Measuring instrument with arcuate movement and correction process

Abstract

Disclosed is a measuring instrument having an arcuate motion and a correction process, comprising: a movable portion configured to rotate in an arcuate motion about a pivot portion; and an electronic position encoder configured to measure an absolute relative position between the detector portion and the scale portion, one of the detector portion and the scale portion forming part of the movable portion. The maximum movement range and the maximum absolute measurement range of the movable encoder part are both smaller than 360 degrees. An offset value corresponding to a radial offset (e.g., of the scale portion or the detector portion) is determined based at least in part on a detector signal received from the detector portion. The determined offset value is utilized to correct one or more values that are used to determine a relative position between the detector portion and the scale portion (e.g., a value corresponding to a spatial step of the scale portion or other spatial value).

Description

Technical Field

[0001] The present disclosure relates to metrology and, more particularly, to measuring instruments, such as may include a movable member (e.g., a stylus) that rotates about a pivot portion in an arcuate motion, and wherein a corresponding measurement result is determined by an electronic position encoder, and some examples of such measuring instruments include test indicators, lever dial indicators, lever micrometers, etc. Background Art

[0002] Certain measuring instruments include a movable member (e.g., including a stylus) that moves in an arcuate motion when in use (e.g., for determining a measurement result of a workpiece being inspected). As an example, a test indicator (e.g., sometimes also referred to as a lever indicator, lever dial indicator, lever micrometer, etc.) is described in U.S. Patent Publication No. 2022 / 0341733 (‘733 publication), which includes a stylus that rotates about a pivot portion at a corresponding rotation angle (e.g., in an arcuate motion). Rotation of the stylus causes movement of a sector gear on the opposite side of the pivot portion, which correspondingly rotates an encoder that detects the rotation angle. As described, such test indicators can be used to inspect workpieces (e.g., where the contact point of the stylus bears against the surface of the workpiece), such as for measuring minute displacements (such as circumferential bending, total bending, flatness, and parallelism), and for precision comparison inspections (such as for determining machining errors of machined workpieces, etc.).

[0003] In certain embodiments, it may be desirable for such measuring instruments to include an encoder (e.g., for measuring such arcuate motion) that provides a desired combination of features, such as a combination of compact size, high resolution, accuracy, low cost, contamination resistance, etc. An encoder configuration that provides an improved combination of such features in such measuring instruments would be desirable. Summary of the Invention

[0004] This Summary of the Invention is provided to introduce a selection of concepts in a simplified form that are further described below in the Detailed Description. This Summary of the Invention is not intended to identify key features of the claimed subject matter nor is it intended 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 part and an electronic position encoder. The movable part is configured to rotate about a pivot portion in an arcuate motion and includes a movable encoder part MEP.

[0006] The electronic position encoder is configured to measure, for example, the absolute relative position between a detector part and a scale part along an arcuate movement direction. The movable encoder part MEP of the movable part includes one of the detector part or the scale part. The scale part extends along a scale direction and includes: a first scale element part including a first signal-modulated scale element; and a second scale element part including a second signal-modulated scale element. The detector part is configured to be close to the scale part, wherein the relative movement between the detector part and the scale part is caused by the arcuate movement of the movable encoder part MEP. The detector part includes: a field generation part configured to generate a varying magnetic flux in response to a drive signal; and a sensing part. The sensing part includes: a first sensing element part including a first group of first sensing elements and arranged together with the first scale element part in a first track part; and a second sensing element part including a first group of second sensing elements and arranged together with the second scale element part in a second track part.

[0007] In various embodiments, the maximum movement range of the arcuate movement of the movable encoder part is less than 360 degrees, and the first scale element part is arranged such that a central reference point is located at a first radial distance RD1 from the pivot part, and the second scale element part is arranged such that a central reference point is located at a second radial distance RD2 from the pivot part, wherein the ratio of RD1 / RD2 is at least 1.4.

[0008] According to another aspect, a method for operating the measuring instrument including the movable part and the electronic position encoder is provided. The method generally includes two steps. The first step includes providing a drive signal to cause the field generation part to generate a varying magnetic flux. The second step includes receiving a detector signal from the detector part, wherein the detector signal includes: a detector signal from the first group of first sensing elements operating in combination with the first signal-modulated scale element; and a detector signal from the first group of second sensing elements operating in combination with the second signal-modulated scale element.

[0009] In various embodiments, the measuring instrument further includes a signal processing configuration configured to: provide a drive signal to cause the field generating portion of the detector portion to generate a varying magnetic flux; receive a detector signal from the detector portion, where the detector signal includes: a detector signal from the first set of first sensing elements operating in conjunction with a first signal modulating scale element; and a detector signal from the first set of second sensing elements operating in conjunction with a second signal modulating scale element; determine, at least in part based on the received detector signal, an offset value corresponding to a radial offset of at least one of the scale portion or the detector portion; and utilize 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 for operating the measuring instrument including the movable portion and the electronic position encoder is provided. The method generally includes four steps. The first step includes providing a drive signal to cause the field generating portion to generate a varying magnetic flux. The second step includes receiving a detector signal from the detector portion, where the detector signal includes: a detector signal from the first set of first sensing elements operating in conjunction with a first signal modulating scale element; and a detector signal from the first set of second sensing elements operating in conjunction with a second signal modulating scale element. The third step includes determining, at least in part based on the received detector signal, an offset value corresponding to a radial offset of at least one of the scale portion or the detector portion. The fourth step includes utilizing 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 a further aspect, there is provided the electronic position encoder configured to measure, for example, an absolute relative position between the detector portion and the scale portion along an arcuate motion direction. The electronic position encoder is configured to be used in the measuring instrument including a movable portion configured to rotate in an arcuate motion about a pivot portion. Description of the Drawings

[0012] Figure 1 is a diagram of a measuring instrument including an electronic position encoder having a transducer, the transducer including a detector portion and a scale portion.

[0013] Figure 2 is a diagram showing additional details of a particular embodiment of a measuring instrument such as Figure 1 of the measuring instrument.

[0014] Figure 3A is a diagram of a particular embodiment of a portion of the transducer configured to be used with an arcuate motion between a detector portion and a scale portion, such as may be used in Figure 2 in a measuring instrument and having a first large separation of the scale track. Figure 3B is Figure 3A an illustrative list of references used in

[0015] Figure 4 is a diagram showing Figure 2 the measuring instrument and Figure 3A certain dimensions and features of the transducer.

[0016] Figure 5 is a diagram showing certain signals generated by the operation of the transducer of Figure 3A and Figure 4 wherein there is an arcuate motion between the detector portion and the scale portion.

[0017] Figure 6 is a diagram of a specific implementation of a part of the transducer configured to be used with the arcuate motion between the detector portion and the scale portion, such as can be used in Figure 2 the measuring instrument and having a relatively small separation of the scale track compared to the specific implementation of Figure 3A

[0018] Figure 7 is a diagram showing Figure 2 the measuring instrument and Figure 6 certain dimensions and features of the transducer.

[0019] FIG. 8A to FIG. 8B is a diagram showing an offset with respect to certain features of Figure 6 and Figure 7

[0020] 9A to 9C is a diagram of a chart showing certain data generated by the operation and calibration process of the transducer of Figure 6 and Figure 7 wherein there is an offset such as shown in FIG. 8A to FIG. 8B

[0021] FIG. 10A to FIG. 10B is a diagram showing an offset with respect to certain features of Figure 3A and Figure 4

[0022] FIG. 11A to FIG. 11C is a diagram of a chart showing certain data generated by the operation and calibration process of the transducer of Figure 3A and Figure 4 wherein there is an offset such as shown in FIG. 10A to FIG. 10B

[0023] Fig.12 is a diagram showing Figure 2Diagram of certain dimensions and features of a measuring instrument and a part of a transducer configured to be used with an arcuate motion between a detector part and a scale part, such as can be used in Figure 2 a measuring instrument and having a second largest separation of the scale tracks.

[0024] FIG. 13A to FIG. 13B is a diagram showing the offset with respect to Fig.12 certain features.

[0025] FIG. 14A to FIG. 14C is a diagram showing a chart of certain data generated by the operation and calibration process of a transducer of Fig.12 wherein there are offsets such as FIG. 13A to FIG. 13B as shown.

[0026] Fig.15 is a diagram showing Figure 2 a measuring instrument and certain dimensions and features of a part of a transducer configured to be used with an arcuate motion between a detector part and a scale part, such as can be used in Figure 2 a measuring instrument and having a second largest separation of the scale tracks.

[0027] FIG. 16A to FIG. 16B is a diagram showing the offset in a first direction with respect to Fig.15 certain features.

[0028] FIG. 17A to FIG. 17B is a diagram showing a chart of certain data generated by the operation and calibration process of a transducer of Fig.15 wherein there are offsets in the first direction such as FIG. 16A to FIG. 16B as shown.

[0029] FIG. 18A to FIG. 18B is a diagram showing the offset in a second direction with respect to Fig.15 certain features.

[0030] FIG. 19A to FIG. 19B is a diagram showing a chart of certain data generated by the operation and calibration process of a transducer of Fig.15 wherein there are offsets in the second direction such as FIG. 18A to FIG. 18B as shown.

[0031] Fig. 20 is a flowchart showing a method for operating a measuring instrument using an arcuate motion to determine the relative position between a detector part and a scale part.

[0032] Fig.21 is a flowchart showing a method for the calibration process of a measuring instrument having an arcuate motion.

[0033] Fig. 22is a plan view schematically showing certain features of a representative prior art electronic position encoder configured to be used with a linear movement between a detector portion and a scale portion and presented as background information relevant to the various principles described herein. Detailed Description

[0034] Figure 1 is a block diagram of exemplary components of a measuring instrument 100 (e.g., a test indicator) including an electronic absolute position encoder 101. In various embodiments, the electronic absolute position encoder 101 includes a scale portion 170 and a detector portion 167, which together form a transducer TDR. As will be described in more detail below, encoder 101 as utilized 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 encoder 101 has a unique signal combination). Generally speaking, ABS encoding may be more robust than incremental (INC) encoding (e.g., counting increments as it moves), and thus more desirable for certain embodiments (e.g., tolerating power cycling without losing position, etc.). The measuring instrument 100 includes suitable user interface features such as a display 138 and / or user-operable control elements 136 (e.g., switches, buttons, etc.). The measuring instrument 100 may additionally include a power supply 165.

[0035] All of these elements of the measuring instrument 100 and / or encoder 101 are coupled to a signal processing configuration 166 (e.g., including one or more signal processors), which in various embodiments may be embodied as signal processing and display electronics circuitry in an integrated circuit (IC) chip. The signal processing configuration 166 receives detector signals from the detector portion 167 and processes these detector signals to determine the 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 embodiments, the signal processing configuration 166 and the detector portion 167 may be included as part of an electronic assembly 160 (e.g., arranged on a substrate, etc.).

[0036] Figure 2 is a diagram showing additional details of one embodiment of a measuring instrument 100 such as Figure 1 The measuring instrument 100 includes an electronic position encoder 101, which includes a transducer TDR. As will be described in more detail below, in Figure 2In the example, the measuring instrument 100 is a test indicator (e.g., sometimes also referred to as a lever indicator, lever type dial indicator, lever type micrometer, etc.). In various specific embodiments, certain aspects of the mechanical structure and operation of the measuring instrument 100 may be similar to those of certain existing test indicators, such as those described in the previously incorporated '733 disclosure.

[0037] As Figure 2 shown, the contact portion CPN (e.g., a stylus) is coupled to the pivot portion PPN and rotates about the pivot portion at a corresponding angle (e.g., in an arcuate motion) (e.g., rotates about the pivot point PPT of the pivot portion PPN). The contact portion CPN includes a contact point CPT at its end, such as may be used to contact a workpiece to perform a measurement operation (e.g., such as for measuring the displacement and / or dimensions of a workpiece, etc.). The measurement result may be displayed on a digital display (e.g., Figure 1 the display 138), such as may be mounted on the measuring instrument body MIB or at other locations of the measuring instrument 100. Certain control elements (e.g., Figure 1 the control element 136) may also be provided on the measuring instrument 100.

[0038] The movable part MPN of the measuring instrument 100 includes a contact portion CPN located on the first side of the pivot portion PPN, and a movable encoder portion support member MEPSM that supports a movable encoder portion MEP on the second side of the pivot portion PPN. The movable part MPN is configured such that a workpiece measurement operation that causes the contact portion CPN to rotate relative to the pivot portion PPN (e.g., for measuring a workpiece) (e.g., generated by contacting the workpiece surface with the contact point CPT or otherwise moving along the workpiece surface) correspondingly causes the support member MEPSM and the movable encoder portion MEP to rotate in an arcuate motion ARCM (e.g., in the arcuate motion direction ARCD). In the measuring instrument 100, the maximum angular movement range θ of the arcuate motion ARCM of the movable encoder portion MEP MAX is less than 360 degrees (e.g., in some specific embodiments, it may be less than 90 degrees, 45 degrees, or 15 degrees, etc.). Such a relatively small angular movement range is typical for certain types of measuring instruments, especially for applications that measure a workpiece using only a relatively small deflection of the contact portion CPM (e.g., a stylus).

[0039] In various specific embodiments, the movable encoder portion MEP may include either a detector portion 167 or a scale portion 170 (e.g., as described above with respect to Figure 1 and as will be described below with respect to Figure 3A(which will be described in more detail). The other of the detector section 167 or the scale section 170 that is not included in the movable encoder section MEP is included in the fixed encoder section FEP (not shown but, for example, fixable to the measuring instrument body MIB) at a position close to the movable encoder section MEP. In one specific illustrative example, the movable encoder section MEP may be arranged parallel to and facing the fixed encoder section FEP, and the front face of the movable encoder section MEP facing the fixed encoder section FEP may be separated from the fixed encoder section FEP by a certain gap (e.g., about 0.1 mm to 0.2 mm) along the z-axis direction. Regardless of whether the detector section 167 is included in the movable encoder section MEP or the fixed encoder section FEP, the front face of the detector section 167 (e.g., including its constituent conductors) may be covered with an insulating coating.

[0040] In Figure 2 the orientation of, the fixed encoder section FEP may be located directly below the movable encoder section MEP (and thus not visible in Figure 2 ). The fixed encoder section FEP and the movable encoder section MEP (e.g., noting that it includes the detector section 167 and the scale section 170) accordingly form the transducer TDR. As described above, the relative movement between the movable encoder section MEP and the fixed encoder section FEP (i.e., which corresponds to the relative movement between the detector section 167 and the scale section 170) is caused by the movement of the movable encoder section MEP in the arcuate movement direction ARCD, as caused by the movement of the contact portion CPN (e.g., as part of a workpiece measurement operation).

[0041] As Figure 2 shown, the first movement limit indicator ML1 and the second movement limit indicator ML2 are shown as dashed lines, which indicate the maximum movement range of the arcuate movement ARCM (e.g., including the maximum movement range of the movable encoder section MEP), and correspond to the maximum angular movement range θ MAX . The electronic position encoder 101 is an absolute position encoder that uses two or more encoder tracks (e.g., see Figure 3A ) to provide absolute positioning (i.e., where each position has a unique signal combination), as corresponding to the absolute angular measurement range θ ABS , as will be described in more detail below. In Figure 2 the example of, the absolute angular measurement range θ ABS is indicated as approximately equal to the maximum angular movement range θ MAX , but it should be understood that in alternative embodiments, the absolute angular measurement range θ ABS and the maximum angular movement range θ MAX may be different (e.g., in most such embodiments, the absolute angular measurement range θABS Greater than the maximum angular movement range θ MAX and, in all cases, the absolute angular measurement range θ ABS is less than 360 degrees). It should be understood that for certain specific implementations, for illustrative purposes, in the Figure 2 example of, the absolute angular measurement range θ ABS and the maximum angular movement range θ MAX are shown and may not be to scale.

[0042] The endpoint ENDPT at the end of the movable encoder portion support member MEPSM also corresponds to the endpoint of the movable part MPN. The endpoint ENDPT is located at the opposite end of the movable part MPN relative to the contact point CPT at the end of the contact portion CPN. As described herein, the contact portion CPN and the contact point CPT are located on the first side of the pivot portion PPN, and the support member MEPSM, the movable encoder portion MEP, and the endpoint ENDPT are located on the second side of the pivot portion PPN.

[0043] It should be understood that Figure 1 and Figure 2 the measuring instrument of is one application in various applications that typically implement an electronic position encoder, which has been developed over the years to provide a relatively optimized combination of compact size, low-power operation (e.g., extended battery life), high-resolution and high-accuracy measurement, low cost, dirt resistance, etc. In any of these applications, even a small improvement in any of these factors is highly desirable but difficult to achieve, especially considering the design limitations imposed for commercial success in various applications. The principles disclosed herein provide improvements in some of these factors for various applications.

[0044] Fig. 22 is a plan view schematically showing certain features of a representative prior art inductive electronic position encoder shown in U.S. Patent No. 6,011,389 ('389 patent), which is hereby incorporated by reference in its entirety and presented as background information related to various principles disclosed elsewhere herein. Fig. 22 Also included are reference numeral annotations to show like reference numerals or symbols used to indicate like elements in other figures included herein. In the following brief description based on the disclosure of the '389 patent, some comparable reference numerals or symbols in other figures of the present disclosure are shown in parentheses close to the original reference numerals of the '389 patent. The complete description related to the prior art Fig. 22 can be found in the '389 patent. Therefore, only a brief description is included herein (e.g., including certain teachings from the '389 patent relevant to the present disclosure).

[0045] As disclosed in the '389 patent, as Fig. 22 shown, the transducer includes at least two substantially coplanar conductors or winding paths. The transmitter winding 102 (PRTFGE”') forms a large planar loop. In this example, the transmitter winding 102 forms the entire field generating portion PRTFGE”'. The receiver winding 104 (PRTSEN”', SETSEN”') is substantially in the same plane as the transmitter winding 102 and is arranged in a zigzag or sinusoidal pattern in one direction as indicated by the arrow and then in the opposite direction as indicated by the arrow such that the winding crosses itself to form alternating loops 106 (SEN+”') and 108 (SEN-”') that are inserted between each other, as shown. Thus, each alternating loop 106 (SEN+”') and 108 (SEN-”') of the receiver winding 104 (PRTSEN”', SETSEN”') has a different winding direction compared to adjacent loops. By applying an alternating (changing) current to the transmitter winding 102 (PRTFGE”'), the transmitter winding generates a time-varying magnetic field (changing magnetic flux) that extends through the loops 106 (SEN+”') and 108 (SEN-”') of the receiver winding 104 (PRTSEN””, SETSEN”'). In various embodiments, the loops 106 (SEN+”') and 108 (SEN-”') can be designated as a set of sensing elements (SETSEN”') of the sensing portion (PRTSEN”').

[0046] If the scale portion (170”') or the scale pattern 112 (180”') (a portion of which is outlined by the edge indicating alternating long and short dashed lines in Fig. 22 including a conductive object (e.g., a signal modulating element such as the conductive plate 114 (SME”'), several of which are outlined by short dashed lines on the scale pattern 112 in Fig. 22 is moved closer (near) to the detector portion (167”'), the changing magnetic field generated by the transmitter winding 102 (PRTFGE”') will induce eddy currents in the conductive object, which in turn establish a magnetic field from the object that cancels the changing transmitter magnetic field (changing magnetic flux). Thus, the magnetic flux received by the receiver winding 104 (PRTSEN”') is changed or interrupted, resulting in the receiver winding outputting a non-zero EMF signal (voltage) at the output terminals V+ and V- of the receiver winding 104, which will change polarity as the conductive object moves between the “+” loop 106 (SEN+”') and the “-” loop 108 (SEN-”').

[0047] The distance between the positions of two loops of the same polarity (e.g., the distance between the position of loop 106 (SEN+”') and the position of the next loop 106 (SEN+”')) is defined as the linear spatial step (e.g., which may also be referred to as pitch or wavelength) 110 (WSEN”') of the set of sensing elements (SETSEN”'), and in certain specific embodiments is equal to the linear spatial step (e.g., which may also be referred to as pitch or wavelength) 110 (WSME”') of the scale pattern (180”') of the scale portion (170”') set 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-”') thus has a length or maximum dimension 0.5*(WSEN”') along the measurement axis direction (MA”'), which measurement axis direction may also be referred to as the scale direction SCD”'. If the above conductive object (e.g., conductive plate 114 (SME”')) approaches the receiver winding 104 (PRTSEN”') and continuously changes its position along the measurement axis 300 (MA”'), then due to the periodic variation of loops 106 (SEN+”') and 108 (SEN-”') and the local interruption of the transmitted magnetic field caused by the conductive object (e.g., conductive plate 114 (SME”')), the AC amplitude of the signal output from the receiver winding (PRTSEN”') will vary continuously and periodically with the linear spatial step (e.g., which may also be referred to as pitch or wavelength) 110 (WSME”'). Therefore, the signal output from the receiver winding (PRTSEN”') can be utilized (e.g., processed) to indicate the relative position between the detector portion (167”') and the scale portion (170”'). It should be understood that Fig. 22 The emitter winding 102 (PRTFGE”') and the receiver winding 104 (PRTSEN”') shown in and described above are an example of a prior art specific implementation of the elements designated as the detector portion (167”').

[0048] Figure 3A A view of a specific implementation that is part of the transducer TDR, which transducer TDR is configured to be used with an arcuate motion ARCM between the detector portion 167 and the scale portion 170, such as may be used in Figure 1 and Figure 2 the electronic position encoder 101 of the measuring instrument 100. The transducer TDR utilizes two track portions TR1 and TR2, as Figure 3A shown. Figure 3B is Figure 3A An illustrative list of references used in

[0049] It should be understood that certain aspects of the field generating elements and sensing elements of the detector portion (e.g., detector portion 167, etc.) as described herein may be at least partially based on the principles described above with respect to Fig. 22 and may be operated and understood. In a Figure 3A specific implementation, the scale portion 170, the detector portion 167, and the signal processing configuration 166 (e.g., Figure 1 and Figure 2 ) work together to provide an electronic position encoder 101 that can be used to measure the relative position between two elements (e.g., between the detector portion 167 and the scale portion 170 and / or an element attached thereto) along an arcuate motion direction. In various specific 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 the measurement operation includes relative movement between the two substrates (e.g., the two substrates may be relatively flat and parallel to each other). In various specific implementations, the detector portion 167 and the scale portion 170 are generally located in respective planes extending along the x-axis direction and the y-axis direction, where the z-axis direction is orthogonal to these planes.

[0050] In various specific implementations, the scale portion 170 extends along a scale direction SCD and includes: a first scale element portion PRTSC1 that includes a first signal modulation element SME1; and a second scale element portion PRTSC2 that includes a second signal modulation element SME2. The first signal modulation element SME1 is arranged along the scale direction SCD according to a first signal modulation element pattern PATSME1 and thus forms the first signal modulation element pattern. The second signal modulation element SME2 is arranged along the scale direction SCD according to a second signal modulation element pattern PATSME2 and thus forms the second signal modulation element pattern. The first signal modulation element pattern PATSME1 and the second signal modulation element pattern PATSME2 are respective portions of the periodic scale pattern 180 of the scale portion 170. In various specific implementations, the periodic scale pattern 180 may alternatively be referred to as a signal modulation pattern 180. In various specific implementations, the first signal modulation element SME1 and / or the second signal modulation element SME2 (i.e., as included in the first scale element portion PRTSC1 and the second scale element portion PRTSC2) may be fabricated on the scale substrate (e.g., using known printed circuit fabrication methods).

[0051] The relative movement between the detector portion 167 and the scale portion 170 (e.g., in the arcuate motion direction) may indicate the relative position and / or the measurement result (e.g., regarding the relative position between the detector portion 167 and the scale portion 170). As described above with respect to Figure 1 and Figure 2 As described, the measured relative position or dimension may be displayed on a display 138 (e.g., a digital display). In various embodiments, control elements 136 may be included, such as on / off switches and other optional control buttons.

[0052] As Figure 3A shown, the detector portion 167 may include a field generation portion PRTFGE and a sensing portion PRTSEN arranged along a scale direction SCD. In various embodiments, with respect to the sensing portion PRTSEN, the scale direction SCD may also or alternatively be referred to as a sensing portion direction SPD. The field generation portion PRTFGE includes a first field generation element portion PRTFGE1 and a second field generation element portion PRTFGE2. The sensing portion PRTSEN includes a first sensing element portion PRTSEN1 and a second sensing element portion PRTSEN2. As will be described in more detail below, the first sensing element portion PRTSEN1 is configured to operate in conjunction with the first field generation element portion PRTFGE1 and the first scale element portion PRTSC1 that are part of a first track portion TR1, and the second sensing element portion PRTSEN2 is configured to operate in conjunction with the second field generation element portion PRTFGE2 and the second scale element portion PRTSC2 that are part of a second track portion TR2.

[0053] In various embodiments, the field generation portion PRTFGE may include a plurality of elongate portions ELP and end portions EDP. The elongate portions may generally extend along and thus be parallel to the scale direction SCD, while the ends may generally be transverse to (e.g., perpendicular to) the scale direction SCD. The elongate portions ELP and the end portions EDP together may form regions (e.g., where a varying magnetic flux may be generated by a current flowing through the elongate and end portions that is produced by a drive signal), and where these regions may include certain sensing elements.

[0054] In various embodiments, the field generation portion PRTFGE may include a first field generation element portion PRTFGE1 and a second field generation element portion PRTFGE2. The first field generation element portion PRTFGE1 is configured to operate in conjunction with the first sensing element portion PRTSEN1 and the first signal modulation element SME1 of the first scale element portion PRTSC1. The first field generation element portion PRTFGE1 includes elongate portions ELP1A, ELP1B, ELP1C, ELP1D and end portions EDP1A, EDP1B, EDP1C, EDP1D (e.g., in some embodiments, these elongate portions and end portions may be considered to form two field generation element loops, such as in an 8-shaped configuration, and / or otherwise considered to be a single field generation element loop that forms two loops in such a configuration to form two internal regions). More specifically, the elongate portions ELP1A and ELP1B and the end portions EDP1A and EDP1D may be considered to form a first half-loop FGE1FHL of the first field generation element having an internal region FGE1FHIA. The first half-internal region FGE1FHIA of the first field generation element is configured to be aligned with the first half-pattern portion FHPP1 of the first scale element portion PRTSC1. The elongate portions ELP1C and ELP1D and the end portions EDP1C and EDP1B may be considered to form a second half-loop FGE1SHL of the first field generation element having an internal region FGE1SHIA. The second half-internal region FGE1SHIA of the first field generation element is configured to be aligned with the second half-pattern portion SHPP1 of the first scale element portion PRTSC1.

[0055] In various embodiments, the end portion EDP (e.g., or other portions of the first field generation element portion PRTFGE1) may include ports or other connection configurations. For example, the end portion EDP1B may be divided into two parts, such as to provide two contact points. The contact points may be used to receive drive signals and may be disposed at locations where signal lines / circuit traces from the processing portion 166 may be connected, etc. In various embodiments, such ports may represent general connection configurations, such as being coupled to field generation drive electronics. In various embodiments, such field generation drive electronics may include electronic components such as capacitors, transistors, etc., and may be at least partially or fully included in or coupled to the processing portion 166 to provide drive signals for causing the first field generation element portion PRTFGE1 to generate a varying magnetic flux.

[0056] During operation, alternating current may be provided, although for simplicity of the following description, only current in one direction is described (e.g., for the purpose of an example in one direction, and / or what may occur in a configuration where diodes or other components / configurations are provided to limit current flow to one direction). As an example, current (e.g., as provided by a drive signal) may flow through the following sequence of portions (e.g., for current in one direction, in the following order), including: end portion EDP1D; elongated portion ELP1A; end portion EDP1A; elongated portion ELP1B; and end portion EDP1B; elongated portion ELP1C; end portion EDP1C; and elongated portion ELP1D. According to this example of current flow, it should be understood that the current flows through the elongated portions (i.e., elongated portions ELP1A and ELP1C) at the outer boundary of the configuration in the same direction (e.g., from left to right in the illustration of Figure 3A ), and flows through the middle elongated portions (i.e., elongated portions ELP1B and ELP1D) of the configuration in the same direction (i.e., from right to left in the illustration of Figure 3A ). This also corresponds to current flow around the first half-loop FGE1FHL of the first field generating element in the counterclockwise direction, and current flow around the first half-loop FGE1SHL of the first field generating element in the clockwise direction (i.e., where the direction of current flowing through the respective loops is considered to be opposite, and the resulting magnetic fluxes from each respective loop have corresponding opposite polarities).

[0057] Such directions / orientations / polarities of current flow and corresponding magnetic fluxes may be advantageous for certain configurations, such as resulting in the generation of a signal in the first sensing element SEN1 (e.g., such as at least partially aligned with the internal regions FGE1FHIA and FGE1SHIA of the first field generating element portion PRTFGE1). As one aspect, it should be noted that with respect to the opposite directions of current flow and the corresponding opposite polarities of the magnetic fluxes generated by the respective loops FGE1FHL and FGE1SHL, the spatially offset first half-pattern portion FHPP1 and second half-pattern portion SHPP1 will produce a detector signal (i.e., from the first sensing element portion PRTSEN1), which indicates the position of the first sensing element portion PRTSEN1 relative to the first scale element portion PRTSC1.

[0058] The second field generating element portion PRTFGE2 is configured to operate in conjunction with a second signal modulating element SME2 of a second sensing element portion PRTSEN2 and a second scale element portion PRTSC2. The second field generating element portion PRTFGE2 includes elongate portions ELP2A, ELP2B, ELP2C, ELP2D and end portions EDP2A, EDP2B, EDP2C, EDP2D (e.g., in some specific implementations, these elongate portions and end portions may be considered to form two field generating element loops, such as in an 8-shaped configuration, and / or otherwise be considered a single field generating element loop that forms two loops in such a configuration to form two internal regions). More specifically, elongate portions ELP2A and ELP2B and end portions EDP2A and EDP2D may be considered to form a first half loop FGE2FHL of a second field generating element having an internal region FGE2FHIA. The first half internal region FGE2FHIA of the second field generating element is configured to be aligned with a first half pattern portion FHPP2 of the second scale element portion PRTSC2. Elongate portions ELP2C and ELP2D and end portions EDP2C and EDP2B may be considered to form a second half loop FGE2SHL of a second field generating element having an internal region FGE2SHIA. The second half internal region FGE2SHIA of the second field generating element is configured to be aligned with a second half pattern portion SHPP2 of the second scale element portion PRTSC2.

[0059] In various specific implementations, the end portion EDP (e.g., or other portions of the second field generating element portion PRTFGE2) may include ports or other connection configurations. For example, the end portion EDP2B may be divided into two parts, such as providing two contact points. The contact points may be used to receive a drive signal and may be disposed at a location where signal lines / circuit traces from the processing portion 266 may be connected, etc. In various specific implementations, such ports may represent a general connection configuration, such as being coupled to field generating drive electronics. In various specific implementations, such field generating drive electronics may include electronic components such as capacitors, transistors, etc., and may be at least partially or fully included in or coupled to the processing portion 266 to provide a drive signal for causing the second field generating element portion PRTFGE2 to generate a varying magnetic flux.

[0060] During operation, alternating current may be provided, although for simplicity of the following description, only current in one direction is described (e.g., for the purpose of an example in one direction, and / or what may occur in a configuration where a diode or other component / configuration is provided to limit current flow to one direction). As an example, current (e.g., as provided by a drive signal) may flow through the following sequence of portions (e.g., for current in one direction, in the following order), including: end portion EDP2D; elongate portion ELP2A; end portion EDP2A; elongate portion ELP2B; and end portion EDP2B; elongate portion ELP2C; end portion EDP2C; and elongate portion ELP2D. According to this example of current flow, it should be understood that the current flows through the elongate portions (i.e., elongate portions ELP2A and ELP2C) at the outer boundary of the configuration in the same direction (e.g., from left to right in the illustration of Figure 3A ), and flows through the elongate portions in the middle of the configuration (i.e., elongate portions ELP2B and ELP2D) in the same direction (i.e., from right to left in the illustration of Figure 3A ). This also corresponds to current flow around the first half-loop FGE2FHL of the second field generating element in the counterclockwise direction, and current flow around the first half-loop FGE2SHL of the second field generating element in the clockwise direction (i.e., where the direction of current flowing through the respective loops is considered to be opposite, and the resulting magnetic fluxes from each respective loop have corresponding opposite polarities).

[0061] Such directions / orientations / polarities of current flow and corresponding magnetic fluxes may be advantageous for certain configurations, such as resulting in the generation of a signal in the second sensing element SEN2 (e.g., such as being at least partially aligned with the internal regions FGE2FHIA and FGE2SHIA of the second field generating element portion PRTFGE2). As an aspect, it should be noted that with respect to the opposite directions of current flow and the corresponding opposite polarities of the magnetic fluxes generated by the respective loops FGE2FHL and FGE2SHL, the spatially offset first half-pattern portion FHPP2 and second half-pattern portion SHPP2 will generate a detector signal (i.e., from the second sensing element portion PRTSEN2), which indicates the position of the second sensing element portion PRTSEN2 relative to the second scale element portion PRTSC2.

[0062] As described above, the sensing section PRTSEN includes a first sensing element section PRTSEN1 and a second sensing element section PRTSEN2 (e.g., each including respective sensing elements SEN1 and SEN2). In the illustrated embodiment, the sensing elements SEN1 and SEN2 include sensing loop elements (alternatively referred to as sensing coil elements or sensing winding elements), which are connected in series and are generally transverse (e.g., nominally perpendicular) 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 embodiment, according to known methods, adjacent loop elements (e.g., conductive loops) in each respective set of sensing elements are connected by conductor configurations on the respective layers of the PCB (e.g., connected by feedthroughs, which in some embodiments may include conductors passing through microvias, which may also be referred to as blind vias or buried vias). For example, adjacent sensing elements SEN1 in each first sensing element section PRTSEN1 and adjacent sensing elements SEN2 in each second sensing element section PRTSEN2 may have opposite winding polarities (e.g., where the sensing elements in each respective set alternate between SEN+ and SEN-, such as described above with respect to Fig. 22 ). That is, if the first loop corresponding to a sensing element contributes a detector signal with a positive polarity in response to a changing magnetic field, the adjacent loop corresponding to the adjacent sensing element contributes a detector signal with a negative polarity. A loop with a positive polarity detector signal contribution may be referred to herein as a SEN+ sensing element, while a loop with a negative polarity detector signal contribution may be referred to as a SEN- sensing element in various contexts herein. In various embodiments, the sensing elements in each respective set are connected in series such that their detector signals or signal contributions are summed by group, and the "summed" detector signals are output to (e.g., Figure 1 ) the signal processing configuration 166 at the detector signal output connection members (e.g., at the connection members for each of signals SIG1A and SIG1B and SIG2A and SIG2B).

[0063] In the illustrated specific 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 simplicity 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) will be similarly understood to correspond to the remaining sensing elements shown. In the illustrated specific 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 simplicity 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) will be similarly understood to correspond to the remaining sensing elements shown.

[0064] It should be understood that in various specific implementations, it is advantageous to configure the detector (e.g., in each of the first sensing element portion PRTSEN1 and the second sensing element portion PRTSEN2) to provide two or more sets of sensing elements (e.g., providing or otherwise corresponding to orthogonal signals, etc.) at different spatial phase positions. Thus, for example, the first set of first sensing elements SET1SEN1 and the second set of first sensing elements SET2SEN1 are at different spatial phase positions. Similarly, the first set of second sensing elements SET1SEN2 and the second set of second sensing elements SET2SEN2 are at different spatial phase positions. However, it should be understood that the configurations of the sensing elements described herein are merely exemplary and not restrictive. As an example, in some specific implementations, separate sensing element loops may output separate signals to corresponding signal processing configurations, such as those disclosed in U.S. Patent No. 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 patterns and signal processing schemes, etc.

[0065] In the illustrated specific implementation of the scale portion 170 and the scale pattern 180, the first signal modulation element pattern PATSME1 in the first scale element portion PRTSC1 of the first track portion TR1 includes a first half-pattern portion FHPP1 and a second half-pattern portion SHPP2, where each half-pattern portion includes a row of first signal modulation elements SME1. Similarly, the second signal modulation unit pattern PATSME2 in the second scale unit portion PRTSC2 of the second track portion TR2 includes a first half-pattern portion FHPP2 and a second half-pattern portion SHPP2, where each half-pattern portion includes a row of second signal modulation elements SME2.

[0066] In various specific implementations, the signal modulation elements SME1 and / or SME2 may include conductive plates (e.g., formed as regions fabricated on a printed circuit board, or formed as raised regions extending from a conductive substrate, or fabricated on a glass substrate, or according to other manufacturing methods, etc.). The scale pattern 180 is typically implemented on the scale portion 170. It should be understood that during operation, there is relative movement (e.g., along an arcuate motion direction) between the scale pattern 180 and the detector portion 167. The scale pattern 180 has spatial characteristics that change as a function of position to provide position-related detector signals that appear in the sensing elements SEN1 and SEN2 of the sensing portion PRTSEN in the detector portion 167. In various specific implementations, the field generation portion PRTFGE and the sensing portion PRTSEN of the detector portion 167 can be formed according to a variety of alternative configurations for use in conjunction with various corresponding signal processing schemes, as will be understood by those skilled in the art.

[0067] In one specific illustrative example, the detector portion 167 can be arranged parallel to and facing the scale portion 170, and the front face of the detector portion 167 facing the scale portion 170 can be separated from the scale portion 170 (and / or the scale pattern 180) by a gap distance (e.g., approximately 0.1 mm to 0.2 mm) along the z-axis direction. The front face of the detector portion 167 (e.g., including its constituent conductors) can be covered with an insulating coating.

[0068] It should be understood that, as needed, various elements can reside on different manufacturing layers located in different planes along the z-axis direction to provide various operating clearances and / or insulating layers, which will be apparent to those of ordinary skill in the art based on the described specific implementations and the incorporated references. In all of the figures of the present disclosure, it should be understood that, for clarity, the shown x-axis, y-axis, and / or z-axis dimensions of one or more elements may be exaggerated, but it should be understood that they are not intended to be inconsistent with the various design principles and relationships described herein.

[0069] The transducer TDR includes a first transducer portion PRTTDR1 and a second transducer portion PRTTDR2. The first transducer portion PRTTDR1 includes a first sensing element portion PRTSEN1, a first field generating element portion PRTFGE1, and a first scale element portion PRTSC1. The second transducer portion PRTTDR2 includes a second sensing element portion PRTSEN2, a second field generating element portion PRTFGE2, and a second scale element portion PRTSC2. The first track portion TR1 and the second track portion TR2 respectively include the first transducer portion PRTTDR1 and the second transducer portion PRTTDR2. As described herein, the operation of the first transducer portion PRTTDR1 of the first track portion TR1 generates detector signals SIG1A and SIG1B, and the operation of the second transducer portion PRTTDR2 of the second track portion TR2 generates detector signals SIG2A and SIG2B. The processing of the signals (e.g., by signal processing configuration 166) enables the determination of the absolute relative position between the detector portion 167 and the scale portion 170.

[0070] The first transducer portion PRTTDR1 of the first track portion TR1 and the second transducer portion PRTTDR2 of the second track portion TR2 can be operated according to a first drive operation and a second drive operation, respectively, and in various embodiments, the first drive operation and the second drive operation can be performed simultaneously or at different timings. As part of the first drive operation, the first field generating element portion PRTFGE1 generates a changing magnetic flux in response to a coil drive signal (e.g., as provided from signal processing configuration 166). The first sensing element SEN1 of the first sensing element portion PRTSEN1 is configured to provide a detector signal (e.g., SIG1A, SIG1B) that responds to the local effect on the changing magnetic flux provided by the first signal modulation element SME1 of the first scale element portion PRTSC1 (e.g., including the first signal modulation element SME1 that is relatively adjacent or otherwise aligned with the sensing element SEN1 along the z-axis direction). As part of the second drive operation, the second field generating element portion PRTFGE2 generates a changing magnetic flux in response to a coil drive signal (e.g., as provided from signal processing configuration 166). The second sensing element SEN2 of the second sensing element portion PRTSEN2 is configured to provide a detector signal (e.g., SIG2A and SIG2B) that responds to the local effect on the changing magnetic flux provided by the second signal modulation element SME2 of the second scale element portion PRTSC2 (e.g., including the first signal modulation element SME2 that is relatively adjacent or otherwise aligned with the sensing element SEN2 along the z-axis direction).

[0071] The signal processing configuration (e.g., Figure 1The signal processing configuration 166, etc., can be configured to determine the position of the sensing portion PRTSEN (e.g., including the first sensing element portion PRTSEN1 and the second sensing element portion PRTSEN2) of the detector portion 167 relative to the scale portion 170 based on the detector signal input from the detector portion 167. For example, the first sensing element portion PRTSEN1 can provide detector signals SIG1A and SIG1B, and the second sensing element portion PRTSEN2 can provide detector signals SIG2A and SIG2B. In various specific embodiments, the detector signal can also or alternatively be referred to as a sensing signal. The signal from the detector portion 167 can 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. Generally speaking, the sensing element portion and the field generating element portion can operate at least in part according to known principles (e.g., for inductive encoders), such as those described above with respect to Fig. 22 as described, and as 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, each of which is hereby incorporated by reference in its entirety.

[0072] Figure 4 is a diagram showing certain dimensions and aspects of the measuring instrument 100 including the transducer TDR. In Figure 4 , certain elements (e.g., the center line CL1 of the first scale element portion PRTSC1, the center line CL2 of the second scale element portion PRTSC2, the movable encoder portion support member MEPSM, etc.) are each represented as a line (e.g., the position of these lines can correspond to the position of the center line or other representations of the corresponding components). A representation of the pivot portion PPN including the pivot point PPT as part of the movable portion MPN is shown (e.g., the contact portion CPN is not shown in Figure 4 , but will be understood to be located below the pivot portion PPN, such as Figure 2 shown).

[0073] The movable encoder portion support member MEPSM is shown rotating around the pivot portion PPN in the arcuate movement direction. The support member MEPSM can move between the first movement limit indicator ML1 and the second movement limit indicator ML2 as part of the movement over the maximum angular movement range θ MAX . In certain specific embodiments, the maximum angular movement range θ MAX can correspond to the absolute angular measurement range θ ABS . In various alternative specific embodiments, the absolute angular measurement range θ ABS and the maximum angular movement range θMAX may be different. As described above with respect to Figure 2 As described, the end point ENDPT corresponds to the end of the movable encoder part support member MEPSM and also corresponds to the end of the movable part MPN, and accordingly moves in an arc along the arc movement direction.

[0074] In some specific embodiments, the first scale element portion PRTSC1 and the second scale element portion PRTSC2 of the scale portion 170 may be attached to the movable encoder part support member MEPSM (e.g., in a specific embodiment where the movable encoder part MEP includes the scale portion 170). In this case, the first scale element portion PRTSC1 and the second scale element portion PRTSC2 will move along the arc movement direction ARCD relative to the detector portion 167 according to the arc movement ARCM. Optionally, if the movable encoder part MEP includes the detector portion 167, the detector portion 167 may be attached to the movable encoder part support member MEPSM and will accordingly move in the arc movement direction ARCD relative to the first scale element portion PRTSC1 and the second scale element portion PRTSC2 of the scale portion 170 according to the arc movement ARCM.

[0075] As Figure 3A and Figure 4 shown, the first scale element portion PRTSC1 and / or the first sensing element portion PRTSEN1 has a first central reference point REF1 (e.g., at the x-axis and / or y-axis position on the center line CL1 of the first scale element portion PRTSC1 and / or the first sensing element portion PRTSEN1), and this central reference point is located at 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 a second central reference point REF2 (e.g., at the central x-axis and / or y-axis position on the center line CL2 of the second scale element portion PRTSC2 and / or the second sensing element portion PRTSEN2), and this second central reference point is located at a second radial distance RD2 from the pivot portion PPN (e.g., from the pivot point PPT of the pivot portion PPN).

[0076] As Figure 3A and Figure 4As shown, the first scale element portions PRTSC1 of the first track portion TR1 and the second track portion 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 the radial distance RD2 of the second central reference point REF2 of the second track portion TR2 is less than the radial distance RD1 of the first central reference point REF1 of the first track portion TR1). As Figure 3A shown, the first signal modulation scale element SME1 is disposed along the first scale element portion PRTSC1 according to the first signal modulation element angular space step θ WSME1 and the second signal modulation scale element SME2 is disposed along the second scale element portion PRTSC2 according to the second signal modulation element angular space step θ WSME2 which is different from the first signal modulation element angular space step θ WSME1 . As will be described in more detail below, in certain embodiments, the first signal modulation element angular space step θ WSME1 or the second signal modulation element angular space step θ WSME2 is not evenly divided into 360 degrees.

[0077] As Figure 4 shown, the first scale element portion PRTSC1 has a first angular range θ RG1 and a corresponding arc length ARC1, and the second scale element portion PRTSC2 has a second angular range θ RG2 and a corresponding arc length ARC2. The angular ranges θ RG1 and θ RG2 are indicated as being nominally equal and in the examples of Figure 3A and Figure 4 are indicated as being nominally equal to the absolute angular measurement range θ ABS and the maximum angular movement range θ MAX . As will be described in more detail below, the first signal modulation element angular space step θ WSME1 and the second signal modulation element angular space step θ WSME2 may be related to the absolute angular measurement range θ ABS . The arrangement of the first scale element portion PRTSC1 having the first angular range θ RG1 and the arc length ARC1 and the second scale element portion PRTSC2 having the second angular range θ RG2 enables the combined implementation of the operation of the absolute angular measurement range θ ABS .

[0078] Indicates the scale direction SCD (e.g., in Figure 3A and Figure 4 In a specific implementation, the scale direction is in an arc direction) (for example, the signal modulation elements SME of the first scale element part PRTSC1 and the second scale element part PRTSC2 can be arranged along this direction, such as according to the corresponding angular space step θ WSME1 and θ WSME2 as shown in Figure 3A . In various specific implementations, the first scale element part PRTSC1 (for example, which is arc-shaped) is arranged at a first radial distance RD1 from the pivot part PPN, and the second scale element part PRTSC2 (for example, which is arc-shaped) is arranged at a second radial distance RD2 from the pivot part PPN, where the first radial distance RD1 is greater than the second radial distance RD2. In various specific implementations, the first scale element part PRTSC1 and the second scale element part PRTSC2 define corresponding absolute angular measurement ranges θ ABS (for example, where within the absolute angular measurement range θ ABS , each relative position between the detector part 167 and the scale part 170 generates a unique combination of detector signals from the detector part 167).

[0079] In various specific implementations, the ratio of the angular space steps of the signal modulation elements θ WSME2 / θ WSME1 can be expressed as equal to at least one of the following equations 1 - 4, where n and m are positive integers in each equation. In certain specific implementations, m is a positive integer of at least 2 (for example, in certain specific implementations, m can be 2, 3, 4, or 5, etc.). It should be noted that this relationship for the configuration with m = 2 or greater corresponds to a relatively large difference between the angular space steps θ WSME1 and θ WSME2 (for example, where the angular space step θ WSME2 is close to an integer multiple of the angular space step θ WSME1 (for example, m = 2 or greater)). In the specific implementation where m = 1, it is noted that the equation can be simplified to a simpler form (for example, where the nm factor is reduced to n). Regarding these equations, it should be noted that a technique for encoding the absolute angular measurement range θ ABS into an encoder using arc motion is to use two scale element parts, which have signal modulation element angular space steps that satisfy a specific relationship. For example, the following equations show certain relationships that the angular space steps θ WSME1 and θ WSME2 of the scale element parts PRTSC1 and PRTSC2 of the track parts TR1 and TR2 can satisfy.

[0080] θWSME2 / θWSME1=(nm / (n - 1)) (Equation 1)

[0081] θWSME2 / θWSME1 = (nm / (n + 1)) (Equation 2)

[0082] θWSME2 / θWSME1 = ((nm + 1) / n) (Equation 3)

[0083] θWSME2 / θWSME1 = ((nm - 1) / n) (Equation 4)

[0084] In various specific embodiments, the absolute angle measurement range θ ABS is equal to nθ WSME1 or nθ WSME2 One of them. For example, in some specific embodiments, the configuration corresponding to Equation 1 or 2 can satisfy the additional condition of the absolute angle measurement range θ ABS = nθ WSME1 And the configuration corresponding to Equation 3 or 4 can satisfy the additional condition of the absolute angle measurement range θ ABS = nθ WSME2 In various specific embodiments, the configuration corresponding to Equation 1 can satisfy the additional condition of the absolute angle measurement range θ ABS = ((n - 1) / m)θ WSME2 The configuration corresponding to Equation 2 can satisfy the additional condition of the absolute angle measurement range θ ABS = ((n + 1) / m)θ WSME2 The configuration corresponding to Equation 3 can satisfy the additional condition of the absolute angle measurement range θ ABS = (nm + 1)θ WSME1 And the configuration corresponding to Equation 4 can satisfy the additional condition of the absolute angle measurement range θ ABS = (nm - 1)θ WSME1 Based on such relationships, it should be understood that a method for selecting the angular spatial step of two signal modulation elements is to set an integer of n angular spatial steps (e.g., for θ WSME1 or θ WSME2 ) to be included in the absolute angle measurement range θ ABS And the angular spatial step of another signal modulation element (e.g., θ WSME2 or θ WSME1 ) can be determined according to relationships such as those indicated above.

[0085] In various specific embodiments, 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 (e.g., as Figure 4as shown), where ARC2 / ARC1 = RD2 / RD1. In various specific implementations, the angular spatial step θ of the second signal modulation element WSME2 is greater than the angular spatial step θ of the first signal modulation element WSME1 (e.g., in a configuration where m is 2 or greater, the angular spatial step θ WSME2 can be close to an integer multiple of the angular spatial step θ WSME1 ).

[0086] As described above, the first signal modulation element pattern PATSME1 in the first scale element portion PRTSC1 of the first track portion TR1 includes a first half pattern portion FHPP1 and a second half pattern portion SHPP1, where each half pattern portion includes a row of first signal modulation elements SME1. In each scale row, the first signal modulation elements SME1 are set (e.g., spaced apart / spatially positioned) according to the angular spatial step θ WSME1 of the first signal modulation element. For two adjacent scale rows in the half pattern portion, the spatial phase of the scale row in the second half pattern portion is offset by 1 / 2 of the angular spatial step θ WSME1 of the first signal modulation element from the spatial phase of the adjacent scale row in the first half pattern portion. Thus, in this example, the signal modulation element spatial phase offset is 1 / 2 of the angular spatial step θ WSME1 of the first signal modulation element (e.g., it can correspond to a 180-degree spatial phase shift / difference between adjacent scale rows).

[0087] As described above, the second signal modulation element pattern PATSME2 in the second scale element portion PRTSC2 of the second track portion TR2 includes a first half pattern portion FHPP2 and a second half pattern portion SHPP2, where each half pattern portion includes a row of second signal modulation elements SME2. In each scale row, the second signal modulation elements SME2 are set (e.g., spaced apart / spatially positioned) according to the angular spatial step θ WSME2 of the second signal modulation element. For two adjacent scale rows in the half pattern portion, the spatial phase of the scale row in the second half pattern portion is offset by 1 / 2 of the angular spatial step θ WSME2 of the second signal modulation element from the spatial phase of the adjacent scale row in the first half pattern portion. Thus, in this example, the signal modulation element spatial phase offset is 1 / 2 of the angular spatial step θ WSME2 of the second signal modulation element (e.g., it can correspond to a 180-degree spatial phase shift / difference between adjacent scale rows).

[0088] In various specific implementations, in the first sensing element portion PRTSEN1, the first set of first sensing elements SET1SEN1 and the second set of first sensing elements SET2SEN1 are in different angular spatial phase positions, separated by the first sensing element angular spatial phase offset. In various specific implementations, the first sensing element angular spatial step θ of the first sensing element portion PRTSEN1 (e.g., of each of the first sensing element sets SET1SEN1 and SET2SEN1) WSEN1 may correspond to (e.g., be equal to) the first signal modulation element angular spatial step θ of the first scale element portion PRTSC1 WSME1 . In various specific implementations, the first sensing element angular spatial phase offset may be equal to approximately 1 / 4 of the first sensing element angular spatial step θ WSEN1 (e.g., according to an orthogonal configuration, as will be understood by those skilled in the art).

[0089] Similarly, in various specific implementations, in the second sensing element portion PRTSEN2, the first set of second sensing elements SET1SEN2 and the second set of second sensing elements SET2SEN2 are in different angular spatial phase positions, separated by the second sensing element angular spatial phase offset. In various specific implementations, the second sensing element angular spatial step θ of the second sensing element portion PRTSEN2 (e.g., of each of the second sensing element sets SET1SEN2 and SET2SEN2) WSEN2 may correspond to (e.g., be equal to) the second signal modulation element angular spatial step θ of the second scale element portion PRTSC2 WSME2 . In various specific implementations, the second sensing element angular spatial phase offset may be equal to approximately 1 / 4 of the second sensing element angular spatial step θ WSEN2 (e.g., according to an orthogonal configuration, as will be understood by those skilled in the art).

[0090] In one exemplary specific implementation, θ WSME1 = 0.0300 radians, and θ WSME2 = 0.625 radians. Regarding 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. Additionally, in various specific implementations, θ ABS may be determined according to θ ABS = nθ WSME1 = 25(0.0300 radians) = 0.75 radians or 25(1.72 degrees) = 43 degrees, and where 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 angular measurement range θ ABS there are 25θ WSME1 (corresponding to 25 SME1) and 12θ WSME2 (corresponding to 12 SME2). Note that the relationships for this configuration can alternatively be written according to Equation 3, where if n = 12 and m = 2, then θ WSME2 / θ WSME1 = ((nm + 1) / n) = 25 / 12 = 0.0625 radians / 0.0300 radians or 3.58 degrees / 1.72 degrees. Additionally, 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.

[0091] As another example, note that within the absolute angular measurement range θ ABS (maintained at 0.75 radians = 43 degrees) includes 25θ WSME1 (corresponding to 25 SME1) (where θ WSME1 is maintained at 0.0300 radians = 1.72 degrees) and includes 13θ WSME2 (corresponding to 13 SME2) (where θ WSME2 = 0.75 radians / 13 = 0.0577 radians or 43 degrees / 13 = 3.31 degrees in an alternative arrangement), the relationships can be expressed by Equation 2 or 4. More specifically, in the case where n = 25 and m = 2, according to Equation 2, θ WSME2 / θ WSME1 = (nm / (n + 1)) = 50 / 26 = 0.0577 radians / 0.0300 radians = 3.31 degrees / 1.72 degrees. In the case where θ ABS = nθ WSME1 = ((n + 1) / m)θ WSME2 within the absolute angular measurement range, there are 25θ WSME1 (corresponding to 25 SME1) and 13θ WSME2 (corresponding to 13 SME2). Alternatively, in the case where n = 13 and m = 2, according to Equation 4, θ WSME2 / θ WSME1 = ((nm - 1) / n) = 25 / 13 = 0.0577 radians / 0.0300 radians = 3.31 degrees / 1.72 degrees. In the case where θ ABS = nθ WSME2=(nm - 1)θ WSME1 In the case of, within the absolute angle measurement range, there is 13θ WSME2 (corresponding to 13SME2) and 25θ WSME1 (corresponding to 25SME1). As another alternative example, in the case of n = 12 and m = 2, according to Equation 4, θ WSME2 / θ WSME1 = ((nm - 1) / n) = 23 / 12 = 0.0625 radians / 0.0326 radians = 3.58 degrees / 1.87 degrees. In the case of θ ABS = nθ WSME2 = (nm - 1)θ WSME1 In the case of, within the absolute angle measurement range, there is 12θ WSME2 (corresponding to 12SME2) and 23θ WSME1 (corresponding to 23SME1).

[0092] In Figure 3A and Figure 4 transducers, the first scale element portion PRTSC1 is located within a first scale track ST1 having a first scale track width STW1 (e.g., the upper and lower edges of the first scale element portion PRTSC1 may correspond to the upper and lower boundaries of the first scale track ST1). The second scale element portion PRTSC2 is located within a second scale track ST2 having a second scale track width STW2 (e.g., the upper and lower edges of the second scale element portion PRTSC2 may correspond to the upper and lower boundaries of the second scale track ST2). The separation distance SEP12 is shown as the radial distance between the first scale track ST1 and the second ST2. A separation region SEPA is shown between the first scale track ST1 and the second scale track ST2 (e.g., having a radial width defined by the separation distance SEP12 and such 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 region SEPA is shown as empty (e.g., not including scale element portions arranged in encoder track portions having sensing element portions). The differential distance D12 is indicated as the distance difference between the central reference points REF1 and REF2 and correspondingly is also the difference between the first radial distance RD1 and the second radial distance RD2. As some specific example dimensions, in one specific 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 may be 25.5 mm, and the differential distance D12 may be 11.625 mm. In various specific implementations, such dimensions may result in certain desired operating characteristics, which will be described in more detail below.

[0093] Figure 5 is a diagram showing certain signals 500 generated by the operation of a transducer TDR of Figure 3A wherein there is an arcuate motion between a detector portion 167 and a scale portion 170. As Figure 5 shown, graph 510A shows the SEN1 signal as a function of angular position. In various embodiments, the signals of graph 510A may correspond to detector signals SIG1A and SIG1B of transducer portion PRTTDR1 of a first track portion TR1. Graph 520A similarly shows the SEN2 signal as a function of angular position. In various embodiments, the signals of graph 520A may correspond to detector signals SIG2A and SIG2B of transducer portion PRTTDR2 of a second track portion TR2. Graphs 510B and 520B show the phase signals of the SEN1 and SEN2 signals of graphs 510A and 520A respectively (e.g., by calculating arctan(SIGxB / SIGxA), such as arctan(SIG1B / SIG1A) and arctan(SIG2B / SIG2A)).

[0094] Graph 530 shows an absolute ABS phase signal (e.g., generated by a combination of other signals, such as including the signals of graphs 510B and 520B). In various embodiments, the absolute ABS phase signal can be expressed as:

[0095] φ ABS = φ SIG1 - mφ SIG2 (Equation 5)

[0096] As indicated in graph 530, the absolute angular measurement range θ ABS extends in the range from -21.5 degrees to +21.5 degrees (i.e., from -0.375 radians to +0.375 radians), such as an absolute angular range corresponding to 43 degrees (i.e., 0.75 radians). Accordingly, in graphs 510A and 510B, 25 cycles / periods are shown in the angular range from -21.5 degrees to +21.5 degrees (i.e., -0.375 radians to +0.375 radians) (e.g., corresponding to 25 SME1 in a first scale element portion PRTSC1 of a first track portion TR1), and in graphs 520A and 520B, 12 cycles / periods are shown in the angular range from -21.5 degrees to +21.5 degrees (i.e., -0.375 radians to +0.375 radians) (e.g., corresponding to 12 SME2 in a second scale element portion PRTSC2 of a second track portion TR2).

[0097] It should be understood that, in accordance with the principles described herein, for a particular application, the absolute angular measurement range θ ABScan be customized / configured for a specific maximum angular movement range θ MAX The above specific numerical examples illustrate an arrangement configured for an absolute angular measurement range θ of 43 degrees (i.e., 0.75 radians). ABS It should be understood that, in accordance with the above principles, other arrangements can be configured for larger or smaller absolute angular measurement ranges. In some specific implementations, a smaller absolute angular measurement range can be used for specific applications (e.g., a range less than 15 degrees, or 10 degrees, or 5 degrees).

[0098] It should be understood that the ability to customize the absolute angular measurement range θ for a specific application ABS may have certain advantages. For example, for a multi-track transducer, a design for a longer absolute angular measurement range generally requires a certain level of resolution and accuracy in order to be able to achieve the longer range (e.g., having appropriate and distinct signal levels throughout the range, such as a high level of information accuracy required for each increment, particularly regarding the relationship between multiple track portions (e.g., TR1 and TR2) in order to distinguish each increment throughout the range). In contrast, for a relatively short absolute angular measurement range in a multi-track transducer (e.g., such as can be formed in accordance with the principles described herein), a higher level of resolution can be achieved over a smaller range (e.g., using smaller and / or distinct increments / spatial steps between multiple tracks, which might otherwise be too fine and / or have other issues for a longer range), and / or sufficient accuracy can be achieved over a smaller range using specific implementations with lower complexity / cost / power requirements, etc.

[0099] In some specific implementations, absolute rotary encoders can be compared that have an integer number of angular space steps in each track portion around a complete 360-degree absolute range (e.g., for use in effectively continuously measuring angular position in implementations that can perform a complete 360-degree rotation and rotations beyond 360 degrees). In accordance with such principles, if a portion of such a rotary encoder is used in an arcuate motion application (e.g., if 1 / 4 or 1 / 8 of such a rotary encoder is used for a 90-degree or 45-degree measurement range), then the angular space steps in each track portion will still be evenly divided into 360 degrees accordingly. For example, if a portion of such a rotary encoder is used, then for each track portion in the transducer, 360 degrees divided by the given angular space step of the track portion will equal an integer.

[0100] It is noted that such a specific implementation that utilizes a part of a rotary encoder has certain disadvantages (e.g., as described above, for a relatively long measurement range (e.g., a full 360-degree angular measurement range), the design generally requires a certain level of resolution and accuracy in order to achieve the full 360-degree range, particularly with respect to the relationship between the track portions, so that each increment is distinguishable). In contrast, as described above, an arc motion encoder can be formed according to the principles described herein, having a relatively small absolute angular measurement range (i.e., less than 360 degrees, and in some specific implementations can be even smaller, such as less than 45 degrees, or 15 degrees, or 5 degrees), and having certain advantages as described above.

[0101] Figure 6 is a view of a specific implementation that is part of the transducer TDR””, which is configured to be used with the arc motion between the detector portion 167”” and the scale portion 170””, such as can be used in Figure 2 a measuring instrument, and has a relatively small separation of the scale tracks ST1 and ST2”” compared to the Figure 3A specific implementation. Figure 7 is a view showing Figure 2 a measuring instrument and Figure 6 certain dimensions and characteristics of the transducer. It is noted that Figure 6 and Figure 7 the specific implementations are in some aspects similar to Figure 3A and Figure 4 the specific implementations, as will be described in more detail below.

[0102] It should be noted that Figure 6 and Figure 7 the first encoder track portion TR1 in the specific implementation is the same as the first encoder track portion TR1 in the Figure 3A and Figure 4 specific implementations, and will be understood based on the above description of the first encoder track portion TR1. Figure 6 and Figure 7 the second encoder track portion TR2”” of are configured to generate a signal similar to the second encoder track portion TR2 of Figure 3A and Figure 4 , and for this signal, Figure 5 represents the signal generated by the operation of the Figure 6 and Figure 7 specific implementations, and represents the signal generated by the operation of the Figure 3A and Figure 4 specific implementations. In this regard, during operation, Figure 6 the signals SIG2A”” and SIG2B”” of the specific implementation can be similar to the signals SIG2A and SIG2B of Figure 3A the specific implementation.

[0103] In addition, Figure 3A each component of the second encoder track portion TR2 of Figure 6 will be understood to have a corresponding component (e.g., which may be denoted by four apostrophes "") in the second encoder track portion TR2"" of

[0104] Generally speaking, Figure 6 the component along the arcuate motion direction ARCD in the second encoder track portion TR2"" of Figure 3A may be greater than the corresponding component of the second encoder track portion TR2 of WSME2 "". And the second signal modulation element angular space step θ WSME2 of the second scale element portion PRTSC2"" may be the same as the second signal modulation element angular space step θ WSEN2 of the second scale element portion PRTSC2, and the second sensing element angular space step θ WSEN2 "" may be the same as the second sensing element angular space step θ

[0105] Similar to the specific implementations of Figure 3A and Figure 4 in Figure 6 and Figure 7In a specific implementation, the first scale element portion PRTSC1 is located within a first scale track ST1 having a first scale track width STW1 (e.g., the upper and lower edges of the first scale element portion PRTSC1 may correspond to the upper and lower boundaries of the first scale track ST1). The second scale element portion PRTSC2"" is located within a second scale track ST2"" having a second scale track width STW2"" (e.g., the upper and lower edges of the second scale element portion PRTSC2"" may correspond to the upper and lower boundaries of the second scale track ST2""). The separation distance SEP12"" is shown as the radial distance between the first scale track ST1 and the second ST2"". A separation region SEPA"" is shown between the first scale track ST1 and the second scale track ST2"" (e.g., having a radial width defined by the separation distance SEP12"", and such 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 region SEPA"" is empty (e.g., does not include a scale element portion arranged in an encoder track portion having a sensing element portion).

[0106] As Figure 7 shown, the first scale element portion PRTSC1 of the first track portion TR1 and the second scale element portion PRTSC2"" of the second track portion TR2"" are arc-shaped and parallel to each other (e.g., form concentric arcs). The second track portion TR2"" is closer to the pivot portion PPN than the first track portion TR1 (e.g., such that the radial distance RD2"" of the second center reference point REF2"" of the second track portion TR2"" is less than the radial distance RD1 of the first center reference point REF1 of the first track portion TR1). In various specific implementations, the reference point REF1 may be located at the center line CL1, and the reference point REF2"" may be located at the center line CL2"". The difference distance D12"" is indicated as the distance difference between the center reference points REF1 and REF2"", and correspondingly is also the difference between the first radial distance RD1 and the second radial distance RD2"".

[0107] The first scale element portion PRTSC1 has a first angular range θ RG1 and a corresponding arc length ARC1, and the second scale element portion PRTSC2"" has a second angular range θ RG2 and a corresponding arc length ARC2"". The angular ranges θ RG1 and θ RG2 are indicated as being nominally equal, and in Figure 6 and Figure 7 the example are indicated as being nominally equal to the absolute angular measurement range θ ABS and the maximum angular movement range θ MAX .

[0108] As some specific example dimensions, in one specific implementation, the first scale track width STW1 can be 4.0 mm, the second scale track width STW2 can be 2.75 mm, the separation distance SEP12 can be 1.25 mm, the first radial distance RD1 can be 37.125 mm, the second radial distance RD2 can be 32.5 mm, and the differential distance D12 can be 4.625 mm. In various specific implementations, such dimensions may result in certain less than ideal operating characteristics (e.g., compared to Figure 3A and Figure 4 implementations), as will be described in more detail below.

[0109] Note that, compared to the Figure 3A and Figure 4 implementations of the corresponding transducer TDR”” with a relatively large overall size, Figure 6 and Figure 7 implementations result in a corresponding transducer TDR with a smaller overall size. This is the main reason why prior art encoders are typically designed with a relatively small spacing between encoder tracks in order to limit the corresponding overall size. Based on such prior art design principles, it may have been considered counterintuitive and / or surprising that implementations (such as Figure 3A and Figure 4 implementations) (i.e., with a relatively large separation between encoder / scale tracks) will result in certain more desirable operating characteristics, as will be described in more detail below.

[0110] Generally speaking, note that for transducers utilizing arcuate motion, the signal periodicity depends on the spatial pitch in the scale track portion and also on the radial distance of the scale portion and / or detector portion from the pivot portion. This can be contrasted with standard transducers that utilize only linear motion, where the signal periodicity depends only on the spatial pitch in the scale track portion. If there is an offset / misalignment, the dependence of the arcuate motion transducer on the radial distance of the scale portion and / or detector portion from the pivot portion may cause certain problems. For example, the transducer can be designed to operate ideally with the scale portion and detector portion centered and aligned with respect to each other along the radial direction, which may 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), then due to the dependence on the radial distance, the signal periodicity may be different from the design, which may result in a linear error in the position determined by the operation of the transducer (e.g., for that position, as the measured position moves away from the reference point, the error may linearly increase with further arcuate motion of the transducer).

[0111] As an example of how a radial offset / misalignment can occur, in such as Figure 2During the manufacture / assembly of a measuring instrument, a movable encoder section MEP (e.g., consisting of a printed circuit board on which a scale section or a detector section is manufactured) can be coupled (e.g., attached, affixed, etc.) to a support member MEPSM. During such manufacture / assembly, a certain amount of radial offset / misalignment can occur in the movable encoder section MEP (e.g., due to manufacturing tolerances, etc., such as for positioning the movable encoder section MEP on the support member MEPSM). The resulting radial offset / misalignment of the movable encoder section MEP (i.e., as coupled to the support member MEPSM) can correspond to a radial offset / misalignment of the scale section (e.g., relative to the detector section). As described above, such radial offset / misalignment can result in an error in the determined position of the transducer. As will be described in more detail below, to address such issues, in accordance with the principles described herein, an offset value corresponding to such radial offset can be determined at least in part based on signals from the transducer, and the determined offset value can be utilized to correct one or more values used to determine the relative position between the detector section and the scale section.

[0112] In various embodiments, the following concepts can involve determining an offset value at least in part based on signals from a transducer. Regarding Figure 5 the signals, the SEN1 signal and the SEN1 phase (e.g., corresponding to the signal phase Φ SIG1 ) correspond to the first signal modulation element angular spatial step θ WSME1 of the first scale element portion PRTSC1 of the first scale track ST1. Similarly, the SEN2 signal and the SEN2 phase (e.g., corresponding to the signal phase Φ SIG2 ) correspond to the second signal modulation element angular spatial step θ WSME2 of the second scale element portion PRTSC2 of the second scale track ST2. As described above, the first signal modulation element angular spatial step θ WSME1 is less than the second signal modulation element angular spatial step θ WSME2 , and wherein the first signal modulation element angular spatial step θ WSME1 can be characterized as a finer or finer spatial step (e.g., of the fine track ST1), while the second signal modulation element angular spatial step θ WSME2 can be characterized as a coarser spatial step (e.g., of the sub-track ST2).

[0113] As shown and described, the spatial step of the first scale element portion PRTSC1 of the first scale track ST1 can provide the finest measurement resolution and thus can be referenced and used as part of determining a high-accuracy absolute measurement position. However, as part of determining the overall absolute measurement position, it is necessary to determine that the current absolute measurement position lies at or otherwise corresponds to the SEN1 phase (i.e., corresponding to the signal phase ΦSIG1 ) which cycle / period (e.g., as may correspond to an integer number of spatial steps that occur, and then the position indicated by SEN1 phase / signal phase Φ SIG1 is added to these spatial steps). For example, in Figure 5 the illustration, there are 25 cycles / periods of the SEN1 phase (i.e., corresponding to the signal phase Φ SIG1 ), corresponding to 25 signal modulation elements SME1 within the absolute range (i.e., as indicated for the absolute ABS phase, within the absolute range θ ABS ) and corresponding 25 spatial steps in the first scale element portion PRTSC1 of the first track portion TR1 of Figure 6 . It should also be noted that there are 12 cycles / periods of the SEN2 phase (i.e., corresponding to the signal phase Φ SIG2 ), corresponding to 12 signal modulation elements SME2 within the absolute range and corresponding 12 spatial steps. Further referring to Figure 5 , in various specific embodiments, the absolute ABS phase (i.e., corresponding to the signal phase Φ ABS ) may have sufficient accuracy to determine which cycle / period the current absolute measurement position corresponds to. In various specific embodiments, such a process may be referred to as a phase unwrapping process or a chaindown process, etc.

[0114] In certain specific embodiments, the absolute ABS phase (i.e., corresponding to the signal phase Φ ABS ) may be considered accurate enough to determine which cycle / period (e.g., among the 25 cycles / periods in the example of SIG1 ) of the SEN1 phase (i.e., corresponding to the signal phase Φ Figure 5 ) the current absolute measurement position corresponds to. Such a corresponding process may be referred to as a direct chaindown process (i.e., only performing a single chaindown step). Alternatively, as part of a more robust process (e.g., more robust to certain types of encoder errors or other accuracy issues), first the absolute ABS phase (i.e., corresponding to the signal phase Φ ABS ) may be used to determine which cycle / period (e.g., among the 12 cycles / periods in the example of SIG2 ) of the SEN2 phase (i.e., corresponding to the signal phase Φ Figure 5 ) the current absolute measurement position corresponds to, and then the result of such a first determination may be used to determine which cycle / period (e.g., among the 25 cycles / periods in the example of SIG1 ) of the SEN1 phase (i.e., corresponding to the signal phase Φ Figure 5Which cycle / period out of the 25 cycles / periods in the example. Such a corresponding process may be referred to as a double chained subtraction process (i.e., performing two chained subtraction steps).

[0115] As part of such a chained subtraction process, a rounding process may be performed (e.g., with respect to the absolute ABS phase / signal phase Φ ABS , such as in a direct chained subtraction process or in the first step of a double chained subtraction process). The quantity to be rounded (e.g., between -0.5 and +0.5) may be referred to as the chained subtraction value and may represent the difference in cumulative position values. In a perfect configuration (e.g., without radial offset, etc.), the chained subtraction value may be close to or zero. However, in an actual configuration (e.g., during manufacturing and assembly, with certain manufacturing / assembly tolerances, etc.), there may be a certain amount of radial offset (e.g., which may result in certain chained subtraction values). As will be described in more detail below, in various specific embodiments, a chained subtraction slope may be determined (i.e., a plotted chained subtraction curve corresponding to the chained subtraction value), and it may be correlated with and / or used to determine an offset value (e.g., a radial offset corresponding to a scale portion, such as relative to a detector portion, or a radial offset corresponding to a detector portion, such as relative to a scale portion). In various specific embodiments, the determined offset value may be utilized to correct one or more values (e.g., a spatial step or values in other spatial dimensions) that are used to determine the relative position between a detector portion and a scale portion.

[0116] As part of the chained subtraction process described below, the absolute phase Φ ABS is in the range [0,1], and the signal phase Φ SIG1 and Φ SIG2 are in the range [-0.5, +0.5], and may be expressed as:

[0117] φ SIG1 =(1 / 2π)arctan(SIG1B / SIG1A) (Equation 6)

[0118] φ SIG2 =(1 / 2π)arctan(SIG2B / SIG2A) (Equation 7)

[0119] The relationship of the absolute phase Φ ABS may be expressed as:

[0120] φ ABS =(φ SIG1 -mφ SIG2 +φ0) % 1 (Equation 8)

[0121] Where Φ0 is the buffered ABS signal phase, which in some specific implementations includes this buffered ABS signal phase to avoid jumps in the ABS spatial range / step size, and %1 represents the modulo / modulus operation, which returns the remainder or signed remainder of a division after dividing a number by a specified divisor. In this case, the specified divisor is 1, so the result is typically a non-integer value (e.g., for a value of 1.2, the operation performed will return 0.2, and so on).

[0122] For the direct chained rounding-down process, the next determination can be according to the following formula:

[0123] n AWSME1 = round((φ ABS (θ ABS / θ WSME1 ) - φ SIG1 + φ1) (Equation 9)

[0124] Where h AWSME1 is an integer of the spatial step size of the first signal modulation element for absolute measurement distance determination, "round" indicates the rounding operation (e.g., for determining the integer of h AWSME1 ), and in some specific implementations includes Φ1 to minimize the first chained rounding-down value, thereby avoiding θ WSME1 spatial step size jumps. Note that θ ABS / θ WSME1 yields the number of angular spatial steps θ ABS of the first signal modulation element in the absolute angular measurement range θ WSME1 (e.g., in the example described above, where θ ABS = 0.75 radians and θ WSME1 = 0.03 radians, then θ ABS / θ WSME1 = 25). After determining the integer number of spatial steps h AWSME1 of the first signal modulation element according to Equation 9, the absolute measurement value can be determined according to Equation 12, as will be described in more detail below.

[0125] As an alternative to the direct chained rounding-down process, for the double chained rounding-down process, as part of the first chained rounding-down step, the next determination after Equation 8 can be according to the following formula:

[0126] n AWSME2 = round((φ ABS (θ ABS / θ WSME2 ) - φ SIG2 + φ1) (Equation 10)

[0127] Where n AWSME2is an integer of the spatial step of the second signal modulation element for absolute measurement distance determination, "rounding" indicates a rounding operation (e.g., for determining the integer of n AWSME2 ), and in some specific embodiments includes Φ1 to minimize the first chained rounding value, thereby avoiding θ WSME2 spatial step jumps. Note that θ ABS / θ WSME2 results in the angular spatial step θ ABS of the second signal modulation element in the absolute angular measurement range θ WSME2 quantity (e.g., in the example described above, where θ ABS = 0.75 radians and θ WSME2 = 0.0625 radians, then θ ABS / θ WSME2 = 12). As a further part of the double chained rounding process, the second / next chained rounding step can be according to the following formula:

[0128] n AWSME1 = rounding(((n AWSME2 + φ SIG2 )(θ WSME2 / θ WSME1 )) - φ SIG1 + φ2) (Equation 11)

[0129] where n AWSME1 is an integer of the spatial step of the first signal modulation element for absolute measurement distance determination, "rounding" indicates a rounding operation (e.g., for determining the integer of n AWSME1 ), in some specific embodiments includes Φ2 to minimize the second chained rounding value, thereby avoiding θ WSME1 spatial step jumps, and θ WSME2 / θ WSME1 is a ratio (e.g., the above example value corresponds to 0.0625 / 0.03 = 2.0833).

[0130] After determining the integer number of spatial steps n AWSME1 of the first signal modulation element according to Equation 9 (e.g., as part of a direct chained rounding process) or according to Equation ll (e.g., as part of a double chained rounding process), the absolute measurement result can be determined according to the following formula:

[0131] MEAS ANG = θ WSME1 (n AWSME1 + φ SIG1 ) - θ0 (Equation 12)

[0132] where MEAS ANGis the absolute angular measurement result (e.g., in radians), and θ0 is the angular origin position. In some specific embodiments, the absolute measurement result can be represented by an arc distance, which is relative to the angular spatial step θ of the first signal modulation element WSME1 and the radial distance RD1 of the first scale element portion PRTSC1 of the first scale track ST1 can be expressed as:

[0133] MEAS ARC =(MEAS ANG )RD1 (Equation 13)

[0134] Note that this corresponds to the arc distance along the first scale track ST1. As described above, the rounded quantity (e.g., in the direct or double chained subtraction process) can be referred to as the chained subtraction value. Regarding the direct chained subtraction process and Equation 9, the chained subtraction value can be expressed as:

[0135] Chained subtraction value = (φ ABS (θ ABS / θ WSME1 ) - φ SIG1 + φ1) - n AWSME1 (Equation 14) Regarding the double chained subtraction process and Equation 10, the chained subtraction value can be expressed as:

[0136] Chained subtraction value = (φ ABS (θ ABS / θ WSME2 ) - φ SIG2 + φ1) - n AWSME2 (Equation 15)

[0137] In various specific embodiments, such chained subtraction values can be included in the chained subtraction plot and / or used in other ways to determine the chained subtraction slope, which can be used to correct linear errors, as will be described in more detail below. Briefly, regarding Equation 12 (and some other equations above), note that if (e.g., due to a radial offset of the scale portion or the detector portion) the signal periodicity of the first scale element portion PRTSC1 of the first scale track ST1 does not match θ WSME1 (e.g., or its arc distance equivalent), then the cumulative error of the determined measurement result. The determined chained subtraction slope can be used to determine the offset value corresponding to the radial offset of the scale portion or the detector portion (e.g., relative to each other), where the determined offset value can be used to correct the value that can be used to determine the relative position between the detector portion and the scale portion (e.g., such as used in Equation 12) (e.g., determining the correction value θ WSME1C ).

[0138] More generally, transducers utilizing arcuate motion are typically sensitive to radial offset / misalignment (e.g., the offset / misalignment of a scale portion relative to a sensing portion), where such radial offset / misalignment results in a linear long-range error (LRE) (e.g., in some embodiments, the slope is approximately equal to the radial offset divided by the radial distance of the scale track). One method for correcting such LRE is to calibrate according to known standards (e.g., such as a reference encoder or gauge block), although in some embodiments, such processes may be too complex, difficult, expensive, etc. As an alternative, and in accordance with certain principles described herein, a dual-track arcuate encoder (i.e., having a transducer utilizing arcuate motion) can be configured to "self-correct" such problems (e.g., at least in part by substantially utilizing the known separation of a first scale track and a second scale track as a reference and / or otherwise for correction values). In other words, in embodiments such as those described herein, where a first scale track portion and a second scale track portion have different radial distances from a pivot portion, when there is a radial offset, that radial offset produces a slope (i.e., a chained subtraction slope) in a chained subtraction plot of chained subtraction values, which can be measured (e.g., without an external reference standard) and used for correction values (e.g., for correcting linear errors). As will be described in more detail below, in various embodiments, a relatively large spacing / difference in the radial distances of the two scale tracks can enable a more / sufficiently accurate determination of an offset value (e.g., corresponding to the radial offset), which can be used for correction values (e.g., for correcting linear errors).

[0139] In accordance with the foregoing principles, the following equations represent certain correspondences.

[0140] LRE slope = OFF / (RD - OFF) ≈ OFF / RD (Equation 16)

[0141] where OFF is the radial offset and RD is the radial distance of the corresponding scale track / scale element portion. Note that the radial offset OFF is typically small enough relative to the radial distance RD such that RD - OFF can be adequately approximated by RD. For a direct chained subtraction process, the chained subtraction slope can be characterized by the following equation:

[0142] CDSLOPE DIR ≈ -OFF((1 / RD2)-(1 / RD1))(n) (Equation 17)

[0143] where CDSLOPE DIR is the chained subtraction slope of the direct chained subtraction process, and RD1 and RD2 are the radial distances of the first scale element portion and the second scale element portion and the corresponding first scale track and second scale track, respectively. In certain embodiments, Equation 17 can be modified to be further specified according to the following equation:

[0144] CDSLOPE DIR ≈ - OFF((1 / RD2) - (1 / RD1))(n - 1) (Equation 18) For a dual chained rounding process, the chained rounding slope can be characterized by:

[0145] CDSLOPE DBL ≈ - OFF((1 / RD2) - (1 / RD1))(n / m) (Equation 19)

[0146] where CDSLOPE DBL is the chained rounding slope of the dual chained rounding process. Note that Equation 19 can be used to solve for the offset according to: - OFF ≈ CDSLOPE DBL / (((1 / RD2) - (1 / RD1))(n / m)). In certain specific implementations, Equation 19 can be modified to further specify according to:

[0147] CDSLOPE DBL ≈ - OFF((1 / RD2) - (1 / RD1))((n - 1) / m) (Equation 20)

[0148] Note that Equation 20 can be used to solve for the offset according to: - OFF ≈ CDSLOPE DBL / (((1 / RD2) - (1 / RD1))((n - 1) / m)). In various specific implementations, the self - calibration / calibration process can be characterized by:

[0149] θ WSME1C = θ WSME1 (1 - (OFF D / RD1)) (Equation 21)

[0150] where θ WSME1C is the corrected value of θ WSME1 and OFF D is the determined radial offset (e.g., as determined based on the chained rounding slope CDSLOPE). The above principles and certain related examples (e.g., related to the above equations, etc.) will be described in more detail below with reference to FIG. 8A to FIG. 21 .

[0151] FIG. 8A to FIG. 8B is a diagram showing the offset of certain features with respect to Figure 6 and Figure 7 (e.g., the radial offset of a scale portion or a detector portion). Fig. 8A can be compared with the representation of a part of the vertical centerline of Figure 7 . In the illustration of Fig. 8A (e.g., which can correspond to the case of zero radial offset in various specific implementations), the first central reference point REF1Z (e.g., at the center x-axis and / or y-axis position at the center line CL1 of the first scale element portion PRTSC1 and / or the first sensing element portion PRTSEN1 of the first scale track ST1) is located at a radial distance RD1 from the pivot portion PPN Z at. The second center reference point REF2 Z ″″ (e.g., at the center x-axis and / or y-axis position at the center line CL2"" of the second scale element portion PRTSC2″″ and / or the second sensing element portion PRTSEN2″″ of the second scale track ST2″″) is located at a radial distance RD2 from the pivot portion PPN Z ″ at.

[0152] The differential distance D12″″ is indicated as the distance difference between the center reference points REF1 Z and REF2 Z ″″, and correspondingly is also the difference between the first radial distance RD1 Z and the second radial distance RD2 Z ″″. As some specific numerical examples, Fig. 8A the illustration in Z indicates that the first radial distance RD1 Z ″″ can be 37.125 mm, and the second radial distance RD2 Figure 6 and Figure 7 described numerical examples), and correspondingly, the differential distance D12″″ can be 4.625 mm. As described above, in Figure 7 the illustration of

[0153] Figure 8B shows a case with an offset OFF P (e.g., a radial offset of the scale portion or the detector portion). In Figure 8B the illustration of P (e.g., which can correspond to the condition of a positive radial offset OFF P in various specific embodiments), the first center reference point REF1 of (e.g., the first scale element portion PRTSC1 of the first scale track ST1) P has been moved upward by the offset OFF P so as to be located at a radial distance RD1 from the pivot portion PPN P ″″. The second center reference point REF2 of (e.g., the second scale element portion PRTSC2″″ of the second scale track ST2″″)P (e.g., since the first scale element portion and the second scale element portion and the corresponding scale tracks are fabricated on a single PCB, the PCB can be coupled to Figure 2 the support member MEPSM such that the scale portion as a whole can have a radial offset OFF P ) and thus be located at a radial distance RD2 from the pivot portion PPN P ””. Note that the differential distance D12”” is indicated in Figure 8B as being the same as in Fig. 8A (e.g., in some particular implementations, a constant known differential distance D12”” and / or corresponding characteristics can be considered to be used as an internal reference for performing self - calibration as described herein).

[0154] Also note that although in this example the scale portion can have a radial offset as indicated, the detector portion including the sensing portion can maintain center reference points REF1 Z and REF2 Z ”” at positions such as Fig. 8A shown. Thus, in some particular implementations, the radial offset of the scale portion can be said to be relative to the detector portion including the sensing portion (e.g., in some particular implementations, the detector portion including the sensing portion can also be or alternatively be said to have a radial offset relative to the scale portion). In an alternative example, the described positions can be swapped, where the center reference points REF1 Z and REF2 Z ”” of the scale portion are maintained at positions such as Fig. 8A indicated, while the center reference points REF1 P and REF2 P ”” of the sensing portion are maintained at positions such as Figure 8B indicated (e.g., the sensing portion can be represented as having a radial offset relative to the scale portion, and / or the scale portion can be represented as having a radial offset relative to the sensing portion). As some particular numerical examples, Figure 8B the illustration in P indicates that the first radial distance RD1 P ”” can be 37.225 mm and the second radial distance RD2 P ”” can be 32.6 mm (e.g., corresponding to a positive radial offset OFF

[0155] 9A to 9C is a diagram 910 - 930 showing certain data resulting from the operation and calibration process of the transducers of Figure 6 and Figure 7 , having such as Fig. 8A and Figure 8B The offset shown. The x-axis of graphs 910 - 930 is the arc distance along the first scale track TR1 (e.g., in various embodiments, equation 13 or a similar calculation, such as known formulas for relating angular values to arc distances, etc., may be utilized to convert angular values to arc distances and vice versa). Regarding Fig.9A and Fig. 9C the graph values plotted in millimeters in, in various embodiments, the equation related to the chain rounding-off value in millimeters may be as follows:

[0156] Chain rounding-off (in millimeters) = chain rounding-off * θ WSME1 *RD1 (Equation 22)

[0157] Note that the θ WSME1 *RD1 term is common to both axes and cancels out each other in the slope calculation. This convention applicable to Fig.9A and Fig. 9B also applies to Fig.11A , Fig. 11B , Fig.14A , Fig. 14B , Fig.17A and Fig.19A . In addition, note that 9A to 9C , 11A to Fig. 11C , FIG. 14A to FIG. 14C , FIG. 17A to FIG. 17B and FIG. 19A to FIG. 19B Some or all of the plotted graphs / curve plots of and the corresponding calculations described below may be according to the -OFF convention, and in the alternative +OFF convention, the plotted graphs / curve plots may be horizontally reversed and the signs of the calculated values may be reversed.

[0158] Fig.9A is the graph 910 of the chain rounding-off curve plot 911 of the chain rounding-off value of the direct chain rounding-off process. Fig. 9B is the graph 920 of the chain rounding-off curve plot 921 of the chain rounding-off value of the double chain rounding-off process. It should be understood (e.g., as indicated by equations 17 - 20) that, according to including the m variable (e.g., equal to 2 in the current example) in the denominator of the chain rounding-off slope equation for the double chain rounding-off process, Fig. 9B the chain rounding-off slope in (i.e., for the double chain rounding-off process) may be Fig.9A half of the chain rounding-off slope in (i.e., for the direct chain rounding-off process).

[0159] Fig. 9CChart 930 shows long-range error curve plots 931 and 933, where long-range error curve plot 931 represents data before the correction process, and long-range error curve plot 933 represents data after performing the correction process according to the principles described herein (e.g., according to Equation 21 and / or other processes). More specifically, in various embodiments, the chained subtraction slope can be determined based on data indicated in charts such as chart 910 or 920. For example, in one embodiment, the determination of the chained subtraction slope can include applying a least squares linear fit to the data.

[0160] The determined chained subtraction slope can be used to determine an offset value (e.g., a radial offset corresponding to a scale portion or a detector portion) according to an equation (e.g., one of Equations 17 to 20) or other calculations or methods that enable the determination of the offset value based on the determined chained subtraction slope or otherwise based on the chained subtraction data. The determined offset value can be used to correct one or more values that are used to determine the relative position between the detector portion and the scale portion. For example, the determined offset value can be used to correct the spatial step value or other spatial values of the scale portion according to Equation 21 or other calculations, and then the offset value can be used in one or more equations (e.g., such as Equation 12) or other calculations to determine the measurement result (i.e., which corresponds to the relative position between the detector portion and the scale portion).

[0161] As described above, long-range error curve plot 933 represents data after such a correction process has been performed. The corrected plot 933 (i.e., the remaining slope is about -0.67 um error / mm measurement) indicates a significant improvement relative to the original error plot 931 (i.e., the slope is about -2.67 um error / mm measurement). However, the remaining error (i.e., -0.67 um / mm) may be too high for some practical applications. In various embodiments, this can be characterized as being at least partially due to the difficulty in accurately determining the chained subtraction slope from the data indicated in charts such as chart 910 or 920.

[0162] For example, considering the nature of such data in practical applications (such as where the data may have a certain amount of variation / fluctuation due to various factors (e.g., noise, amplitude variation, misalignment, etc.), as indicated by the variation / oscillation in plots 911 and 921), the accuracy of the determination of the chained subtraction slope may be affected. This limited accuracy in determining the chained subtraction slope may result in limited accuracy in determining the offset value (e.g., a radial offset corresponding to a scale portion or a detector portion), and correspondingly limited accuracy of the correction process, which results in the error curve plot 933 indicating the remaining error. Such characteristics may be at least partially due to Figure 6 and Figure 7result from certain dimensional relationships in specific implementations. Instead, Figure 3A and Figure 4 specific implementations can provide improved characteristics that offer sufficient accuracy for certain practical applications, as will be described in more detail below.

[0163] FIG. 10A to FIG. 10B is a diagram showing the offset (e.g., radial offset of a scale portion or a detector portion) with respect to certain features of Figure 3A and Figure 4 Note that Fig. 10A and Fig. 10B have certain similarities with Fig. 8A and Figure 8B Fig. 10A can be compared with the representation of a portion of the vertical centerline of Figure 4 and generally corresponds to the representation of a portion of the vertical centerline of Figure 4 In the illustration of Fig. 10A (e.g., which can correspond to the case of zero radial offset in various specific implementations), the first central reference point REF1 Z (e.g., located at the center x-axis and / or y-axis position on the centerline CL1 of the first scale element portion PRTSC1 and / or the first sensing element portion PRTSEN1 of the first scale track ST1) is located at a radial distance RD1 Z from the pivot portion PPN. The second central reference point REF2 Z (e.g., located at the center x-axis and / or y-axis position on the centerline CL2 of the second scale element portion PRTSC2 and / or the second sensing element portion PRTSEN2 of the second scale track ST2) is located at a radial distance RD2 Z from the pivot portion PPN.

[0164] The differential distance D12 is indicated as the distance difference between the central reference points REF1 Z and REF2 Z and correspondingly is also the difference between the first radial distance RD1 Z and the second radial distance RD2 Z As some specific numerical examples, Fig. 10A the illustration in Z indicates that the first radial distance RD1 Z can be 37.125 mm, and the second radial distance RD2 Figure 3A and Figure 4 (e.g., corresponding to the numerical example described above regarding Figure 4 ​In the illustration, the numerical example may 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.

[0165] Fig. 10B Shows a case with an offset OFF P (e.g., a radial offset of the scale part or the detector part). In Fig. 10B the illustration (e.g., which may correspond to a positive radial offset OFF P in various specific embodiments), the first center reference point REF1 (e.g., of the first scale element part PRTSC1 of the first scale track ST1) P has been moved upward by the offset OFF P , so as to be located at a radial distance RD1 from the pivot part PPN P . The second center reference point REF2 (e.g., of the second scale element part PRTSC2 of the second scale track ST2) P has also been moved upward by the offset OFF P (e.g., since the first scale element part and the second scale element part and the corresponding scale tracks are fabricated on a single PCB, which can be coupled to Figure 2 the support member MEPSM such that the scale part as a whole can have a radial offset OFF P ), so as to be located at a radial distance RD2 from the pivot part PPN P . It should be noted that the difference distance D12 is indicated as the same in Fig. 10B as in Fig. 10A (e.g., in some specific embodiments, a constant known difference distance D12 and / or the corresponding characteristics can be regarded as being used as an internal reference for performing self - calibration as described herein).

[0166] It should also be noted that although in this example, the scale part can have a radial offset as indicated, the detector part including the sensing part can keep the center reference points REF1 Z and REF2 Z in the positions shown in Fig. 10A . Thus, in some specific embodiments, the radial offset of the scale part can be said to be related to the detector part including the sensing part (e.g., in some specific embodiments, the detector part including the sensing part can also be said to have a radial offset relative to the scale part). In an alternative example, the described positions can be exchanged, where the center reference points REF1 Z and REF2 Z of the scale part are kept in the positions indicated in, for example, Fig. 10A , while the center reference point REF1 of the sensing partP and REF2 P be maintained at positions such as Fig. 10B as indicated (e.g., the sensing portion may be represented as having a radial offset relative to the scale portion, and / or the scale portion may be represented as having a radial offset relative to the sensing portion). As some specific numerical examples, Fig. 10B the illustration in P indicates that the first radial distance RD1 P may be 37.225 mm and the second radial distance RD2 P may be 25.6 mm (e.g., as corresponding to a positive radial offset OFF that may be 0.1 mm

[0167] FIG. 11A to FIG. 11C is a diagram of Chart 1110 - 1130 showing certain data generated by the operation and calibration process of the transducers of Figure 3A and Figure 4 with offsets such as FIG. 10A to FIG. 10B as shown. The x - axis of Chart 1110 - 1130 is the arc distance along the first scale track TR1. Chart 1110 - 1130 has certain similarities with the chart 910 - 930 of 9A to 9C and will be understood at least in part based on the description of 9A to 9C unless otherwise described below.

[0168] Fig.11A is Chart 1110 of the chain - cancellation curve plot 1111 of the chain - cancellation values of the direct chain - cancellation process. Fig. 11B is Chart 1120 of the chain - cancellation curve plot 1121 of the chain - cancellation values of the double chain - cancellation process. It should be understood (e.g., as indicated by Equations 17 - 20) that, depending on including the m variable (e.g., equal to 2 in the current example) in the denominator of the chain - cancellation slope equation for the double chain - cancellation process, Fig. 11B the chain - cancellation slope in Fig.11A (i.e., for the double chain - cancellation process) can be 1 / 2 of the chain - cancellation slope in DIR (i.e., for the direct chain - cancellation process). As a specific numerical example related to Equation 17, if the offset OFF to be determined is approximately 0.1 mm, and where RD1 = 37.125 mm, RD2 = 25.5 mm and n = 25, then Equation 17 indicates that CDSLOPE

[0169] Fig. 11CChart 1130 shows long-range error curve plots 1131 and 1133, where long-range error curve plot 1131 represents data before the correction process, and long-range error curve plot 1133 represents data after performing the correction process according to the principles described herein (e.g., according to Equation 21 and / or other processes). More specifically, in various embodiments, the chained subtraction slope can be determined based on data indicated in charts such as 1110 or 1120. For example, in one embodiment, determining the chained subtraction slope can include applying a least squares linear fit to the data.

[0170] The determined chained subtraction slope can be used to determine the offset value OFF (e.g., the radial offset corresponding to the scale portion or the detector portion) such as according to an equation (e.g., one of Equations 17 to 20) or other calculations or methods that enable the determination of the offset value based on the determined chained subtraction slope or otherwise based on the chained subtraction data. The determined offset value can be used to correct one or more values that are used to determine the relative position between the detector portion and the scale portion. For example, the determined offset value can be used to correct the spatial step value or other spatial values of the scale portion according to Equation 21 or other calculations, and then the offset value can be used in one or more equations (e.g., such as Equation 12) or other calculations to determine the measurement result (i.e., which corresponds to the relative position between the detector portion and the scale portion).

[0171] As described above, long-range error curve plot 1133 represents data after such a correction process has been performed. The corrected plot 1133 (i.e., the remaining slope is about -0.2 um error / mm measurement) indicates a significant improvement relative to the original error plot 1131 (i.e., the slope is about -2.67 um error / mm measurement). This may be more than sufficient for certain practical applications (e.g., as opposed to the results indicated in 9A to 9C where there is still a significantly higher error level after the correction process). Compared with the embodiments of 9A to 9C such improved characteristics may be at least partially due to Figure 6 to Figure 7 in the embodiments of FIG. 11A to FIG. 11C certain dimensional relationships in Figure 3A and Figure 4 .

[0172] As described above, Figure 3A and Figure 4 a key aspect of the embodiments of FIG. 3A to FIG. 4Example values for a specific implementation are RD2 = 25.5 mm and RD1 = 37.125 mm, (1 / RD2) - (1 / RD1) = 0.01228 mm -1 , which corresponds to FIG. 11A to FIG. 11C the desired result. This can be compared with Figure 6 and Figure 7 a specific implementation where, for example values RD2 = 32.5 mm and RD1 = 37.125 mm, (1 / RD2) - (1 / RD1) = 0.00383 mm -1 . Note that for the calibration process, the 0.01228 mm -1 factor is approximately 3.2 times better than the 0.00383 mm -1 factor. In some specific implementations, it may be desirable for the (1 / RD2) - (1 / RD1) factor to be at least 0.01 mm -1 .

[0173] Another way to represent / characterize the large separation of the scale tracks is according to the ratio RD1 / RD2. In Figure 3A and Figure 4 a specific implementation, RD1 / RD2 = 1.456. This can be compared with Figure 6 and Figure 7 a specific implementation where RD1 / RD2 = 1.142. In some specific implementations, it may be desirable for the ratio of RD1 / RD2 to be at least 1.4.

[0174] Another way to represent / characterize the large separation of the scale tracks is according to the separation distance SEP12 between the first scale track and the second scale track, such as relative to the width of the first scale track and / or the second scale track. In Figure 6 and Figure 7 a specific implementation, note that the separation distance SEP12 is 1.25 mm, which is less than the first scale track width of 4.0 mm and the second scale track width of 2.75 mm, respectively. In contrast, in Figure 3A and Figure 4In a specific implementation, the separation distance SEP12 is 8.25 mm, which is greater than the width of the first scale track and / or the second scale track. In various specific 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 specific implementations, it may be desirable for the separation distance SEP12 to be greater than the combined width of the first scale track and the second scale track. In various specific 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 twice the width of the second scale track. In various specific implementations, it may also be desirable for the separation region between the first scale track and the second scale track to have a width defined by the separation distance SEP12, and for this separation region, the separation region is relatively empty (e.g., it does not include a scale element portion arranged in a track portion having a sensing element portion).

[0175] Fig.12

[0176] is a diagram showing Figure 2 certain dimensions and features of a measuring instrument and a part of the transducer TDR', which transducer is configured for arcuate movement between a detector portion and a scale portion, such as may be used in Figure 2 a measuring instrument, and having the second largest separation of the scale tracks. Fig.12 The transducer TDR' of Figure 3A and Figure 4 is configured to generate signals similar to those of the transducer TDR of Figure 5 and for which signal Fig.12 represents the signal generated by the operation of the specific implementation of Figure 3A and Figure 4 and the signal generated by the operation of the specific implementation of Fig.12 In this regard, during operation, the signal of the specific implementation of Figure 3A may be similar to the signals SIG1A, SIG1B, SIG2A, and SIG2B of the specific implementation of

[0177] Furthermore Figure 3A each component of the transducer TDR of Fig.12 will be understood to have a corresponding component (e.g., denoted by an apostrophe ') in the transducer TDR' of

[0178] In Fig.12In the transducer, a first scale element portion PRTSC1' is located within a first scale track ST1' having a first scale track width STW1' (e.g., the upper and lower edges of the first scale element portion PRTSC1' may correspond to the upper and lower boundaries of the first scale track ST1'). A second scale element portion PRTSC2' is located within a second scale track ST2' having a second scale track width STW2' (e.g., the upper and lower edges of the second scale element portion PRTSC2' may correspond to the upper and lower boundaries of the second scale track ST2'). A separation distance SEP12' is shown as the radial distance between the first scale track ST1' and the second ST2'. A separation region SEPA' is shown between the first scale track ST1' and the second scale track ST2' (e.g., having a radial width defined by the separation distance SEP12' and such as defined by the lower boundary of the first scale track ST1' and the upper boundary of the second scale track ST2'). The separation region SEPA' is empty (e.g., does not include a scale element portion arranged in an encoder track portion having a sensing element portion).

[0179] The second scale element portion PRTSC2' of the second scale track ST2' (such as being 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' (such as being included as part of a first encoder track portion) (e.g., such that the radial distance RD2' of the second center reference point REF2' of the second scale element portion PRTSC2' of the second scale track ST2' of the second encoder track portion is less than the radial distance RD1' of the first center reference point REF1' of the first scale element portion PRTSC1' of the first scale track ST1' of the first encoder track portion). In various embodiments, the reference point REF1' may be located at the center line CL1', and the reference point REF2' may be located at the center line CL2'. A difference distance D12' is indicated as the distance difference between the center reference points REF1' and REF2', and correspondingly is also the difference between the first radial distance RD1' and the second radial distance RD2'.

[0180] The first scale element portion PRTSC1' has a first angular range θ RG1 and a corresponding arc length ARC1', and the second scale element portion PRTSC2' has a second angular range θ RG2 and a corresponding arc length ARC2'. The angular ranges θ RG1 and θ RG2 are indicated as being nominally equal, and in Fig.12 the example are indicated as being nominally equal to the absolute angular measurement range θ ABS and the maximum angular movement range θ MAX. In these examples, the arc length can be determined according to standard arc length equations such as ARC1' = RD1'(θ ABS ) and ARC2' = RD2'(θ ABS )(e.g., where the θ ABS value is in radians). As some specific example dimensions, in one specific implementation, the first scale track width STW1' can be 4.0 mm, the second scale track width STW2' can be 2.75 mm, the separation distance SEP12' can be 13.85 mm, the first radial distance RD1' can be 38.725 mm, the second radial distance RD2' can be 21.5 mm, and the differential distance D12' can be 17.225 mm. In various specific implementations, such dimensions can result in certain desired operating characteristics, which will be described in more detail below.

[0181] FIG. 13A to FIG. 13B is a diagram showing the offset of certain features with respect to Fig.12 (e.g., the radial offset of the scale portion or the detector portion). Note that Fig.13A and Fig. 13B are similar to Fig. 10A and Fig. 10B , and will be understood based on the description of Fig. 10A and Fig. 10B , unless otherwise stated below. Fig.13A and Fig. 13B The main difference is the numerical example of the dimensions, which will be described in more detail below. In the diagram of Fig.13A (e.g., which can correspond to the case of zero radial offset in various specific implementations), the first central reference point REF1 Z ' is located at a radial distance RD1 Z ' from the pivot portion PPN. The second central reference point REF2 Z ' is located at a radial distance RD2 Z ' from the pivot portion PPN.

[0182] As some specific numerical examples, Fig.13A the diagram in Z indicates that the first radial distance RD1 Z ' can be 38.725 mm, the second radial distance RD2 Figure 12 ' can be 21.5 mm (e.g., as corresponding to the numerical example described above regarding Figure 12 ), and correspondingly, the differential distance D12' can be 17.225 mm. As described above, in the diagram of

[0183] In Figure 13B the illustration (e.g., which may correspond to a positive radial offset OFF P in various specific implementations), the first central reference point REF1 P ' of (e.g., the first scale element portion PRTSC1' of the first scale track ST1') has been moved upward by an offset OFF P , and thus is located at a radial distance RD1 P ' from the pivot portion PPN. The second central reference point REF2 P ' of (e.g., the second scale element portion PRTSC2' of the second scale track ST2') has also been moved upward by the offset OFF P , and thus is located at a radial distance RD2 P ' from the pivot portion PPN. It should be noted that the differential distance D12' is indicated as being the same in Figure 13B as in Figure 13A (e.g., in some specific implementations, a constant known differential distance D12' and / or corresponding characteristics may be considered to be used as an internal reference for performing self - calibration as described herein).

[0184] It should also be noted that although in this example the scale portion may have a radial offset as indicated, the detector portion including the sensing portion may keep the central reference points REF1 Z ' and REF2 Z ' in positions such as Figure 13A shown. Thus, in some specific implementations, the radial offset of the scale portion may be referred to as being related to the detector portion including the sensing portion (e.g., in some specific implementations, the detector portion including the sensing portion may also be referred to as having a radial offset relative to the scale portion). In an alternative example, the described positions may be swapped, where the central reference points REF1 Z ' and REF2 Z ' of the scale portion are kept in positions such as Figure 13A indicated, while the central reference points REF1 P ' and REF2 P ' of the sensing portion are kept in positions such as Figure 13B indicated (e.g., the sensing portion may be represented as having a radial offset relative to the scale portion, and / or the scale portion may be represented as having a radial offset relative to the sensing portion). As some specific numerical examples, Figure 13B the illustration in P indicates that the first radial distance RD1 P ' may be 38.825 mm and the second radial distance RD2 P)。The constant differential distance D12' can continue to be 17.225 mm.

[0185] Figures 14A to 14C is a view of chart 1410 - 1430 showing certain data generated by the operation and calibration process of the transducer of Figure 12 with offsets such as Figures 13A to 13B shown. The x - axis of chart 1410 - 1430 is the arc distance along the first scale track TR1. Chart 1410 - 1430 has certain similarities with Figures 11A to 11C chart 1110 - 1130 of Figures 11A to 11C and will be understood at least in part based on the description of

[0186] Figure 14A is chart 1410 of the chain - round - off curve plot 1411 of the chain - round - off values of the direct chain - subtraction process. Figure 14B is chart 1420 of the chain - round - off curve plot 1421 of the chain - round - off values of the double chain - subtraction process. As a specific numerical example related to Equation 17, if the offset OFF to be determined is approximately 0.1 mm, and where RD1 = 38.725 mm, RD2 = 21.5 mm and n = 25, then Equation 17 indicates that CDSLOPE DIR should be ≈0.05, which is approximately the chain - round - off slope observed in the chain - round - off curve plot 1411 and can thus be used to approximately determine the offset OFF.

[0187] Figure 14C is chart 1430 showing the long - range error curve plots 1431 and 1433, where the long - range error curve plot 1431 represents the data before the calibration process and the long - range error curve plot 1433 represents the data after the calibration process is performed according to the principles described herein (e.g., according to Equation 21 and / or other processes). More specifically, in various specific embodiments, the chain - round - off slope can be determined based on data indicated in charts such as 1410 or 1420. For example, in one specific embodiment, the determination of the chain - round - off slope can include applying a least - squares linear fit to the data.

[0188] The determined chain subtraction slope can be used to determine an offset value OFF (e.g., a radial offset corresponding to a scale portion or a detector portion) according to an equation (e.g., one of equations 17 to 20) or other calculations or methods that enable the determination of the offset value based on the determined chain subtraction slope or otherwise based on chain subtraction data. The determined offset value can be used to correct one or more values that are used to determine the relative position between the detector portion and the scale portion. For example, the determined offset value can be used to correct the spatial step value or other spatial values of the scale portion according to equation 21 or other calculations, and then the offset value can be used in one or more equations (e.g., such as equation 12) or other calculations to determine the measurement result (i.e., which corresponds to the relative position between the detector portion and the scale portion).

[0189] As described above, the long-range error curve plot 1433 represents the data after such a correction process has been performed. The corrected plot 1433 (i.e., with a remaining slope of approximately -0.1 um error / mm measurement) indicates a significant improvement relative to the original error plot 1431 (i.e., with a slope of approximately -2.67 um error / mm measurement). This may be more than sufficient for certain practical applications (e.g., as opposed to the results indicated in Figures 9A to 9C where, after the correction process, there is still a significantly higher error level). Compared to the specific implementation of Figures 9A to 9C such improved characteristics may be due at least in part to certain dimensional relationships in the specific implementations of Figures 14A to 14C and Figures 12 to 13B . Figure 6 and Figure 7 .

[0190] According to the principles described herein, Figures 12 to 13B a key aspect of the specific implementation is the large separation of the scale tracks. Regarding certain relationships (e.g., as indicated by equations 17 - 20), the large separation of the scale tracks in certain examples can be represented by the relationship (1 / RD2)-(1 / RD1). For Figures 12 to 13B an example value of RD2 = 21.5 mm and RD1 = 38.725 mm for the specific implementation, (1 / RD2)-(1 / RD1) = 0.02069 mm -1 , which corresponds to Figures 14A to 14C the desired result. This can be contrasted with Figure 6 and Figure 7 where, for example values of RD2 = 32.5 mm and RD1 = 37.125 mm, (1 / RD2)-(1 / RD1) = 0.00383 mm -1 . In certain specific implementations, it may be desirable for the (1 / RD2)-(1 / RD1) factor to be at least 0.01 mm -1, or at least 0.015 mm -1 .

[0191] Another way to represent / characterize the large separation of the scale track is according to the ratio RD1 / RD2. In Figures 12 to 13B specific implementations, RD1 / RD2 = 1.801. This can be compared with Figure 6 and Figure 7 specific implementations, where RD1 / RD2 = 1.142. In some specific implementations, it may be desirable for the ratio of RD1 / RD2 to be at least 1.4, or at least 1.5.

[0192] Another way to represent / characterize the large separation of the scale track is according to the separation distance SEP12 between the first scale track and the second scale track, such as relative to the width of the first scale track and / or the second scale track. In Figure 6 and Figure 7 specific implementations, it should be noted that the separation distance SEP12 is 1.25 mm, which is respectively less than the width of the first scale track of 4.0 mm and the width of the second scale track of 2.75 mm. In contrast, in Figures 12 to 13B specific implementations, the separation distance SEP12 is 13.85 mm, which is greater than the width of the first scale track and / or the second scale track. In various specific 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 specific implementations, it may be desirable for the separation distance SEP12 to be greater than the combined width of the first scale track and the second scale track. In various specific 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.

[0193] Figure 15 is a diagram showing some dimensions and features of the measuring instrument of Figure 2 and a part of the transducer TDR”, which is configured for arcuate movement between the detector part and the scale part, such as can be used in Figure 2 the measuring instrument, and has the second largest separation of the scale track. Figure 15 The transducer TDR” of Figure 3A and Figure 4The transducer TDR' operates substantially similarly. Thus, a person skilled in the art will understand the components of the transducer TDR' based on the corresponding components of the transducer TDR, unless otherwise described below. Therefore, a complete description of the components of the transducer TDR' will not be provided herein. Some differences between the transducer TDR' and the transducer TDR are certain dimensional relationships, some of which will be described in more detail below.

[0194] In Figure 15 the transducer, a first scale element portion PRTSC1' is located within a first scale track ST1' having a first scale track width STW1' (e.g., the upper and lower edges of the first scale element portion PRTSC1' may correspond to the upper and lower boundaries of the first scale track ST1'). A second scale element portion PRTSC2' is located within a second scale track ST2' having a second scale track width STW2' (e.g., the upper and lower edges of the second scale element portion PRTSC2' may correspond to the upper and lower boundaries of the second scale track ST2'). A separation distance SEP12' is shown as the radial distance between the first scale track ST1' and the second ST2'. A separation region SEPA' is shown between the first scale track ST1' and the second scale track ST2' (e.g., having a radial width defined by the separation distance SEP12' and such as defined by the lower boundary of the first scale track ST1' and the upper boundary of the second scale track ST2'). The separation region SEPA' is empty (e.g., does not include a scale element portion arranged in an encoder track portion having a sensing element portion).

[0195] The second scale element portion PRTSC2' of the second scale track ST2' (such as being 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' (such as being included as part of a first encoder track portion) (e.g., such that the radial distance RD2' of the second center reference point REF2' of the second scale element portion PRTSC2' of the second scale track ST2' of the second encoder track portion is less than the radial distance RD1' of the first center reference point REF1' of the first scale element portion PRTSC1' of the first scale track ST1' of the first encoder track portion). In various embodiments, the reference point REF1' may be located at the center line CL1', and the reference point REF2' may be located at the center line CL2'. A difference distance D12' is indicated as the distance difference between the center reference points REF1' and REF2', and correspondingly is also the difference between the first radial distance RD1' and the second radial distance RD2'.

[0196] The first scale element portion PRTSC1' has a first angular range θ RG1and a corresponding arc length ARC1”, and the second scale element portion PRTSC2” has a second angular range θ RG2 and a corresponding arc length ARC2”. The angular ranges θ RG1 and θ RG2 are indicated as being nominally equal, and in Figure 15 the example of ABS is indicated as being nominally equal to the absolute angular measurement range θ MAX and the maximum angular movement range θ ABS . In these examples, the arc lengths can be determined according to standard arc length equations such as ARC1” = RD1”(θ ABS ) and ARC2” = RD2”(θ ABS ) (e.g., where the θ

[0197] Figures 16A to 16B is a diagram showing an offset (e.g., a radial offset of the scale portion) of certain features relative to Figure 15 in a first direction (e.g., in the positive direction). Note that Figure 16A and Figure 16B are similar to Figure 10A and Figure 10B , and will be understood based on the description of Figure 10A and Figure 10B unless otherwise stated below. Figure 16A and Figure 16B The main difference is the numerical example of the dimensions, which will be described in more detail below. In Figure 16A the illustration of Z ” (e.g., which in various specific embodiments can correspond to the condition of zero radial offset), the first central reference point REF1 Z ” is located at a radial distance RD1 Z ” from the pivot portion PPN. The second central reference point REF2 Z ” is located at a radial distance RD2

[0198] As some specific numerical examples, Figure 16A the illustration in Z ” indicates that the first radial distance RD1 Z” can be 20 mm (e.g., corresponding to the numerical examples described above regarding Figure 15 ), and correspondingly, the differential distance D12” can be 20 mm. As described above, in Figure 15 's illustration, the numerical examples can also 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 16.625 mm.

[0199] In Figure 16B 's illustration (e.g., which can correspond to the condition of positive radial offset OFF P in various specific implementations), (e.g., of the first scale element portion PRTSC1” of the first scale track ST1”) the first center reference point REF1 P ” has been moved upward by an offset OFF P , so as to be located at a radial distance RD1 P ” from the pivot portion PPN. (e.g., of the second scale element portion PRTSC2” of the second scale track ST2”) the second center reference point REF2 P ” has also been moved upward correspondingly by an offset OFF P , so as to be located at a radial distance RD2 P ” from the pivot portion PPN. It should be noted that the differential distance D12” is indicated as being the same in Figure 16B as in Figure 16A (e.g., in some specific implementations, the constant known differential distance D12” and / or the corresponding characteristics can be considered to be used as an internal reference for performing self - calibration as described herein).

[0200] It should also be noted that although in this example, the scale portion can have a radial offset as indicated, the detector portion including the sensing portion can keep the center reference points REF1 Z ” and REF2 Z ” in positions such as Figure 16A shown. Thus, in some specific implementations, the radial offset of the scale portion can be said to be related to the detector portion including the sensing portion (e.g., in some specific implementations, the detector portion including the sensing portion can also be said to have a radial offset relative to the scale portion). In an alternative example, the described positions can be swapped, where the center reference points REF1 Z ” and REF2 Z ” of the scale portion are kept in positions such as Figure 16A indicated, while the center reference points REF1 P ” and REF2 P ” of the sensing portion are kept in positions such as Figure 16BThe indicated positions (e.g., the sensing portion may be represented as having a radial offset relative to the scale portion, and / or the scale portion may be represented as having a radial offset relative to the sensing portion). As some specific numerical examples, Figure 16B the illustration in P ” may be 40.1 mm, and the second radial distance RD2 P ” may be 20.1 mm (e.g., as corresponding to a positive radial offset OFF that may be 0.1 mm P ). The constant difference distance D12” may continue to be 20 mm.

[0201] Figure 17A and Figure 17B are diagrams 1720 and 1730 respectively showing certain data generated by the operation and calibration process of the transducers of Figure 15 with offsets such as Figures 16A to 16B shown. The x - axis of diagrams 1720 and 1730 is the arc distance along the first scale track TR1. Diagrams 1720 and 1730 have certain similarities with Figure 11B and Figure 11C the diagrams 1120 and 1130 of Figure 11B and Figure 11C and will be understood at least in part based on the description of

[0202] Figure 17A is diagram 1720 of the chained - subtraction curve plot 1721 of the chained - subtraction values of the double - chained subtraction process. As a specific numerical example related to Equation 19, if the offset OFF to be determined is approximately 0.1 mm, and where RD1 = 40 mm, RD2 = 20 mm, n = 60 and, m = 2, Equation 19 indicates that CDSLOPE DIR should be ≈0.075, which is approximately the chained - subtraction slope observed in the chained - subtraction curve plot 1721 and can thus be used to approximately determine the offset OFF.

[0203] Figure 17B is diagram 1730 showing long - range error curve plots 1731, 1732, and 1733, where long - range error curve plot 1731 represents data from the first scale track before the calibration process, long - range error curve plot 1732 represents data from the second scale track before the calibration process, and long - range error curve 1733 represents data after performing the calibration process according to the principles described herein (e.g., according to Equation 21 and / or other processes). More specifically, in various specific embodiments, the chained - subtraction slope may be determined based on the data indicated in diagrams such as 1720. For example, in one specific embodiment, the determination of the chained - subtraction slope may include applying a least - squares linear fit to the data.

[0204] The determined chain subtraction slope can be used to determine an offset value OFF (e.g., a radial offset corresponding to a scale portion or a detector portion) according to an equation (e.g., one of equations 19 to 20) or other calculations or methods that enable determination of the offset value based on the determined chain subtraction slope or otherwise based on chain subtraction data. The determined offset value can be used to correct one or more values that are used to determine the relative position between the detector portion and the scale portion. For example, the determined offset value can be used to correct the spatial step value or other spatial values of the scale portion according to equation 21 or other calculations, and then the offset value can be used in one or more equations (e.g., such as equation 12) or other calculations to determine the measurement result (i.e., which corresponds to the relative position between the detector portion and the scale portion).

[0205] As described above, the long-range error curve plot 1733 represents the data after such a correction process has been performed. The corrected plot 1733 (i.e., the remaining slope is about less than -0.1 um error / mm measurement) indicates a significant improvement relative to the original error plot 1731 (i.e., the slope is about -2.5 um error / mm measurement). This may be sufficient for certain practical applications (e.g., as opposed to the results indicated in Figures 9A to 9C where there is still a significantly higher error level after the correction process). Compared with the specific implementations of Figures 9A to 9C and Figure 6 and Figure 7 , such improved characteristics of Figures 17A to 17B may be at least partially due to certain dimensional relationships in the specific implementation of Figures 15 to 16B .

[0206] According to the principles described herein, Figures 15 to 16B a key aspect of the specific implementation of Figures 15 to 16B is the large separation of the scale tracks. Regarding certain relationships (e.g., as indicated by equations 19 - 20), the large separation of the scale tracks in certain examples can be represented by the relationship (1 / RD2)-(1 / RD1). For example values of RD2 = 20 mm and RD1 = 40 mm for the specific implementation of -1 , (1 / RD2)-(1 / RD1) = 0.02500 mm Figures 17A to 17B , which corresponds to the desired result of Figure 6 and Figure 7 . This can be contrasted with the specific implementations of -1 where for example values of RD2 = 32.5 mm and RD1 = 37.125 mm, (1 / RD2)-(1 / RD1) = 0.00383 mm -1, or at least 0.015 mm -1 , or at least 0.017 mm -1 , or at least 0.020 mm -1 .

[0207] Another way to represent / characterize the large separation of the scale tracks is according to the ratio RD1 / RD2. In Figures 15 to 16B specific implementations, RD1 / RD2 = 2.0. This can be contrasted with Figure 6 and Figure 7 specific implementations, where RD1 / RD2 = 1.142. In some specific 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.

[0208] Another way to represent / characterize the large separation of the scale tracks is according to the separation distance SEP12 between the first scale track and the second scale track, such as relative to the widths of the first scale track and / or the second scale track. In Figure 6 and Figure 7 specific implementations, it should be noted that the separation distance SEP12 is 1.25 mm, which is respectively less than the width of the first scale track of 4.0 mm and the width of the second scale track of 2.75 mm. In contrast, in Figures 15 to 16B specific implementations, the separation distance SEP12 is 16.625 mm, which is greater than the width of the first scale track and / or the second scale track. In various specific 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 specific implementations, it may be desirable for the separation distance SEP12 to be greater than the combined width of the first scale track and the second scale track. In various specific 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.

[0209] Figures 18A to 18B is a diagram showing the offset (e.g., the radial offset of the scale part) of certain features with respect to Figure 15 in the second direction (e.g., the negative direction). It is noted that Figure 18A and Figure 18B are similar to Figure 16A and Figure 16B , and will be understood based on the description of Figure 16A and Figure 16B , except having an offset OFFn in the negative direction and unless otherwise specified below. In the illustration of Figure 18A (e.g., which may correspond to the condition of zero radial offset in various specific implementations), the first central reference point REF1 Z”at a radial distance RD1 from the pivot portion PPN Z ”The second central reference point REF2 Z ”is located at a radial distance RD2 from the pivot portion PPN Z ”Note that Figure 18A is the same as Figure 16A and will be understood based on the above description of Figure 16A

[0210] In the illustration of Figure 18B (for example, which may correspond to the condition of a negative radial offset OFFn in various specific embodiments), the first central reference point REF1n” of the first scale element portion PRTSC1” of the first scale track ST1” has been moved downward by the offset OFFn, so as to be located at a radial distance RD1n” from the pivot portion PPN. The second central reference point REF2n” of the second scale element portion PRTSC2” of the second scale track ST2” has also been moved downward by the offset OFFn accordingly, so as to be located at a radial distance RD2n” from the pivot portion PPN. It should be noted that the differential distance D12” is indicated as being the same in Figure 18B as in Figure 16A and Figure 18A (for example, in some specific embodiments, the constant known differential distance D12” and / or the corresponding characteristics may be regarded as being used as an internal reference for performing self-calibration as described herein).

[0211] It should also be noted that although in this example, the scale portion may have a radial offset as indicated, the detector portion including the sensing portion may keep the central reference points REF1 Z ” and REF2 Z ” at positions such as Figure 16A and Figure 18A indicated. Therefore, in some specific embodiments, the radial offset of the scale portion can be referred to as being related to the detector portion including the sensing portion (for example, in some specific embodiments, the detector portion including the sensing portion can also be referred to as having a radial offset relative to the scale portion). In an alternative example, the described positions can be exchanged, where the central reference points REF1 Z ” and REF2 Z ” of the scale portion are kept at positions such as Figure 18A indicated, while the central reference points REF1n” and REF2n” of the sensing portion are kept at positions such as Figure 18B indicated (for example, the sensing portion can be represented as having a radial offset relative to the scale portion, and / or the scale portion can be represented as having a radial offset relative to the sensing portion). As some specific numerical examples, Figure 18B ​The illustration therein 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., as corresponding to a positive radial offset OFFn that can be 0.1 mm). The constant difference distance D12” can continue to be 20 mm.

[0212] Figure 19A and Figure 19B are diagrams 1920 and 1930 respectively showing certain data generated by the operation and calibration process of the transducers of Figure 15 wherein there are offsets such as Figures 18A to 18B shown. The x - axes of diagrams 1920 and 1930 are the arc distances along the first scale track TR1. Diagrams 1920 and 1930 have certain similarities with Figure 17A and Figure 17B diagrams 1720 and 1730, except that they are for conditions with negative offsets instead of positive offsets. It should be understood that any specific implementation as described herein can similarly operate with a negative offset (e.g., where such operation can be comparable to the operation with a positive offset, as shown by comparing the operation of Figure 19A and Figure 19B with the operation of Figure 17A and Figure 17B ).

[0213] Figure 19A is diagram 1920 of the chain - rounding curve plot 1921 of the chain - rounding values of the double - chain rounding - down process. As a specific numerical example related to Equation 19, if the offset OFF to be determined is approximately - 0.1 mm (i.e., corresponding to a negative offset), and where RD1 = 40 mm, RD2 = 20 mm, n = 60 and m = 2, then Equation 19 indicates that CDSLOPE DIR should be ≈ - 0.075, which is approximately the chain - rounding slope observed in the chain - rounding curve plot 1921 and can thus be used to approximately determine the offset OFF.

[0214] Figure 19B is diagram 1930 showing the long - range error curve plots 1931, 1932 and 1933, where the long - range error curve plot 1931 represents data from the first scale track before the calibration process, the long - range error curve plot 1932 represents data from the second scale track before the calibration process, and the long - range error curve 1933 represents data after performing the calibration process according to the principles as described herein (e.g., according to Equation 21 and / or other processes). More specifically, in various specific implementations, the chain - rounding slope can be determined based on the data indicated in diagrams such as 1920. For example, in one specific implementation, the determination of the chain - rounding slope can include applying a least - squares linear fit to the data.

[0215] The determined chain subtraction slope can be used to determine an offset value OFF (e.g., a radial offset corresponding to a scale portion or a detector portion) according to an equation (e.g., one of equations 19 to 20) or other calculations or methods that enable determination of the offset value based on the determined chain subtraction slope or otherwise based on chain subtraction data. The determined offset value can be used to correct one or more values that are used to determine the relative position between the detector portion and the scale portion. For example, the determined offset value can be used to correct the spatial step value or other spatial values of the scale portion according to equation 21 or other calculations, and then the offset value can be used in one or more equations (e.g., such as equation 12) or other calculations to determine the measurement result (i.e., which corresponds to the relative position between the detector portion and the scale portion).

[0216] As described above, the long-range error curve plot 1933 represents the data after such a correction process has been performed. The corrected plot 1933 (i.e., the remaining slope is about less than 0.1 um error / mm measurement) indicates a significant improvement relative to the original error plot 1931 (i.e., the slope is about 2.5 um error / mm measurement). This may be more than sufficient for certain practical applications (e.g., contrary to the results indicated in Figures 9A to 9C where there is still a significantly higher error level after the correction process). Compared with the specific implementations of Figures 9A to 9C such improved characteristics of Figure 6 and Figure 7 may be due at least in part to certain dimensional relationships in the specific implementation of Figures 19A to 19B According to the principles described herein, a key aspect of the specific implementation of Figures 15 to 16B is the large separation of the scale tracks. After the descriptions of

[0217] the various aspects and relationships of the large separation of the scale tracks in the specific implementation of Figures 15 to 16B are described above. Figure 17A and Figure 17B After the description of Figures 15 to 16B the various aspects and relationships of the large separation of the scale tracks in the specific implementation of

[0218] Figure 20It is a flowchart showing a method 2000 of operating a measuring instrument using an arcuate motion to determine a relative position between a detector part and a scale part. Block 2010 includes providing a drive signal to cause a field generation part PRTFGE to generate a varying magnetic flux. Block 2020 includes receiving a detector signal from the detector part 167, where the detector signal includes: a detector signal from a first set of first sensing elements SET1SEN1 operating in conjunction with modulating a scale element SME1 with a first signal; and a detector signal from a first set of second sensing elements SET1SEN2 operating in conjunction with modulating a scale element SME2 with a second signal. The maximum movement range of the arcuate motion of the movable encoder part is less than 360 degrees, and a first scale element part is arranged such that a central reference point is located at a first radial distance RD1 from a pivot part, and a second scale element part is arranged such that a central reference point is located at a second radial distance RD2 from the pivot part, where the ratio of RD1 / RD2 is at least 1.4. Block 2030 includes determining at least in part a relative position between the detector part 167 and the scale part 170 based on the detector signal input from the detector part 167.

[0219] Regarding the operation at block 2030 for determining at least in part a relative position between the detector part (167) and the scale part (170) based on the detector signal from the detector part, various processing and / or signal combination techniques can be utilized (e.g., as would be understood by those skilled in the art and at least in part according to the teachings incorporated in the references). In short, in various embodiments, two drive operations can be utilized to generate and process the signal from the detector part. In various embodiments, the two drive operations can be performed simultaneously or at different timings.

[0220] More specifically, as part of a first driving operation, a first field generation element portion PRTFGE1 can be driven (e.g., using a corresponding drive signal from signal processing configuration 166). When driving the first field generation element portion PRTFGE1, corresponding signals (e.g., signals SIG1A and SIG1B) of a first sensing element SEN1 of a first sensing element portion PRTSEN1 of the detector portion can be read (e.g., received, processed, etc.). As part of a second driving operation, a second field generation element portion PRTFGE2 can be driven (e.g., using a corresponding drive signal from signal processing configuration 166). When driving the second field generation element portion PRTFGE2, corresponding signals (e.g., signals SIG2A and SIG2B) of a second sensing element SEN2 of a second sensing element portion PRTSEN2 of the detector portion can be read (e.g., received, processed, etc.). Detector signals (i.e., from the detector portion) generated during the first driving operation and the second driving operation can be utilized to determine a relative position (e.g., an absolute position between the detector portion and the scale portion). In various embodiments, the detector signals can include four signals (e.g., SIG1A, SIG1B, SIG2A, SIG2B) that can be used to determine the relative position, such as signals SIG1A and SIG1B of the first driving operation, and signals SIG2A and SIG2B of the second driving operation.

[0221] Figure 21 is a flowchart showing a method 2100 for a calibration process of a measuring instrument having an arcuate motion. Block 2110 includes providing a drive signal to cause a field generation portion PRTFGE to generate a varying magnetic flux. Block 2120 includes receiving a detector signal from a detector portion 167, where the detector signal includes: a detector signal from a first set of first sensing elements SET1SEN1 operating in conjunction with a first signal modulation scale element SME1; and a detector signal from a first set of second sensing elements SET1SEN2 operating in conjunction with a second signal modulation scale element SME2. Block 2130 includes determining an offset value at least partially based on the received detector signal, the offset value corresponding to a radial offset of a scale portion including the first signal modulation scale element and the second signal modulation scale element. Block 2140 includes using the determined offset value to correct one or more values for determining a relative position between the detector portion and the scale portion. For example, the determined offset value can be used to correct a spatial step value or other spatial value of the scale portion according to Equation 21 or other calculations, and then the offset value can be used in one or more equations (e.g., such as Equation 12) or other calculations or processes to determine a measurement result (i.e., which corresponds to the relative position between the detector portion and the scale portion).

[0222] In various embodiments, determining the offset value at block 2130 includes determining a differential slope (e.g., a chained subtraction slope). In various embodiments, the differential slope can correspond to the slope of the difference between the absolute position signal and at least one of: a first position signal that at least partially corresponds to a detector signal from a first sensing element (e.g., as part of a direct chained subtraction process as described herein); or a second position signal that at least partially corresponds to a detector signal from a second sensing element (e.g., as part of a first step of a chained subtraction process as described herein). In various embodiments, the difference between the absolute position signal and at least one of the first position signal or the second position signal at least partially corresponds to a difference between the phases of the respective signals (e.g., as indicated by equations 9, 10, 14, and 15).

[0223] In various embodiments, using the determined offset value to correct one or more values at block 2140 includes at least partially dividing the determined offset value by at least a radial distance of a first scale element portion. For example, as indicated by equation 21, where the corrected value can be characterized as including the determined offset value OFF D divided by the radial distance RD1 of the first scale element portion and multiplied by the spatial step of the first scale element portion (e.g., θ WSME1 ). Then, this corrected value (i.e., corresponding to -θ WSME1 (OFF D / RD1)) can be added to the spatial step of the first scale element portion (e.g., added to θ WSME1 ) in order to determine a corrected spatial step value θ WSME1C , which is subsequently used (e.g., in equation 12 or other calculations) to determine the relative position between the detector portion and the scale portion (e.g., as part of a measurement operation). In various embodiments, method 2100 (e.g., as configured to be performed by a signal processing configuration) further includes at least partially determining an absolute relative position between the detector portion and the scale portion based on detector signals input from the detector portion, the detector signals including detector signals from a first set of first sensing elements and detector signals from a first set of second sensing elements (e.g., similar to Figure 20 block 2030 and as may correspond to entering a normal measurement mode for performing normal measurement operations after completion of a calibration process).

[0224] Generally speaking, according to the principles described herein, in embodiments configured such that the first radial distance between the first scale element portion and correspondingly the first scale track and the second radial distance between the second scale element portion and correspondingly the second scale track have a large relative difference (e.g., or otherwise where there is a large difference between the positions of the scale tracks), the effect of radial offset / misalignment (e.g., of the scale portion relative to the sensing portion of the detector portion) is also relatively large. As part of the determination of an absolute measurement, effects / differences can be seen, detected, etc. from the process of determining an integer number of spatial steps (e.g., corresponding to an integer number of signal modulation elements of the scale element portion of the scale track). For example, as part of a chained subtraction process, the determination of an integer number of spatial steps includes a rounding process, where the quantity being rounded is referred to as the chained subtraction value. A chained subtraction slope can be determined (e.g., which can be determined based on a plot of the chained subtraction curve of the chained subtraction values, or based on the chained subtraction values), and this chained subtraction slope can be used to determine an offset value (e.g., corresponding to the radial offset of the scale portion, such as relative to the sensing portion of the detector portion and / or relative to a pivot portion or other reference, or corresponding to the radial offset of the sensing portion of the detector portion, such as relative to the scale portion and / or relative to a pivot portion or other reference). The determined offset value can be utilized to correct one or more values that are used to determine the relative position between the detector portion and the scale portion. For example, values (e.g., such as the spatial steps corresponding to the first scale element portion and correspondingly the first scale track or the absolute measurement range, or other spatial values used as part of the 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 the determination of an absolute measurement (e.g., which corresponds to the determination of the relative position between the detector portion and the scale portion).

[0225] In various embodiments, the calibration 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., when the measuring instrument is first assembled, such as after a movable encoder portion MEP is coupled to a support member MEPSM, or at any other time when such calibration is to be performed). While the measuring instrument is moved in an arcuate motion at a series of positions (e.g., where there is relative movement between a scale portion and a detector portion), measurement data (e.g., corresponding to detector signals received from the detector portion) may be collected in a memory. The measurement data may be analyzed, and an offset value may be determined (e.g., such as a radial offset corresponding to the movable encoder portion MEP, which may correspond to a radial offset of the scale portion relative to the detector portion, or a radial offset of the detector portion relative to the scale portion, etc.). Determining the offset value may include determining a differential slope (e.g., a chained subtraction slope). In various embodiments, if the differential slope is very large, the data set may wrap around (e.g., such as jumping from -0.5 to +0.5 or from +0.5 to -0.5), where a de-wrapping process may be performed or otherwise utilized such that a total differential slope may be determined. In various embodiments, the offset value may be determined based on the differential slope. Then, the determined offset value may be used to correct one or more values that are used to determine the relative position between the detector portion and the scale portion. When calibration is complete, the measuring instrument may be placed or otherwise enter a normal operating mode (e.g., during which accurate measurement results may be determined based on the calibration that has been performed). It should be understood that such calibration may help ensure the accuracy of the measuring instrument, particularly with respect to possible radial offsets (e.g., with respect to assembly and / or manufacturing tolerances of components, such as with respect to the coupling of the movable encoder portion MEP to the support member MEPSM, as this may result in a radial offset of the relative position with respect to the scale portion and the detector portion, etc.).

[0226] While some examples described herein are primarily directed to an electronic position encoder having arcuate motion and an arcuate encoder track portion, it should be understood that certain similar or identical principles may apply to an electronic position encoder having arcuate motion and a linear-shaped encoder track portion, and the techniques described herein may similarly apply to such electronic position encoders. Some examples of electronic position encoders having arcuate motion and a linear-shaped encoder track portion are described in U.S. Patent Application Serial No. 18 / 391,275, filed December 20, 2023, which is hereby incorporated by reference in its entirety. Some examples of electronic position encoders having arcuate motion and an arcuate encoder track portion are described in U.S. Patent Application Serial 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 may be used in combination with the teachings described herein to form an electronic position encoder having the characteristics and operations described herein.

[0227] As used herein, the term "nominal" encompasses variations in one or more parameters that fall within an acceptable tolerance range. As an example, in a particular implementation, a term such as "nominal" may correspond to a minimum variance from a specified value (e.g., such as less than 5%, or less than 2%, or less than 1% according to an acceptable tolerance, etc.).

[0228] It should be understood that the principles disclosed and claimed herein may be readily and desirably combined with the various features disclosed in the incorporated references. The various specific implementations described above may be combined to provide further specific implementations. The entire contents of all U.S. patents and U.S. patent applications cited in this specification are hereby incorporated by reference. Aspects of the specific implementations may be modified if necessary to employ concepts from the various patents and applications to provide further specific implementations. These and other changes may be made to the specific implementations in light of the foregoing detailed description. In general, in the following claims, the terms used should not be construed to limit the claims to the specific implementations disclosed in the specification and claims, but should be construed to include all possible specific implementations and the full scope of equivalents to which such claims are entitled.

Claims

1. A 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 encoder configured to measure an absolute relative position between a detector portion and a scale portion, wherein the movable encoder portion comprises one of the detector portion or the scale portion, the electronic position encoder comprising: The scale portion, the scale portion extends along the scale direction, and the scale portion includes: a first scale element portion, the first scale element portion comprising a first signal modulating scale element; and a second scale element portion, the second scale element portion comprising a second signal modulating scale element; and The detector portion, the detector portion being arranged to be proximate to the scale portion, wherein relative movement between the detector portion and the scale portion is caused by an arcuate movement of the movable encoder portion, the detector portion comprising: a field generating portion configured to generate a varying magnetic flux in response to a drive signal; and A sensing part, the sensing part comprising: a first sensing element portion comprising a first set of first sensing elements and arranged in a first track portion together 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 together with the second scale element portion; and A signal processing configuration, the signal processing configuration being configured to: providing a drive signal to cause the field generating portion to generate a varying magnetic flux; receiving a detector signal from the detector portion, the detector signal comprising: detector signals from said first set of first sensing elements operating in conjunction with a first signal modulation scale element; and detector signals from said first set of second sensing elements operating in conjunction with a second signal modulation scale element; 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 signal; and The determined offset value is used to correct one or more values ​​used to determine the relative position between the detector portion and the scale portion.

2. The measuring instrument of claim 1, wherein determining the offset value comprises determining a chained rounding slope.

3. The measuring instrument of claim 2, wherein the chained rounding slope is determined according to at least one of a direct chained rounding process or a double chained rounding process.

4. The measuring instrument of claim 3, wherein the chained rounding slope corresponds to a chained rounding curve plot of chained rounding values.

5. The measurement instrument of claim 1, wherein correcting one or more values ​​using the determined offset value comprises at least in part dividing the determined offset value by at least a radial distance of the first scale element portion from the pivot portion.

6. A measuring instrument as described in claim 1, wherein the signal processing configuration is also configured to determine the absolute relative position between the detector part and the scale part based at least in part on a detector signal input from the detector part, the detector signal including a detector signal from the first group of first sensing elements and a detector signal from the first group of second sensing elements.

7. The measuring instrument of claim 1, wherein the field generating portion comprises: a first field generating element portion disposed in the first track portion and configured to operate in conjunction with a first signal modulating scale element of the first scale element portion and the first sensing element of the first sensing element portion; and A second field generating element portion is arranged in the second track portion and is configured to operate in conjunction with a second signal modulating scale element of the second scale element portion and the second sensing element of the second sensing element portion.

8. The measuring instrument of claim 1, wherein: the first scale element portion and the second scale element portion of the first track portion and the second track portion are arcuate and parallel to each other, wherein the second track portion is closer to the pivot portion than the first track portion; The first signal modulation scale element is configured to modulate the first signal according to the first signal modulation element angular space step length θ WSME1 The second signal modulating scale element is arranged along the first scale element portion, and the second signal modulating scale element is arranged according to the second signal modulating element angular space step θ WSME2 The second signal modulation element angular space step length is different from the first signal modulation element angular space step length θ along the second scale element portion. WSME1 ;and The first scale element portion and the second scale element portion define a corresponding absolute angular range θ ABS .

9. The measuring instrument of claim 8, wherein the ratio of the angular space step lengths of the signal modulation element θ WSME2 / θ WSME1 can be expressed as being equal to at least one of the following equations: (nm / (n-1)); (nm / (n+1)); ((nm+1) / n); ((nm-1) / n); wherein n is a positive integer, and m is a positive integer of at least 2.

10. The measuring instrument of claim 8, wherein the absolute angular range θ ABS Equal to nθ WSME1 or nθ WSME2 One of, wherein n is a positive integer, and the absolute angle range θ ABS Less than 360 degrees.

11. The measuring instrument of claim 1, wherein θ WSME2 Greater than θ WSME1 .

12. The measuring instrument of claim 1, wherein: Operation of the first track portion includes the first set of first sensing elements providing a detector signal responsive to a localized effect of a varying magnetic flux provided by a first signal modulated scale element of the first scale element portion; and Operation of the second track portion includes the first set of second sensing elements providing detector signals responsive to localized effects on a varying magnetic flux provided by second signal modulated scale elements of the second scale element portion.

13. The measuring instrument of claim 1, wherein: The first sensing element portion further comprises one or more sets of additional first sensing elements, wherein each set of additional first sensing elements has a spatial phase offset relative to the first set of first sensing elements; and The second sensing element portion further includes one or more groups of additional second sensing elements, wherein each group of additional second sensing elements has a spatial phase offset relative to the first group of second sensing elements.

14. The measurement instrument of claim 1, wherein the first signal modulating scale element and the second signal modulating scale element comprise conductive plates, and the first sensing element and the second sensing element comprise conductive loops.

15. A method for operating a measuring instrument, The measuring instrument comprises: a movable portion that rotates in an arcuate motion about a pivot portion, the movable portion including a movable encoder portion; and An electronic position encoder configured to measure an absolute relative position between a detector portion and a scale portion, wherein the movable encoder portion of the movable portion comprises one of the detector portion or the scale portion, the electronic position encoder comprising: The scale portion, the scale portion extends along the scale direction, and the scale portion includes: a first scale element portion, the first scale element portion comprising a first signal modulating scale element; and a second scale element portion, the second scale element portion comprising a second signal modulating scale element; and The detector portion, the detector portion being arranged to be proximate to the scale portion, wherein relative movement between the detector portion and the scale portion is caused by an arcuate movement of the movable encoder portion, the detector portion comprising: a field generating portion configured to generate a varying magnetic flux in response to a drive signal; and A sensing part, the sensing part comprising: a first sensing element portion comprising a first set of first sensing elements and arranged in a first track portion together with the first scale element portion; and a second sensing element portion, the second sensing element portion comprising a first set of second sensing elements and arranged in a second track portion together with the second scale element portion; The method comprises: providing a drive signal to cause the field generating portion to generate a varying magnetic flux; receiving a detector signal from the detector portion, the detector signal comprising: detector signals from said first set of first sensing elements operating in conjunction with a first signal modulation scale element; and detector signals from said first set of second sensing elements operating in conjunction with a second signal modulation scale element; 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 signal; and The determined offset value is used to correct one or more values ​​used to determine the relative position between the detector portion and the scale portion. The method of claim 15 , wherein determining the offset value comprises determining a chained rounding 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 signal input from the detector portion.

18. The method of claim 15, wherein: Operation of the first set of first sensing elements in conjunction with the first signal modulating scale element includes the first set of first sensing elements providing a detector signal responsive to a localized effect on a varying magnetic flux provided by the first signal modulating scale element of the first scale element portion; and Operation of the first set of second sensing elements in conjunction with the second signal modulating scale element includes the first set of second sensing elements providing a detector signal responsive to a localized effect on a varying magnetic flux provided by the second signal modulating scale element of the second scale element portion.

19. An electronic position encoder configured to measure the absolute relative position between a detector portion and a scale portion and for use in a measuring instrument, the measuring instrument comprising a movable portion configured to rotate in an arcuate motion, the electronic position encoder comprising: The scale portion, the scale portion extends along the scale direction, and the scale portion includes: a first scale element portion, the first scale element portion comprising a first signal modulating scale element; and a second scale element portion, the second scale element portion comprising a second signal modulating scale element; The detector portion, the detector portion being arranged to be proximate to the scale portion, wherein relative movement between the detector portion and the scale portion is caused by an arcuate movement of the movable portion, the detector portion comprising: a field generating portion configured to generate a varying magnetic flux in response to a drive signal; and A sensing part, the sensing part comprising: a first sensing element portion comprising a first set of first sensing elements and arranged in a first track portion together 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 together with the second scale element portion; and A signal processing configuration, the signal processing configuration being configured to: providing a drive signal to cause the field generating portion to generate a varying magnetic flux; receiving a detector signal from the detector portion, the detector signal comprising: detector signals from said first set of first sensing elements operating in conjunction with a first signal modulation scale element; and detector signals from said first set of second sensing elements operating in conjunction with a second signal modulation scale element; 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 signal; and The determined offset value is used to correct one or more values ​​used to determine the relative position between the detector portion and the scale portion.

20. The electronic position encoder of claim 19, wherein determining the offset value comprises determining a difference slope.

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