown tilt or otherwise based on chaindown data. The determined offset value can be used to correct one or more values ​​used to determine a relative position between the detector portion and the scale portion. For example, the determined offset value can be used according to EQUATION 21 or another calculation to correct a spatial step value or other spatial value of the scale portion, which is then used in one or more equations (e.g.,EQUATION 12) or other calculation to determine a measurement (i.e., corresponding to a relative position between the detector section and the scale section).

[0153] As noted above, the long-range error trace 1733 represents data after such a correction process has been performed. The trace 1733 with the correction (i.e., with a remaining slope of approximately -0.1 µm error per mm measurement) indicates a significant improvement relative to the original error trace 1731 (i.e., with a slope of approximately -2.5 µm error per mm measurement). This may be more than sufficient for certain practical applications (e.g., in contrast to the Fig. 9A-9C, where significantly higher error levels remained after the correction process). Such improved properties of the Fig. 17A-17B may differ, at least in part, due to certain dimensional relationships in the implementation of the Fig. 15-16B compared to the implementation of the Fig. 6 and Fig. 7 result.

[0154] An essential aspect of the implementation of the Fig. 15-16B is the large separation of the scale traces according to the principles described herein. With regard to certain relationships (e.g., as given by EQUATIONS 19-20), the large separation of the scale traces can be represented in certain examples by the relationship (1 / RD2)-(1 / RD1). For the exemplary values ​​of the implementation of the Fig. 15-16B of RD2=20 mm and RD1=40 mm, (1 / RD2)-(1 / RD1) = 0.02500 mm -1 , which corresponds to the desired results of the Fig. 17A-17B. This is in contrast to the implementation of the Fig. 6 and Fig. 7, for which the exemplary values ​​RD2=32.5 mm and RD1=37.125 mm (1 / RD2)-(1 / RD1) = 0.00383 mm -1In certain implementations, it may be desirable that the factor (1 / RD2)-(1 / RD1) is at least 0.01 mm -1 or at least 0.015 mm -1 or at least 0.017 mm -1 or at least 0.020 mm -1 amounts.

[0155] Another way to represent / characterize the large separation of the scale tracks is the ratio RD1 / RD2. In the implementation of the Fig. 15-16B, RD1 / RD2 = 2.0. This is in contrast to the implementation of the Fig. 6 and Fig. 7, where RD1 / RD2 = 1.142. In certain implementations, it may be desirable for the ratio of RD1 / RD2 to be at least 1.4, or at least 1.5, or at least 1.6.

[0156] Another way to represent / characterize the large separation of the scale tracks is to consider the separation distance SEP12 between the first and second scale tracks, such as in relation to the width of the first and / or second scale tracks. Fig. 6 and Fig. 7, it should be noted that the separation distance SEP12 is 1.25 mm, which is smaller than the width of the first and second scale tracks of 4.0 mm and 2.75 mm, respectively. In contrast, in the implementation of the Fig. 15-16B, the separation distance SEP12 is 16.625 mm, which is greater than the width of the first and / or second scale track. In various implementations, it may be desirable for the separation distance SEP12 to be greater than the width of the first scale track and greater than the width of the second scale track. In various implementations, it may be desirable for the separation distance SEP12 to be greater than the width of the first and second scale tracks combined. In various implementations, it may be desirable for the separation distance SEP12 to be greater than a multiple of the width of the second scale track, such as equal to or greater than 2 times the width of the second scale track, or equal to or greater than 3 times the width of the second scale track, or equal to or greater than 4 times the width of the second scale track.

[0157] The Fig. 18A-18B are diagrams illustrating an offset (e.g., a radial offset of the scale section) in a second direction (e.g., in a negative direction) with respect to certain features of the Fig. 15. The Fig. 18A and Fig. 18B are the Fig. 16A and Fig. 16B and are based on the description of the Fig. 16A and Fig. 16B, except for an offset OFFn in the negative direction and unless otherwise noted below. In the illustration of the Fig. 18A (which, for example, in various implementations may correspond to a condition of a radial offset of zero) the first central reference point REF1 Z '' at a radial distance RD1 Z '' from the pivot section PPN. The second central reference point REF2 Z '' is located at a radial distance RD2 Z '' from the swivel section PPN. Fig. 18A is identical to Fig. 16A and is based on the above description of Fig. 16A to understand.

[0158] In the illustration of the Fig. 18B (which, for example, in various implementations may correspond to a condition of a negative radial offset OFFn), a first central reference point REF1n'' (e.g., of the first scale element section PRTSC1'' of the first scale track ST1'') was shifted upwards by the offset OFFn so that it lies at a radial distance RD1n'' from the pivot section PPN. Correspondingly, the second central reference point REF2n'' (e.g., of the second scale element section PRTSC2'' of the second scale track ST2'') was shifted upwards by the offset OFFn so that it lies at a radial distance RD2n'' from the pivot section PPN. It should be noted that the difference distance D12'' in Fig. 18B as identical to the one in Fig. 16A and Fig. 18A (for which, for example, in certain implementations, the constant known differential distance D12'' and / or corresponding properties can be considered as an internal reference for performing the self-correction described herein).

[0159] It should also be noted that while in this example the scale section may have a radial offset as indicated, the detector section including the sensing section with central reference points REF1 Z '' and REF2 Z '' can remain in positions as in Fig. 16A and Fig. 18A. Thus, in some implementations, the radial offset of the scale portion may be referenced with respect to the detector portion including the sensing portion (e.g., and in some implementations, the detector portion including the sensing portion may also be referenced as radially offset with respect to the scale portion). In an alternative example, the described positions may be interchanged, with the scale portion being aligned with the central reference points REF1 Z '' and REF2 Z '' in positions like Fig. 18A and the detection section with the central reference points REF1n'' and REF2n'' at positions as shown in Fig. 18B (where, for example, the sensing portion may be shown to have a radial offset with respect to the scale portion, and / or the scale portion may be shown to have a radial offset with respect to the sensing portion). As some specific numerical examples, the illustrations in Fig. 18B indicates that the first radial distance RD1n'' can be 39.9 mm, and the second radial distance RD2n'' can be 19.9 mm (e.g., corresponding to the positive radial offset OFFn, which can be 0.1 mm). The constant differential distance D12'' can still be 20 mm.

[0160] The Fig. 19A and Fig. 19B are diagrams of 1920 and 1930, respectively, illustrating certain data resulting from the operations and a correction process of the converter of the Fig. 15, with an offset as shown in the Fig. 18A-18B. The x-axis of the curves 1920 and 1930 lies along the first scale track TR1 with respect to the arc spacing. The curves 1920 and 1930 show certain similarities to the curves 1720 and 1730 of the Fig. 17A and Fig. 17B, ​​except that they are directed to a condition with a negative offset rather than a positive offset. It should be understood that any of the implementations described herein may operate similarly with negative offset (e.g., such operations may be comparable to the operations with positive offset, as can be seen by comparing the operations of Fig. 19A and Fig. 19B with the events of the Fig. 17A and Fig. 17B).

[0161] Fig. Figure 19A is a chaindown curve 1920 of chaindown values ​​for a double chaindown process. As a specific numerical example with respect to Equation 19, when an offset OFF to be determined is approximately -0.1 mm (i.e., corresponding to a negative offset) and when RD1=40 mm, RD2=20 mm, n=60, and m=2, Equation 19 indicates that CDSLOPE DIR ≈ -0.075, which corresponds approximately to the chaindown slope observed in the 1921 chaindown curve, and could therefore be used to approximately determine the offset OFF.

[0162] Fig. 19B is a trace 1930 illustrating long-range error traces 1931, 1932, and 1933, where long-range error trace 1931 represents data from the first scale trace before a correction process, long-range error trace 1932 represents data from the second scale trace before a correction process, and long-range error trace 1933 represents data after a correction process has been performed according to principles described herein (e.g., according to EQUATION 21 and / or other processes). More specifically, in various implementations, the chaindown bias may be determined based on data, such as indicated in trace 1920. For example, in a specific implementation, determining the chaindown bias may include applying a linear least squares fit to the data.

[0163] The determined chaindown tilt can be used to determine an offset value OFF (e.g., corresponding to a radial offset of the scale portion or the detector portion), such as according to an equation (e.g., one of EQUATIONS 19-20) or another calculation or method that allows for the determination of an offset value based on a determined chaindown tilt or otherwise based on chaindown data. The determined offset value can be used to correct one or more values ​​used to determine a relative position between the detector portion and the scale portion. For example, the determined offset value can be used according to EQUATION 21 or another calculation to correct a spatial step value or other spatial value of the scale portion, which is then used in one or more equations (e.g.,EQUATION 12) or other calculation to determine a measurement (i.e., corresponding to a relative position between the detector section and the scale section).

[0164] As noted above, the long-range error trace 1933 represents data after such a correction process has been performed. The trace 1933 with the correction (i.e., with a remaining slope of approximately 0.1 µm error per mm of measurement) indicates a significant improvement relative to the original error trace 1931 (i.e., with a slope of approximately 2.5 µm error per mm of measurement). This may be more than sufficient for certain practical applications (e.g., in contrast to the Fig. 9A-9C, where significantly higher error levels remained after the correction process). Such improved properties of the Fig. 19A-19B may differ, at least in part, due to certain dimensional relationships in the implementation of the Fig. 15-16B compared to the implementation of the Fig. 6 and Fig. 7 result.

[0165] An essential aspect of the implementation of the Fig. 15-16B is the large separation of the scale tracks according to the principles described herein. Various aspects and relationships regarding the large separation of the scale tracks in the implementation of the Fig. 15-16B were described above after the description of the Fig. 17A and Fig. 17B.

[0166] Fig. 20 is a flowchart illustrating a method 2000 for operating an arcuate measuring instrument to determine a relative position between a detector section and a scale section. Block 2010 includes providing drive signals to cause a field generating section PRTFGE to generate a changing magnetic flux. Block 2020 includes receiving detector signals from a detector section 167, the detector signals including: detector signals from a first set of first sensing elements SET1SEN1 cooperating with first signal-modulating scale elements SME1; and detector signals from a first set of second sensing elements SET1SEN2 cooperating with second signal-modulating scale elements SME2.A maximum range of arcuate motion of the movable encoder portion is less than 360 degrees, and the first scale element portion is arranged with a central reference point at a first radial distance RD1 from the pivot portion, and the second scale element portion is arranged with a central reference point at a second radial distance RD2 from the pivot portion, wherein the ratio of RD1 / RD2 is at least 1.4. Block 2030 includes determining a relative position between the detector portion 167 and the scale portion 170 based at least in part on the detector signals input from the detector portion 167.

[0167] In connection with the operations at block 2030 for determining a relative position between the detector portion (167) and the scale portion (170) based at least in part on the detector signals from the detector portion, various processing and / or signal combining techniques may be utilized (e.g., as will be apparent to one of ordinary skill in the art and at least in part in accordance with the teachings in the incorporated references). Briefly, in various implementations, two drive operations may be utilized to generate and process the signals from the detector portion. In various implementations, the two drive operations may be performed simultaneously or at different times.

[0168] More specifically, as part of a first drive operation, the first field-generating element section PRTFGE1 can be driven (e.g., with corresponding drive signals from the signal processing configuration 166). While the first field-generating element section PRTFGE1 is driven, corresponding signals (e.g., signals SIG1A and SIG1B) can be read (e.g., received, processed, etc.) from the first sensing elements SEN1 of the first sensing element section PRTSEN1 of the detector section. As part of a second drive operation, the second field-generating element section PRTFGE2 can be driven (e.g., with corresponding drive signals from the signal processing configuration 166). While the second field-generating element section PRTFGE2 is driven, corresponding signals (e.g., signals SIG2A and SIG2B) can be read (e.g.,received, processed, etc.). The detector signals (i.e., from the detector section) generated during the first and second drive operations can be used to determine a relative position (e.g., an absolute position between the detector section and the scale section). In various implementations, the detector signals can include four signals (e.g., SIG1A, SIG1B, SIG2A, SIG2B) that can be used to determine the relative position, such as the signals SIG1A and SIG1B of the first drive operation and the signals SIG2A and SIG2B of the second drive operation.

[0169] Fig. 21 is a flowchart illustrating a method 2100 for a correction process for a measuring instrument with arc motion. Block 2110 includes providing drive signals to cause a field generating section PRTFGE to generate a changing magnetic flux. Block 2120 includes receiving detector signals from a detector section 167, the detector signals including: detector signals from a first set of first sensing elements SET1SEN1 cooperating with first signal-modulating scale elements SME1; and detector signals from a first set of second sensing elements SET1SEN2 cooperating with second signal-modulating scale elements SME2.Block 2130 includes determining, based at least in part on the received detector signals, an offset value corresponding to a radial offset of a scale portion including the first signal-modulating scale elements and the second signal-modulating scale elements. Block 2140 includes using the determined offset value to correct one or more values ​​used to determine a relative position between the detector portion and the scale portion. For example, the determined offset value may be used according to EQUATION 21 or another calculation to correct a spatial step value or other spatial value of the scale portion, which may then be used in one or more equations (e.g., EQUATION 12) or other calculation or processing for determining a measurement (i.e., corresponding to a relative position between the detector portion and the scale portion).

[0170] In various implementations, determining the offset value at block 2130 includes determining a differential slope (e.g., a chaindown slope). In various implementations, the differential slope may correspond to a slope of a difference between an absolute position signal and at least one of: a first position signal corresponding at least in part to detector signals from the first sensing elements (e.g., as part of a direct chaindown process, as described herein); or a second position signal corresponding at least in part to detector signals from the second sensing elements (e.g., as part of a first step of a double chaindown process, as described herein).In various implementations, the difference between the absolute position signal and the at least one of the first position signal or the second position signal corresponds at least in part to a difference between the phases of the respective signals (such as indicated by EQUATIONS 9, 10, 14 and 15).

[0171] In various implementations, using the determined offset value at block 2140 to correct one or more values ​​includes at least partially dividing the determined offset value by at least one radial distance of the first scale element portion. For example, as indicated by EQUATION 21, a correction value may be characterized by the determined offset value OFF D divided by the radial distance RD1 of the first scale element section and multiplied by a spatial step (e.g. θ WSME1) of the first scale element section. This correction value (ie corresponding to -θ WSME1 (OFF D / RD1)) can then be added to the spatial step of the first scale element section (e.g. added to θ WSME1 ) are added to obtain the corrected value of the spatial step θ WSME1Cwhich is subsequently used (e.g., in EQUATION 12 or another calculation) to determine a relative position between the detector portion and the scale portion (e.g., as part of measurement operations). In various implementations, the method 2100 (e.g., the signal processing configuration is configured to perform) further includes determining an absolute relative position between the detector portion and the scale portion based at least in part on detector signals input from the detector portion, wherein the detector signals include detector signals from the first set of first sensing elements and detector signals from the first set of second sensing elements (e.g., similar to block 2030 of Fig. 20, and possibly corresponding to entering a normal measurement mode to perform normal measurement operations after completion of a calibration process).

[0172] Generally, according to the principles described herein, in implementations configured such that the first radial distance of the first scale element portion and corresponding to the first scale track has a large relative difference to the second radial distance of the second scale element portion and corresponding to the second scale track (e.g., or where there is otherwise a large difference between the positions of the scale tracks), the effect of a radial offset / radial misalignment (e.g., of the scale portion with respect to the sensing portion of the detector portion) is also relatively large. The effect / difference is recognizable, detectable, etc., from a process that, as part of an absolute measurement determination, includes an integer number of spatial steps (e.g., corresponding to an integer number of signal-modulating elements of a scale element portion of a scale track).For example, determining an integer number of spatial steps as part of a chaindown process involves a rounding process in which the rounded-off amounts are referred to as chaindown values. A determination of a chaindown slope (which may be determined, for example, from a chaindown plot of the chaindown values ​​or otherwise from the chaindown values) may be made, which may be used to determine an offset value (which may correspond, for example, to a radial offset of the scale portion, such as with respect to the sensing portion of the detector portion and / or with respect to the pivot portion or other reference, or which may correspond to a radial offset of the sensing portion of the detector portion, such as with respect to the scale portion and / or with respect to the pivot portion or other reference).The determined offset value can be used to correct one or more values ​​used to determine a relative position between the detector section and the scale section. For example, a value (e.g., corresponding to a spatial step of a first scale element section and corresponding to a first scale track, or an absolute measurement range, or other spatial value used as part of a determination of an absolute measurement) can be corrected (e.g., as part of a correction and / or calibration process) and subsequently used as part of determinations of an absolute measurement (e.g., corresponding to determinations of a relative position between the detector section and the scale section).

[0173] In various implementations, the correction process may be performed as part of a calibration procedure (i.e., a calibration process). As part of such a process, the measuring instrument may be placed in a calibration mode (e.g., upon initial assembly of the measuring instrument, such as after coupling the movable encoder section MEP to the support member MEPSM, or at any other time when such calibration is to be performed). Measurement data (e.g., corresponding to detector signals received from the detector section) may be collected in memory as the measuring instrument is moved with an arcuate motion over a range of positions (e.g., with relative movement between the scale section and the detector section). The measurement data may be analyzed, and an offset value may be determined (e.g.,corresponding to a radial offset of the movable encoder section MEP, which may correspond to a radial offset of the scale section relative to the detector section or of the detector section relative to the scale section, etc.). Determining the offset value may involve determining a differential tilt (e.g., a chaindown tilt). In various implementations, for very large differential tilts, the data set may be reversed (e.g., jumped from -0.5 to +0.5 or from +0.5 to -0.5), for which a reverse process may be performed or otherwise utilized so that an overall differential tilt can be determined. In various implementations, the offset value may be determined from the differential tilt. The determined offset value may then be used to correct one or more values ​​used to determine a relative position between the detector section and the scale section.Once calibration is complete, the measuring instrument may be placed in or otherwise enter a normal operating mode (during which, for example, accurate measurements can be determined based on the calibration performed). It is understood that such calibration can help ensure the accuracy of the measuring instrument, particularly with regard to any radial misalignments that may be present (e.g., with regard to assembly and / or manufacturing tolerances for the components, such as with regard to the coupling of the movable encoder section MEP to the support member MEPSM, which may result in a radial misalignment with respect to the relative positions of the scale section and the detector section, etc.).

[0174] While certain of the examples described herein have primarily referred to arcuate electronic position encoders with arcuate encoder track sections, it should be understood that certain similar or identical principles may be applied to arcuate electronic position encoders with linearly shaped encoder track sections, and the techniques described herein may be similarly applicable. Some examples of arcuate electronic position encoders with linearly shaped encoder track sections are described in U.S. Patent Application No. 18 / 391,275, filed December 20, 2023, which is hereby incorporated by reference in its entirety. Some examples of arcuate electronic position encoders with arcuate encoder track sections are described in U.S. Patent Application No. 18 / 391,294, filed December 20, 2023, which is hereby incorporated by reference in its entirety.Each of these applications describes certain design principles that can be used in combination with the teachings described herein to form electronic position sensors having the features and operations described herein.

[0175] As used herein, the term "nominal" covers variations in one or more parameters that are within acceptable tolerances. As an example, in one implementation, a term such as "nominal" may correspond to a minimal deviation from a defined value (such as a deviation of less than 5%, or less than 2%, or less than 1%, as per acceptable tolerances, etc.).

[0176] It should be understood that the principles disclosed and claimed herein may be readily and desirably combined with various features disclosed in the incorporated references. The various implementations described above may be combined to provide further implementations. All U.S. patents and U.S. patent applications referred to in this specification are incorporated herein by reference in their entirety. Aspects of the implementations may be modified to utilize concepts of the various patents and applications, if desired, to provide still further implementations. These and other changes may be made to the implementations in light of the foregoing detailed description.In general, the terms used in the following claims should not be construed to limit the claims to the specific implementations disclosed in the description and claims, but should be construed to include all possible implementations, together with the full scope of equivalents to which such claims are entitled. QUOTES CONTAINED IN THE DESCRIPTION

[0000] This list of documents submitted by the applicant was generated automatically and is included solely for the convenience of the reader. This list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions. Cited patent literature

[0000] US 2022 / 0341733

[0002] US 6,011,389

[0022] US 9,958,294

[0042] US 5,841,274

[0049] US 5,886,519

[0049] US 5,894,678

[0049] US 6,124,708

[0049] US 10,520,335

[0049] US 10,612,943

[0049] US 10,775,199

[0049] US 18 / 391,275

[0174] US 18 / 391,294

[0174]

Claims

[1] Measuring instrument comprising: a movable portion configured to rotate in an arcuate motion about a pivot portion, the movable portion including a movable encoder portion; an electronic position sensor configured to measure an absolute relative position between a detector portion and a scale portion, wherein the movable sensor portion comprises one of the detector portion or the scale portion, the electronic position sensor comprising: the scale portion extending along a scale direction, the scale portion comprising: a first scale element section comprising first signal-modulating scale elements; and a second scale element section comprising second signal-modulating scale elements; and the detector portion configured to be proximate to the scale portion upon relative movement between the detector portion and the scale portion resulting from the arcuate movement of the movable encoder portion, the detector portion comprising: a field-generating section configured to generate a changing magnetic flux in response to drive signals; and a recording section comprising: a first sensing element portion comprising a first set of first sensing elements and arranged in a first track portion with the first scale element portion; and a second sensing element portion comprising a first set of second sensing elements and arranged in a second track portion with the second scale element portion; and a signal processing configuration configured to: Providing drive signals to cause the field generating section to generate a changing magnetic flux; Receiving detector signals from the detector section, the detector signals comprising: Detector signals from the first set of first sensing elements cooperating with first signal modulating scale elements; and Detector signals from the first set of second sensing elements cooperating with second signal modulating scale elements; Determining an offset value corresponding to a radial offset of at least one of the scale portion or the detector portion based at least in part on the received detector signals; and Using the determined offset value to correct one or more values ​​used to determine a relative position between the detector section and the scale section. [2] The measuring instrument of claim 1, wherein determining the offset value comprises determining a chaindown slope. [3] The measuring instrument of claim 2, wherein the chaindown slope is determined from at least one of a direct chaindown process or a double chaindown process. [4] The measuring instrument of claim 3, wherein the chaindown slope corresponds to a chaindown curve of chaindown values. [5] The measuring instrument of claim 1, wherein using the determined offset value to correct one or more values ​​includes at least partially dividing the determined offset value by at least a radial distance of the first scale element portion from the pivot portion. [6] The measuring instrument of claim 1, wherein the signal processing configuration is further configured to determine an absolute relative position between the detector portion and the scale portion based at least in part on detector signals input from the detector portion, the detector signals including detector signals from the first set of first sensing elements and detector signals from the first set of second sensing elements. [7] A measuring instrument according to claim 1, wherein the field generating section comprises: a first field-generating element section arranged in the first track section and configured to cooperate with first signal-modulating scale elements of the first scale element section and the first sensing elements of the first sensing element section; and a second field generating element section arranged in the second track section and configured to cooperate with second signal modulating scale elements of the second scale element section and the second sensing elements of the second sensing element section. [8] Measuring instrument according to claim 1, wherein: the first and second scale element portions of the first and second track portions are arcuate and parallel to each other, the second track portion being closer to the pivot portion than the first track portion; the first signal-modulating scale elements according to an angular spatial step θ WSME1 a first signal-modulating element are arranged along the first scale element section and the second signal-modulating scale elements are arranged according to an angular spatial step θ WSME2a second signal modulating element which differs from the angular spatial step θ WSME1 of the first signal-modulating element, are arranged along the second scale element section; and the first and second scale element sections have a corresponding absolute angular range θ ABS define. [9] Measuring instrument according to claim 8, wherein a ratio of the angular spatial steps θ WSME2 / θ WSME1 of the signal modulating elements can be expressed so that it is equal to at least one of the following equations: (nm / (n−1)); (nm / (n+1)); ((nm+1) / n); ((nm−1) / n); where n is a positive integer and m is a positive integer that is at least 2. [10] Measuring instrument according to claim 8, wherein the absolute angular range θ ABS equal to one of nθ WSME1 or nθ WSME2where n is a positive integer and the absolute angular range θ ABS is less than 360 degrees. [11] Measuring instrument according to claim 1, wherein θ WSME2 greater than θ WSME1 is. [12] Measuring instrument according to claim 1, wherein: operating the first track section comprises the first set of first sensing elements providing detector signals responsive to a local effect on a changing magnetic flux provided by first signal-modulating scale elements of the first scale element section; and operating the second track section comprises the first set of second sensing elements providing detector signals responsive to a local effect on a changing magnetic flux provided by second signal modulating scale elements of the second scale element section. [13] Measuring instrument according to claim 1, wherein: the first sensing element section further comprises one or more additional sets of first sensing elements, each additional set of first sensing elements having a spatial phase offset relative to the first set of first sensing elements; and the second sensing element portion further comprises one or more additional sets of second sensing elements, each additional set of second sensing elements having a spatial phase offset relative to the first set of second sensing elements. [14] The measuring instrument of claim 1, wherein the first and second signal modulating scale elements comprise conductive plates and the first and second sensing elements comprise conductive loops. [15] A method for operating a measuring instrument, the measuring instrument comprising: a movable portion rotating in an arcuate motion about a pivot portion, the movable portion including a movable encoder portion; and an electronic position sensor configured to measure an absolute relative position between a detector portion and a scale portion, wherein the movable sensor portion of the movable portion comprises one of the detector portion or the scale portion, the electronic position sensor comprising: the scale portion extending along a scale direction, the scale portion comprising: a first scale element section comprising first signal-modulating scale elements; and a second scale element section comprising second signal-modulating scale elements; and the detector portion configured to be proximate to the scale portion upon relative movement between the detector portion and the scale portion resulting from the arcuate movement of the movable encoder portion, the detector portion comprising: a field-generating section configured to generate a changing magnetic flux in response to drive signals; and a recording section comprising: a first sensing element portion comprising a first set of first sensing elements and arranged in a first track portion with the first scale element portion; and a second sensing element portion comprising a first set of second sensing elements and arranged in a second track portion with the second scale element portion; the method comprising: Providing drive signals to cause the field generating section to generate a changing magnetic flux; Receiving detector signals from the detector section, the detector signals comprising: Detector signals from the first set of first sensing elements cooperating with first signal modulating scale elements; and Detector signals from the first set of second sensing elements cooperating with second signal modulating scale elements; Determining an offset value corresponding to a radial offset of at least one of the scale portion or the detector portion based at least in part on the received detector signals; and Using the determined offset value to correct one or more values ​​used to determine a relative position between the detector section and the scale section. [16] The method of claim 15, wherein determining the offset value comprises determining a chaindown slope. [17] The method of claim 15, further comprising determining a relative position between the detector portion and the scale portion based at least in part on the detector signals input from the detector portion. [18] The method of claim 15, wherein: the cooperation of the first set of first sensing elements with first signal-modulating scale elements includes the first set of first sensing elements providing detector signals responsive to a local effect on a changing magnetic flux provided by first signal-modulating scale elements of the first scale element section; and the cooperation of the first set of second sensing elements with second signal-modulating scale elements includes the first set of second sensing elements providing detector signals responsive to a local effect on a changing magnetic flux provided by second signal-modulating scale elements of the second scale element section. [19] An electronic position sensor configured to measure an absolute relative position between a detector portion and a scale portion and for use in a measuring instrument comprising a movable portion configured to rotate in an arcuate motion, the electronic position sensor comprising: the scale portion extending along a scale direction, the scale portion comprising: a first scale element section comprising first signal-modulating scale elements; and a second scale element section comprising second signal modulating scale elements; the detector portion configured to be proximate to the scale portion upon relative movement between the detector portion and the scale portion resulting from the arcuate movement of the movable portion, the detector portion comprising: a field-generating section configured to generate a changing magnetic flux in response to drive signals; and a recording section comprising: a first sensing element portion comprising a first set of first sensing elements and arranged in a first track portion with the first scale element portion; and a second sensing element portion comprising a first set of second sensing elements and arranged in a second track portion with the second scale element portion; and a signal processing configuration configured to: Providing drive signals to cause the field generating section to generate a changing magnetic flux; Receiving detector signals from the detector section, the detector signals comprising: Detector signals from the first set of first sensing elements cooperating with first signal modulating scale elements; and Detector signals from the first set of second sensing elements cooperating with second signal modulating scale elements; Determining an offset value corresponding to a radial offset of at least one of the scale portion or the detector portion based at least in part on the received detector signals; and Using the determined offset value to correct one or more values ​​used to determine a relative position between the detector section and the scale section. [20] The electronic position sensor of claim 19, wherein determining the offset value comprises determining a differential inclination.

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