Measurement unit with arcuate motion and separation-type encoder track

Abstract

To provide a movable part configured to rotate in an arcuate motion about a pivoting part, and an electronic position encoder configured to measure the absolute relative position of a detection part and a scale part, one of the detection part and the scale part forming the movable part.SOLUTION: The largest movable range of a movable encoder part is less than 360 degrees. In the scale part, a first scale element part and a second scale element part are arranged so that there are center reference points for the first scale element part and the second scale element part distant from the pivoting part by a first radial distance RD1 and a second radial distance RD2, respectively, and the ratio of RD1 / RD2 is at least 1.4. In various different embodiments, the separation distance between a first scale track and a second scale track including their respective scale element parts is larger than a first scale track width and a second scale track width.SELECTED DRAWING: Figure 4

Description

Technical Field

[0001] This specification relates to a measuring instrument that includes a measuring unit (e.g., a stylus) that rotates in an arc motion around a rotating part in the metric system, and more specifically, a corresponding measurement value is determined by an electronic position encoder. Examples of such measuring instruments include test indicators, lever-type dial indicators, lever-type dial gauges, and the like.

Background Art

[0002] Some measuring instruments have a moving member (e.g., including a stylus) that moves in an arc motion during use (e.g., to determine the measurement value of a processed product to be inspected). As an example, a test indicator (which may also be referred to as a lever indicator, lever-type dial indicator, lever-type dial gauge, etc.) is described in U.S. Patent Publication No. 2022 / 0341733 (‘733 publication), and includes a stylus that rotates at a corresponding rotation angle around a rotating part (e.g., in an arc motion). Due to the rotation of the stylus, a sector gear on the opposite side of the rotating part moves, and accordingly, an encoder that detects the rotation angle rotates. As described above, such a test indicator may be used to inspect a processed product (e.g., with the contact point of the stylus pressed against the surface of the processed product), thereby measuring minute displacements such as circumferential deflection, overall deflection, flatness, and parallelism, or performing precise comparative inspections such as determining the processing error of the processed product.

[0003] In certain embodiments, it may be desirable for such a measuring instrument to include an encoder (e.g., for measuring arc motion) that combines desirable characteristics such as a compact size, high resolution, high precision, low cost, and robustness against contamination. In such a measuring instrument, a configuration of an encoder that provides an improved combination of these characteristics is desirable.

Summary of the Invention

[0004] This summary is provided to introduce, in a simplified manner, some of the concepts described later in the detailed description of the invention. This summary 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 device is provided that includes a movable part and an electronic position encoder. The movable part is configured to rotate in an arc motion about a rotating part and includes a movable encoder part MEP.

[0006] The electronic position encoder is configured to measure the absolute relative position between a detection part and a scale part, for example, along the arc motion direction. The movable encoder part MEP of the movable part includes one of the detection part or the scale part. The scale part extends along a scale direction and has a first scale element part including a first signal modulation scale element and a second scale element part including a second signal modulation scale element. The detection part is configured to be close to the scale part by the relative movement between the detection part and the scale part caused by the arc motion of the movable encoder part MEP. The detection part includes a magnetic field generation part configured to generate a magnetic flux that changes in response to a drive signal, and a sensing part. The sensing part has i) a first set of first sensing elements and a first sensing element part arranged in a first track part together with the first scale element part, and ii) a first set of second sensing elements and a second sensing element part arranged in a second track part together with the second scale element part.

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

[0008] According to another aspect, a method of operating a measuring device including a movable part and an electronic position encoder is provided. This method includes the following two steps. The first step is to supply a drive signal to generate a changing magnetic flux in a magnetic field generating part. The second step is to receive a detection signal from a detection part. The detection signal includes a detection signal from a first set of first sensing elements operating in conjunction with a first signal modulation scale element and a detection signal from a first set of second sensing elements operating in conjunction with a second signal modulation scale element.

[0009] In various implementations, the measuring device is also configured to: i) provide a drive signal for generating a changing magnetic flux in the magnetic field generating part of the detection part; ii) receive, from the detection part, a detection signal including a detection signal from a first set of first sensing elements operating in conjunction with a first signal modulation scale element and a detection signal from a first set of second sensing elements operating in conjunction with a second signal modulation scale element; iii) determine an offset value corresponding to a radial offset of at least one of the scale part or the detection part, at least partially based on the received detection signal; and iv) utilize the determined offset value to correct one or more values used to determine the relative position between the detection part and the scale part, and includes a signal processing configuration.

[0010] According to another aspect, a method of operating a measuring instrument including a movable part and an electronic position encoder is provided. This method generally includes four steps. The first step includes supplying a drive signal for generating a changing magnetic flux to a magnetic field generating part. The second step includes receiving a detection signal from a detector, the detection signal including a detector signal from a first set of first sensing elements operating in conjunction with a first signal modulation scale element and a detection signal from a first set of second sensing elements operating in conjunction with a second signal modulation scale element. The third step includes determining an offset value corresponding to a radial offset of at least one of a scale part or a detection part based at least in part on the received detection signal. The fourth step includes correcting one or more values used to determine a relative position between the detection part and the scale part using the determined offset value.

[0011] According to a further aspect, an electronic position encoder is provided, which is configured to measure an absolute relative position between a detection part and a scale part, for example, along an arc motion. The electronic position encoder is configured to be used in a measuring instrument including a movable part configured to rotate in an arc motion about a rotating part.

Brief Description of the Drawings

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Embodiments for Carrying Out the Invention

[0013] FIG. 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 implementations, the electronic absolute position encoder 101 includes a scale unit 170 and a detection unit 167, and together they form a transducer TDR. As will be described in more detail below, the encoder 101 utilized herein is an absolute position (ABS) encoder that provides an absolute position using two or more encoder tracks (i.e., all positions within the absolute range of the encoder 101 have a unique combination of signals). Generally, ABS encoding may be more robust than incremental (INC) encoding (e.g., counting increments during motion), and thus may be more desirable for certain implementations (e.g., being able to withstand a power cycle without losing position). The measuring instrument 100 includes appropriate user interface functions such as a display 138 and / or user-operable control elements 136 (e.g., switches, buttons, etc.). Additionally, the measuring instrument 100 may further include a power supply 165.

[0014] All of these elements of the measuring instrument 100 and / or the encoder 101 are connected to a signal processing configuration 166 (e.g., including one or more signal processors), and in various implementations, may be implemented in an integrated circuit (IC) chip as electronic circuitry for signal processing and display. The signal processing configuration 166 receives a detection signal from the detection unit 167, processes the detection signal, and determines the absolute position of the detection unit 167 along the scale unit 170. It will be understood that the signal processing configuration 166 may comprise any combination of signal processing and physical circuitry. In various implementations, the signal processing configuration 166 and the detection unit 167 may be included as part of an electronic assembly 160 (e.g., disposed on a substrate).

[0015] Figure 2 shows further details of one implementation form of the measuring instrument 100, such as the measuring instrument in Figure 1. As will be described in more detail below, the measuring instrument 100 includes an electronic position encoder 101 including a transducer TDR. In the example of Figure 2, the measuring instrument 100 is a test indicator (which may also be referred to as, for example, a lever indicator, a lever-type dial indicator, a lever-type dial gauge, etc.). In various implementation forms, specific aspects of the mechanical structure and operation of the measuring instrument 100 may be similar to those of conventional test indicators, such as those described in the aforementioned '733 publication.

[0016] As shown in Figure 2, the contact part CPN (for example, a stylus) is coupled to the rotating part PPN (for example, rotating about the rotation point PPT of the rotating part PPN) and rotates about the rotating part PPN at a corresponding angle (for example, in an arc motion). The contact part CPN has a contact point CPT at its end that can be used to contact the inspection object in order to perform a measurement operation (for example, to measure the displacement and / or dimensions of the inspection object, etc.). The measured value may be displayed on a digital display (for example, the display 138 in Figure 1) that can be attached to the measuring instrument body MIB or other locations of the measuring instrument 100. The measuring instrument 100 may be provided with several control elements (for example, the control element 136 in Figure 1).

[0017] The movable part MPN of the measuring instrument 100 includes the contact part CPN on the first side of the rotating part PPN and a movable encoder part support member MEPSM that supports the movable encoder part MEP on the second side of the rotating part PPN. The movable part MPN is configured to rotate the support member MEPSM and the movable encoder part MEP in an arc motion ARCM (for example, the arc motion direction ARCD) corresponding to an inspection object measurement operation (for example, for measuring the inspection object) that rotates the contact part CPN relative to the rotating part PPN (for example, caused by the contact point CPT contacting or moving along the surface of the inspection object). In the measuring instrument 100, the maximum angular movement range θ of the arc motion ARCM of the movable encoder part MEP MAXis less than 360 degrees (e.g., in some implementations, less than 90 degrees, or less than 45 degrees, or less than 15 degrees, etc.). Such a relatively small angular movement range is common in some types of measuring instruments, especially in applications where the inspection object is measured using only a relatively small deflection of the contact part CPM (e.g., a stylus).

[0018] In various implementations, the movable encoder unit MEP may include one of the detection unit 167 or the scale unit 170 (e.g., as described above in relation to FIG. 1 and as will be described in more detail below in relation to FIG. 3A). One of the detection unit 167 or the scale unit 170 that is not included in the movable encoder unit MEP is included in a fixed encoder unit FEP (not shown, but may be fixed to, for example, the measuring instrument body MIB) located in the vicinity of the movable encoder unit MEP. As a specific example, the movable encoder unit MEP may be arranged to face the fixed encoder unit FEP in parallel, and the front surface of the movable encoder unit MEP facing the fixed encoder unit FEP may be separated from the fixed encoder unit FEP via a gap (e.g., 0.1 mm to 0.2 mm) along the z-axis direction. Regardless of whether the detection unit 167 is included in the movable encoder unit MEP or the fixed encoder unit FEP, the front surface of the detection unit 167 (e.g., including its constituent conductors) may be covered by an insulating coating.

[0019] In the orientation of FIG. 2, the fixed encoder unit FEP may be located directly below the movable encoder unit MEP (and thus not visible in FIG. 2). The fixed encoder unit FEP and the movable encoder unit MEP (note that it includes, for example, the detection unit 167 and the scale unit 170) correspondingly form a transducer TDR. As described above, the relative movement between the movable encoder unit MEP and the fixed encoder unit FEP (i.e., corresponding to the relative movement between the detection unit 167 and the scale unit 170) is due to the movement of the movable encoder unit MEP in the arc movement direction ARCD caused by the movement of the contact part CPN (e.g., as part of the inspection object measurement operation).

[0020] As shown in FIG. 2, the first and second movement limit indicators ML1 and ML2 are shown by dashed lines, which indicate the maximum movement range of the arc movement ARCM (e.g., including the movable encoder part MEP), and the maximum angular movement range θ MAX corresponds to. The electronic position encoder 101 is an absolute position encoder that utilizes two or more encoder tracks (e.g., see FIG. 3A) to provide absolute positioning (i.e., every position has a unique combination of signals) corresponding to the absolute angle measurement range θ ABS as will be described in more detail below. In the example of FIG. 2, the absolute angle measurement range θ ABS is shown as being approximately equal to the maximum angular movement range θ MAX , but it will be understood that in another implementation, the absolute angle measurement range θ ABS and the maximum angular movement range θ MAX may be different (e.g., in most such implementations, the absolute angle measurement range θ ABS is greater than the maximum angular movement range θ MAX , and in all cases, the absolute angle measurement range θ ABS is less than 360 degrees). In some implementations, the absolute angle measurement range θ ABS and the maximum angular movement range θ MAX are shown in the example of FIG. 2 for illustrative purposes and may not be to scale.

[0021] The end point ENDPT of the end of the movable encoder part support member MEPSM also corresponds to the end point of the movable part MPN. The end point ENDPT is at the end of the movable part MPN opposite to the contact point CPT at the end of the contact part CPN. As referred to herein, the contact part CPN and the contact point CPT are on the first side surface of the rotating part PPN, and the support member MEPSM, the movable encoder part MEP, and the end point ENDPT are above the second side surface of the rotating part PPN.

[0022] The measuring instruments shown in FIGS. 1 and 2 are one of various applications that implement an electronic position encoder that has evolved over the years to provide a relatively optimized combination of elements such as a compact size, low-power operation (e.g., for long battery life), high resolution and high-precision measurement, low cost, and robustness against contamination. It will be understood that in any application, even a slight improvement in any of these elements is highly desirable, but particularly difficult to achieve considering the design constraints imposed to achieve commercial success in various applications. The principles disclosed herein improve some of these elements for various applications.

[0023] 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 shown as background information related to various principles disclosed elsewhere herein. FIG. 22 further includes reference number annotations for showing common reference numbers or symbols used to designate common elements in other figures included herein. The following simplified description is based on '389, and some of the common reference numbers or symbols in other figures herein are shown in parentheses near the original reference numbers of the '389 patent. For a detailed description of FIG. 22 with respect to the prior art, refer to the '389 patent. Accordingly, only a simplified description (e.g., including specific disclosure content of the '389 patent relevant herein) is described herein.

[0024] As disclosed in the ‘389 patent, a transducer as shown in FIG. 22 includes at least two substantially coplanar paths of wires or windings. The transmit winding 102 (PRTFGE’’’) forms a large planar loop. In this example, the transmit winding 102 forms the entirety of the magnetic field generating section PRTFGE’’’. The receive winding 104 (PRTSEN’’, SETSEN’’’) is disposed substantially in the same plane as the transmit winding 102 and is laid in one direction as indicated by the arrows in a zigzag or sine wave pattern and then in the opposite direction as indicated by the arrows, such that the windings cross to form alternatingly arranged loops 106 (SEN+’’’) and 108 (SEN-’’’), as shown. As a result, each of the alternating loops 106 (SEN+’’’) and 108 (SEN-’’’) of the receive winding 104 (PRTSEN’’, SETSEN’’’) has a different winding direction compared to the adjacent loops. By applying an alternating (changing) current to the transmit winding 102 (PRTFGE’’’), the transmit winding generates a time-varying magnetic field (changing magnetic flux) that extends through the loops 106 (SEN+’’’) and 108 (SEN-’’’) of the receive winding 104 (PRTSEN’’, SETSEN’’’). In various implementations, the loops 106 (SEN+’’’) and 108 (SEN-’’’) may be designated as a set (SETSEN’’’) of sensing elements of a sensing section (PRTSEN’’’).

[0025] A scale unit (170’’’) or a scale pattern 112 (180’’’) including a conductive object (for example, a signal modulation element such as a conductive plate 114 (SME’’’), some of which are outlined by short dashed lines in FIG. 22), when the conductive object moves (comes close) near a detection unit (167’’’), a variable magnetic field generated by a transmission coil 102 (PRTFGE’’’) induces eddy currents in the conductive object, thereby generating a magnetic field from the object that opposes the changing transmission magnetic field (changing magnetic flux). As a result, the magnetic flux received by the reception coil 104 (PRTSEN’’’) changes or is interrupted, causing the reception coil to output a non-zero EMF signal (voltage) at the output terminals V+ and V- of the reception coil 104, and the polarity changes as the conductive object moves between the “+” loop 106 (SEN+’’’) and the “-” loop 108 (SEN-’’’).

[0026] The distance between the positions of two loops of the same polarity (e.g., the distance from the position of loop 106 (SEN+’’’) to the position of the next loop 106 (SEN+’’’)) is defined as the linear spatial step 110 (WSEN’’’) of the set of sensing elements (SETSEN’’’) (which may also be referred to as pitch or wavelength), and in a specific implementation form, it may be equal to the linear spatial step 110 (WSME’’’) of the scale pattern 180’’’ of the scale portion (170’’’) arranged along the scale direction SCD’’’ and / or the measurement axis direction MA’’’. Therefore, it can be seen that each loop 106 (SEN+’’’) and / or 108 (SEN-’’’) has a length or maximum dimension 0.5*(WSEN’’’) along the measurement axis direction (MA’’’), which may also be referred to as the scale direction SCD’’’. When the above-mentioned conductive object (e.g., conductive plate 114 (SME’’’)) is near the receiving coil 104 (PRTSEN’’’) and its position changes continuously along the measurement axis 300 (MA’’’), the AC amplitude of the signal output from the receiving coil (PRTSEN’’’) changes continuously and periodically along with the linear spatial step 110 (WSME’’’) due to the periodic change of loops 106 (SEN+’’’) and 108 (SEN-’’’) and the local disruption of the transmitted magnetic field by the conductive object (e.g., conductive plate 114 (SME’’’)). Therefore, the signal output from the receiving coil (PRTSEN’’’) may be used (e.g., processed) to indicate the relative position between the detection unit (167’’’) and the scale unit (170’’’). As shown in FIG. 22, it will be understood that the above-described transmitting coil 102 (PRTFGE’’’) and receiving coil 104 (PRTSEN’’’) are an example of a prior art implementation form of the element designated as the detection unit (167’’’).

[0027] FIG. 3A shows a partial implementation of a transducer TDR configured to be utilized with an arc motion ARCM between a detection unit 167 and a scale unit 170, such as that utilized in the electronic position encoder 101 of the measuring instrument 100 of FIGS. 1 and 2. The transducer TDR utilizes two track portions TR1 and TR2, as shown in FIG. 3A. FIG. 3B is a list of explanations of the symbols used in FIG. 3A.

[0028] Some aspects of the magnetic field generating element and the sensing element of a detection unit (e.g., detection unit 167, etc.) as described herein may operate and be understood to operate at least in part based on the principles as described above in connection with FIG. 22. In the implementation of FIG. 3A, the scale unit 170, the detection unit 167, and the signal processing configuration 166 (e.g., of FIGS. 1 and 2) cooperate to provide an electronic position encoder 101 that can be used to measure the relative position between two elements (e.g., between the detection unit 167 and the scale unit 170 and / or an element attached thereto), such as along the arc motion direction. In various implementations, the detection unit 167 is formed on a detection substrate and includes a periodic scale pattern 180, and the scale unit 170 is formed on a scale substrate. The measurement operation includes relative movement between two substrates (which may be relatively planar and parallel to each other, for example). In various implementations, the detection unit 167 and the scale unit 170 may generally be in respective planes extending along the x-axis direction and the y-axis direction, and the z-axis direction may be orthogonal to these planes.

[0029] In various implementation forms, the scale unit 170 extends along the scale direction SCD and includes a first scale element unit PRTSC1 including a first signal modulation element SME1 and a second scale element unit PRTSC2 including a second signal modulation element SME2. The first signal modulation element SME1 is arranged along the scale direction SCD to form a first signal modulation element pattern PATSME1. The second signal modulation element SME2 is arranged along the scale direction SCD to form a second signal modulation element pattern PATSME2. The first signal modulation element pattern PATSME1 and the second signal modulation element pattern PATSME2 are each part of the periodic scale pattern 180 of the scale unit 170. In various implementation forms, the periodic scale pattern 180 may sometimes be referred to as a signal modulation pattern 180. In various implementation forms, the first and / or second signal modulation elements SME1 and SME2 (i.e., those included in the first and second scale element units PRTSC1 and PRTSC2) may be fabricated on the scale substrate (e.g., using a known printed circuit manufacturing method).

[0030] The relative movement between the detection unit 167 and the scale unit 170 (e.g., in the arc movement direction) may indicate a relative position and / or a measured value (e.g., with respect to the relative position between the detection unit 167 and the scale unit 170). As described above in connection with FIGS. 1 and 2, the measured relative position or dimension may be displayed on the display 138 (e.g., a digital display). In various implementation forms, control elements 136 such as on / off switches and other arbitrary control buttons may be included.

[0031] As shown in FIG. 3A, the detection unit 167 may include a magnetic field generation unit PRTFGE and a sensing unit PRTSEN arranged along the scale direction SCD. In various implementation forms, with respect to the sensing unit PRTSEN, the scale direction SCD may be referred to as the sensing unit direction SPD, or alternatively called. The magnetic field generation unit PRTFGE includes a first magnetic field generation element unit PRTFGE1 and a second magnetic field generation element unit PRTFGE2. The sensing unit PRTSEN includes a first sensing element unit PRTSEN1 and a second sensing element unit PRTSEN2. As will be described in more detail below, the first sensing element unit PRTSEN1 is configured to operate in conjunction with the first magnetic field generation element unit PRTFGE1 and the first scale element unit PRTSC1 as a part of the first track unit TR1, and the second sensing element unit PRTSEN2 is configured to operate in conjunction with the second magnetic field generation element unit PRTFGE2 and the second scale element unit PRTSC2 as a part of the second track unit TR2.

[0032] The magnetic field generation unit PRTFGE may include a number of extensions ELP and ends EDP. The extensions generally extend along the scale direction SCD and can thus be parallel to the scale direction SCD, while the ends may generally be transverse (e.g., perpendicular) to the scale direction SCD. The extensions ELP and ends EDP can be combined to form a region (e.g., a changing magnetic flux can be generated by a current passing through the extensions and ends resulting from a drive signal), and that region may include a specific sensing element.

[0033] The magnetic field generating unit PRTFGE includes a first magnetic field generating element unit PRTFGE1 and a second magnetic field generating element unit PRTFGE2. The first magnetic field generating element unit PRTFGE1 is configured to operate in conjunction with the first signal modulation element SME1 of the first sensing element unit PRTSEN1 and the first scale element unit PRTSC1. The first magnetic field generating element unit PRTFGE1 includes extension parts ELP1A, ELP1B, ELP1C, ELP1D and end parts EDP1A, EDP1B, EDP1C, EDP1D (for example, in some implementation forms, it is assumed to form two magnetic field generating element loops such as a figure-eight configuration, and / or otherwise, it can be regarded as a single electric field generating element loop that forms two loops in a configuration that forms two internal regions). More specifically, the extension parts ELP1A and ELP1B and the end parts EDP1A and EDP1D can be regarded as forming a first magnetic field generating element first half loop FGE1FHL having an internal region FGE1FHIA. The first magnetic field generating element first half internal region FGE1FHIA is configured to be aligned with the first half pattern part FHPP1 of the first scale element unit PRTSC1. The extension parts ELP1C and ELP1D and the end parts EDP1C and EDP1B can be regarded as forming a first magnetic field generating element second half loop FGE1SHL having an internal region FGE1SHIA. The first magnetic field generating element second half internal region FGE1SHIA is configured to be aligned with the second half pattern part SHPP1 of the first scale element unit PRTSC1.

[0034] In various implementation forms, the end EDP (for example, or other parts of the first magnetic field generating element part PRTFGE1) may include ports or other connection configurations. For example, the end EDP1B may be divided into two parts such as two contact points being provided. The contact points may be used to receive drive signals and may be provided at positions where signal lines / circuit traces from the processing unit 166 are connected, etc. In various implementation forms, such ports may represent common connection configurations such as being connected to magnetic field generation drive electronics. Such magnetic field generation drive electronics may include electronic components such as capacitors and transistors in various implementation forms to provide drive signals for the first magnetic field generating element part PRTFGE1 to generate a varying magnetic flux, and may be at least partially or completely included in or connected to the processing unit 166.

[0035] During operation, an alternating current may be provided, but for the sake of simplicity of the following description, only a unidirectional current will be described (for example, as an example of a unidirectional direction and / or because diodes and other components / configurations may be provided to limit the flow of current in one direction). As an example, the current (such as provided by a drive signal) may flow through the following series of portions (for example, as the order in the case of a unidirectional current), including end portion EDP1D, extension portion ELP1A, end portion EDP1A, extension portion ELP1B, and end portion EDP1B, extension portion ELP1C, end portion EDP1C, and extension portion ELP1D. According to this example of the current flow, it will be understood that the current flow is in the same direction (for example, from left to right in FIG. 3A) through the extension portions (i.e., extension portions ELP1A and ELP1C) at the outer boundary of the configuration, and in the same direction (i.e., from right to left in FIG. 3A) through the extension portions (i.e., extension portions ELP1B and ELP1D) at the center of the configuration. This also corresponds to the current flowing around the first magnetic field generating element first half loop FGE1FHL in the counterclockwise direction and the current flowing around the first magnetic field generating element first half loop FGE1SHL in the clockwise direction (i.e., note that the direction of the current flowing through each loop is opposite, and correspondingly, the polarities of the magnetic fluxes generated from each loop are also opposite).

[0036] Such directions / orientations / polarities of the current flow and the corresponding magnetic flux may be advantageous for a particular configuration, such as resulting in a signal generated in the first sensing element SEN1 (e.g., such that it is at least partially aligned with the internal regions FGE1FHIA and FGE1SHIA of the first magnetic field generating element portion PRTFGE1). As one aspect, in relation to the reverse directions of the currents generated by the respective loops FGE1FHL and FGE1SHL and the reverse polarities of the corresponding magnetic fluxes, the spatially offset first and second half-pattern portions FHPP1 and SHPP1 provide a detection signal (i.e., from the first sensing element portion PRTSEN1) indicating the position of the first sensing element portion PRTSEN1 relative to the first scale element portion PRTSC1.

[0037] The second magnetic field generating element section PRTFGE2 is configured to operate in conjunction with the second signal modulation element SME2 of the second sensing element section PRTSEN2 and the second scale element section PRTSC2. The second magnetic field generating element section PRTFGE2 includes extension portions ELP2A, ELP2B, ELP2C, ELP2D and end portions EDP2A, EDP2B, EDP2C, EDP2D (for example, in some implementations, it is configured to form two magnetic field generating element loops such as a figure-eight configuration, and / or otherwise, it can be regarded as a single electric field generating element loop that forms two loops to form two internal regions). More specifically, the extension portions ELP2A and ELP2B and the end portions EDP2A and EDP2D can be regarded as forming a first half-loop FGE2FHL of the second magnetic field generating element having an internal region FGE2FHIA. The first half internal region FGE2FHIA of the second magnetic field generating element is configured to be aligned with the first half pattern portion FHPP2 of the second scale element section PRTSC2. The extension portions ELP2C and ELP2D and the end portions EDP2C and EDP2B can be regarded as forming a second half-loop FGE2SHL of the second magnetic field generating element having an internal region FGE2SHIA. The second half internal region FGE2SHIA of the second magnetic field generating element is configured to be aligned with the second half pattern portion SHPP2 of the second scale element section PRTSC2.

[0038] In various implementation forms, the end EDP (for example, or other parts of the second magnetic field generating element part PRTFGE2) may include ports or other connection configurations. For example, the end EDP2B may be divided into two parts, such as where two contact points are provided. The contact points may be used to receive drive signals and may be provided at locations where signal lines / circuit traces from the processing unit 266 can be connected. In various implementation forms, such ports may represent a general connection configuration, such as being coupled to magnetic field generation drive electronics. Such magnetic field generation drive electronics may include electronic components such as capacitors and transistors in various implementation forms to provide drive signals for the second magnetic field generating element part PRTFGE2 to generate a varying magnetic flux, and may be at least partially or completely included in or connected to the processing unit 266.

[0039] During operation, an alternating current may be provided, but for the sake of simplicity in the following explanation, only a unidirectional current will be described (for example, as an example of a unidirectional current and / or because diodes or other components / configurations may be provided to limit the flow of current in one direction). As an example, the current (such as provided by a drive signal) may flow through the following series of parts (for example, as the order in the case of a unidirectional current), including end EDP2D, extension ELP2A, end EDP2A, extension ELP2B, and end EDP2B, extension ELP2C, end EDP2C, and extension ELP2D. According to this example of the current flow, it will be understood that the current flow is in the same direction (for example, from left to right in FIG. 3A) through the extensions (i.e., extensions ELP2A and ELP2C) at the outer boundary of the configuration, and in the same direction (i.e., from right to left in FIG. 3A) through the extensions (i.e., extensions ELP2B and ELP2D) at the center of the configuration. This also corresponds to the current flowing around the second magnetic field generating element's first half-loop FGE2FHL in the counterclockwise direction and the current flowing around the second magnetic field generating element's second half-loop FGE2SHL in the clockwise direction (i.e., note that the direction of the current flowing through each loop is opposite, and correspondingly, the polarity of the magnetic flux generated from each loop is also opposite).

[0040] Such directions / orientations / polarities of the current flow and the corresponding magnetic flux may be advantageous for certain configurations, such as resulting in a signal generated in the second sensing element SEN2 (e.g., such that it is at least partially aligned with the internal regions FGE2FHIA and FGE2SHIA of the second magnetic field generating element portion PRTFGE2). As one aspect, in relation to the opposite directions of the currents generated by the respective loops FGE2FHL and FGE2SHL and the opposite polarities of the corresponding magnetic fluxes, the spatially offset first and second half-pattern portions FHPP2 and SHPP2 provide a detection signal (i.e., from the second sensing element portion PRTSEN2) indicating the position of the second sensing element portion PRTSEN2 relative to the second scale element portion PRTSC2.

[0041] As such, the sensing unit PRTSEN includes first and second sensing element units PRTSEN1 and PRTSEN2 (e.g., each including respective sensing elements SEN1 and SEN2). In the illustrated implementation form, the sensing elements SEN1 and SEN2 are connected in series and include a sensing loop element (or a sensing coil element or a sensing winding element, which is generally in a lateral direction (e.g., nominally perpendicular) with respect to the scale direction SCD). The first sensing element unit PRTSEN1 includes a first set SET1SEN1 of the first sensing elements and a second set SET2SEN1 of the first sensing elements. The second sensing element unit PRTSEN2 includes a first set SET1SEN2 of the second sensing elements and a second set SET2SEN2 of the second sensing elements. In the illustrated implementation form, adjacent loop elements (e.g., conductive loops) in each set of the sensing elements are connected by the configuration of conductors on various layers of the PCB according to known methods (e.g., in some implementation forms, connected by a feedthrough that may include conductors passing through microvias, also sometimes referred to as blind vias or buried vias). For example, adjacent sensing elements SEN1 in each set of the first sensing element unit PRTSEN1 and adjacent sensing elements SEN2 in each set of the second sensing element unit PRTSEN2 may have opposite winding polarities (e.g., as described above with respect to FIG. 22, the sensing elements in each set alternate between SEN+ and SEN-). That is, when the first loop corresponding to a sensing element responds with a positive-polarity sensing signal contribution to a changing magnetic field, the adjacent loop corresponding to the adjacent sensing element responds with a negative-polarity sensing signal contribution. In various contexts of this specification, a loop having a positive-polarity sensing signal contribution may be referred to as an SEN+ sensing element, and a loop having a negative-polarity sensing signal contribution may be referred to as an SEN- sensing element. In various implementation forms, the sensing elements in each set are connected in series such that their sensing signals or signal contributions are summed for each set, and the "summed" sensing signal is output to the signal processing configuration 166 (e.g., as in FIG. 1) at the sensing signal output connection parts (e.g., the connection parts for signals SIG1A and SIG1B, and SIG2A and SIG2B respectively).

[0042] In the illustrated implementation form, the first set SET1SEN1 of the first sensing elements includes 16 first sensing elements SEN1 (i.e., including the first sensing elements SEN1-A1 to SEN1-A12), and the second set SET2SEN1 of the first sensing elements includes 16 first sensing elements SEN1 (i.e., including the first sensing elements SEN1-B1 to SEN1-B12). For the sake of simplicity of illustration, only the first two sensing elements (i.e., A1 to A2 and B1 to B2) and the last two sensing elements (i.e., A15 to A16 and B15 to B16) of each set are labeled, but it will be understood that the sensing elements (i.e., A3 to A14 and B3 to B14) also correspond to the remaining sensing elements as shown. In the illustrated implementation form, the first set SET1SEN2 of the second sensing elements includes 8 second sensing elements SEN2 (i.e., including the second sensing elements SEN2-A1 to SEN2-A8), and the second set SET2SEN2 of the second sensing elements includes 8 second sensing elements SEN2 (i.e., including the second sensing elements SEN2-B1 to SEN2-B6). For the sake of simplicity of illustration, only the first two sensing elements (i.e., A1 to A2 and B1 to B2) and the last two sensing elements (i.e., A7 to A8 and B7 to B8) of each set are labeled, but it will be understood that the sensing elements (i.e., A3 to A6 and B3 to B6) also correspond to the remaining sensing elements as shown.

[0043] As will be understood by those skilled in the art, in various implementation forms, it will be understood that it is advantageous to configure a detector to provide two or more sets of sensing elements at different spatial phase positions (for example, in each of the first sensing element unit PRTSEN1 and the second sensing element unit PRTSEN2). Thus, for example, the first set SET1SEN1 of the first sensing element and the second set SET2SEN1 of the first sensing element are at different spatial phase positions. Similarly, the first set SET1SEN2 of the second sensing element and the second set SET2SEN2 of the second sensing element are at different spatial phase positions. However, it should be understood that the configuration of the sensing elements as described herein is not intended to be limiting and is merely illustrative. As an example, in some implementation forms, individual sensing element loops may output individual signals to corresponding signal processing configurations, as disclosed, for example, in U.S. Patent No. 9,958,294, which is incorporated herein by reference in its entirety. More generally, various known sensing element configurations can be used in combination with the principles described herein for use in combination with various scale patterns, signal processing schemes, and the like.

[0044] In the illustrated implementation form of the scale unit 170 and the scale pattern 180, the first signal modulation element pattern PATSME1 of the first scale element unit PRTSC1 in the first track unit TR1 includes a first half pattern unit FHPP1 and a second half pattern unit SHPP2, and each half pattern unit includes a column of the first signal modulation element SME1. Similarly, the second signal modulation element pattern PATSME2 of the second scale element unit PRTSC2 in the second track unit TR2 includes a first half pattern unit FHPP2 and a second half pattern unit SHPP2, and each half pattern unit includes a column of the second signal modulation element SME2.

[0045] In various implementation forms, the signal modulation element SME1 and / or SME2 may include a conductive plate (for example, one formed by a region fabricated on a printed circuit board, one formed by a raised region extending from a conductive substrate, one fabricated on a glass substrate, or one fabricated according to other fabrication methods, etc.). The scale pattern 180 is generally mounted on the scale portion 170. During operation, it will be understood that there is relative movement between the scale pattern 180 and the detection unit 167 (for example, along the arc movement direction). The scale pattern 180 has spatial characteristics that vary as a function of position so as to provide detection signals that are position-dependent and occur in the sensing elements SEN1 and SEN2 of the sensing portion PRTSEN within the detection unit 167. As will be understood by those skilled in the art, in various implementation forms, the magnetic field generation portion PRTFGE and the sensing portion PRTSEN of the detection unit 167 may be formed according to various alternative configurations that are used in combination with various corresponding signal processing methods.

[0046] In one particular exemplary embodiment, the detection unit 167 is disposed opposite and parallel to the scale portion 170, and the front surface of the detection unit 167 facing the scale portion 170 may be separated from the scale portion 170 (and / or the scale pattern 180) by a gap distance (for example, 0.1 mm to 0.2 mm) along the z-axis direction. The front surface of the detection unit 167 (for example, including its constituent conductors) may be covered by an insulating coating.

[0047] Based on the described embodiments and the incorporated references, it will be apparent to those skilled in the art that various elements may be present on different manufacturing layers located in different planes along the z-axis direction as necessary to provide various operating gaps and / or insulating layers. Throughout the drawings of the present disclosure, the illustrated x-axis, y-axis, and / or z-axis dimensions of one or more elements may be exaggerated for clarity, but it will be understood that they are not intended to be inconsistent with the various design principles and relationships described herein.

[0048] The transducer TDR includes a first transducer unit PRTTDR1 and a second transducer unit PRTTDR2. The first transducer unit PRTTDR1 includes a first sensing element unit PRTSEN1, a first magnetic field generating element unit PRTFGE1, and a first scale element unit PRTSC1. The second transducer unit PRTTDR2 includes a second sensing element unit PRTSEN2, a second magnetic field generating element unit PRTFGE2, and a second scale element unit PRTSC2. The first and second track units TR1 and TR2 each include a first oscillator unit PRTTDR1 and a second oscillator unit PRTTDR2. As described herein, the operation of the first transducer unit PRTTDR1 of the first track unit TR1 generates detection signals SIG1A and SIG1B, and the operation of the second transducer unit PRTTDR2 of the second track unit TR2 generates detection signals SIG2A and SIG2B. By processing the signals (e.g., by the signal processing configuration 166), it becomes possible to determine the absolute relative position between the detection unit 167 and the scale unit 170.

[0049] The first transducer unit PRTTDR1 of the first track unit TR1 and the second transducer unit PRTTDR2 of the second track unit TR2 can each operate according to first and second driving operations, and these operations can be executed simultaneously or at different timings in various implementation forms. As part of the first driving operation, the first magnetic field generating element unit PRTFGE1 generates a magnetic flux that changes in response to a coil driving signal (e.g., provided from the signal processing configuration 166). The first sensing element SEN1 of the first sensing element unit PRTSEN1 provides detection signals (e.g., SIG1A and SIG1B) that respond to the local effects on the changing magnetic flux provided by the first signal modulation element SME1 of the first scale element unit PRTSC1 (e.g., including the first signal modulation element SME1 that is relatively adjacent to the sensing element SEN1 along the z-axis direction or aligned in other ways). As part of the second driving operation, the second magnetic field generating element unit PRTFGE2 generates a magnetic flux that changes in response to a coil driving signal (e.g., provided from the signal processing configuration 166). The second sensing element SEN2 of the second sensing element unit PRTSEN2 provides detection signals (e.g., SIG2A and SIG2B) that respond to the local effects on the changing magnetic flux provided by the second signal modulation element SME2 of the second scale element unit PRTSC2 (e.g., including the second signal modulation element SME2 that is relatively adjacent to the sensing element SEN2 along the z-axis direction or aligned in other ways).

[0050] The signal processing configuration (e.g., the signal processing configuration 166 in FIG. 1) may be configured to determine the position of the sensing unit PRTSEN (e.g., including the first sensing element unit PRTSEN1 and the second sensing element unit PRTSEN2) of the detection unit 167 with respect to the scale unit 170 based on the detection signal input from the detection unit 167. For example, the first sensing element unit PRTSEN1 may provide detection signals SIG1A, SIG1B, and the second sensing element unit PRTSEN2 may provide detection signals SIG2A, SIG2B. In various implementation forms, the detection signal may be referred to as a sensing signal, additionally or alternatively. The signal from the detection unit 167 is input to the signal processing configuration 166 and may be used to determine the measured value / position of the detection unit 167 with respect to the scale unit 170. Generally, the sensing element unit and the magnetic field generating element unit are at least partially as described above in relation to FIG. 22 (e.g., of an inductive encoder), and at least partially those described 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.

[0051] FIG. 4 shows some dimensions and aspects of the measuring instrument 100 including the transducer TDR. In FIG. 4, certain elements (e.g., the center line CL1 of the first scale element unit PRTSC1, the center line CL2 of the second scale element unit PRTSC2, the movable encoder unit support member MEPSM, etc.) are each represented as a line (e.g., its position may correspond to the center line of the corresponding component or the position of other representations). A representation of the rotating part PPN including the rotation point PPT as part of the movable part MPN is shown (e.g., the contact part CPN is not shown in FIG. 4, but it will be understood that, as shown in FIG. 2, it is located under the rotating part PPN).

[0052] The movable encoder unit support member MEPSM is shown as rotating in the arc motion direction around the rotating part PPN. The support member MEPSM has a maximum angular movement range θ MAXAs part of moving thereacross, it may move between the first and second movement limit indicators ML1 and ML2. In some implementations, the maximum angular movement range θ MAX may correspond to the absolute angular measurement range θ ABS In various alternative implementations, the absolute angular measurement range θ ABS and the maximum angular movement range θ MAX may be different. As described above in connection with FIG. 2, the end point ENDPT corresponds to the end of the movable encoder unit support member MEPSM and the end of the movable part MPN, and correspondingly moves in an arc along the arc movement direction.

[0053] In some implementations, the first and second scale element parts PRTSC1 and PRTSC2 of the scale part 170 may be attached to the movable encoder unit support member MEPSM (for example, in an implementation where the movable encoder unit MEP includes the scale part 170), in which case, the first and second scale element parts PRTSC1 and PRTSC2 move relative to the detection part 167 according to the arc movement ARCM along the arc movement direction ARCD. Alternatively, when the movable encoder unit MEP includes the detection part 167, the detection part 167 may be attached to the movable encoder unit support member MEPSM, and correspondingly, moves relative to the first and second scale element parts PRTSC1 and PRTSC2 of the scale part 170 according to the arc movement ARCM in the arc movement direction ARCD.

[0054] As shown in FIGS. 3A and 4, the first scale element part PRTSC1 and / or the first sensing element part PRTSEN1 have a first central reference point REF1 located at a first radial distance RD1 from the rotating part PPN (e.g., from the rotation point PPT of the rotating part PPN), which is arranged at the central x and / or y-axis position such as the center line CL1 of the first scale element part PRTSC1 and / or the first sensing element part PRTSEN1. The second scale element part PRTSC2 and / or the second sensing element part PRTSEN2 have a second central reference point REF2 located at a second radial distance RD2 from the rotating part PPN (e.g., from the rotation point PPT of the rotating part PPN), which is arranged at the central x and / or y-axis position such as the center line CL2 of the second scale element part PRTSC2 and / or the second sensing element part PRTSEN2.

[0055] As shown in FIGS. 3A and 4, the first and second scale element parts PRTSC1 and PRTSC2 of the first and second track parts TR1 and TR2 are arc-shaped and parallel to each other (e.g., form concentric arcs). The second track part TR2 is closer to the rotating part PPN than the first track part TR1 (e.g., the radial distance RD2 of the second central reference point REF2 of the second track part TR2 is smaller than the radial distance RD1 of the first central reference point REF1 of the first track part TR1). As shown in FIG. 3A, the first signal modulation scale element SME1 is arranged along the first scale element part PRTSC1 according to the first signal modulation element angular space step θ WSME1 and the second signal modulation scale element SME2 is arranged along the second scale element part PRTSC2 according to a second signal modulation element angular space step θ WSME1 different from the first signal modulation element angular space step θ WSME2 As will be described in more detail below, in some implementations, at least one of 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.

[0056] As shown in FIG. 4, the first scale element part PRTSC1 has a first angular range θ RG1and has 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 shown as being nominally equal, and in the examples of FIGS. 3A and 4, the absolute angular measurement range θ ABS and the maximum angular movement range θ MAX are shown as being nominally equal. As will be described in more detail below, the first and second signal modulation element angular space steps θ WSME1 and θ WSME2 may be related to the absolute angular measurement range θ ABS . By arranging 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 and the arc length ARC2, an operation of realizing the absolute angular measurement range θ ABS by combination becomes possible.

[0057] The scale direction SCD (for example, the arc direction in the implementations of FIGS. 3A and 4) is shown (for example, along which the signal modulation elements SME of the first and second scale element portions PRTSC1 and PRTSC2 are arranged according to their respective angular space steps θ WSME1 and θ WSME2 as shown in FIG. 3A, for example). In various implementations, the first scale element portion PRTSC1 (for example, arc-shaped) is arranged at a first radius distance RD1 from the rotating portion PPN, and the second scale element portion PRTSC2 (for example, arc-shaped) is arranged at a second radius distance RD2 from the rotating portion PPN, and the first radius distance RD1 is greater than the second radius distance RD2. In various implementations, the first and second scale element portions PRTSC1 and PRTSC2 define the corresponding absolute angular measurement range θ ABS (for example, each relative position between the detection unit 167 and the scale unit 170 within the absolute angular measurement range θ ABS generates a unique combination of detection signals from the detection unit 167).

[0058] In various implementation forms, the ratio of the signal modulation element angular space step θ WSME2 / θ WSME1 can be expressed according to at least one of the following equations (1) to (4) where n and m are positive integers in each equation. In some implementation forms, m is a positive integer of at least 2 (for example, in some implementation forms, m may be 2, 3, 4, or 5, etc.). Note that for the configuration where m is 2 or more, such a relationship is applicable when the difference between the signal modulation element angular space step θ WSME1 and θ WSME2 is relatively large (for example, when the angular space step θ WSME2 is close to an integer multiple of the angular space step θ WSME1 (for example, m = 2 or more)). It should be noted that in the implementation form where m = 1, these equations can be further simplified (for example, the nm coefficient is simplified to n). Regarding these equations, as one method for encoding an encoder using circular motion, note that an absolute angle measurement range θ ABS can be obtained by using two scale element parts having signal modulation element angular space steps that satisfy a certain relationship. For example, the following equations show a certain relationship that the signal modulation element angular space steps θ WSME1 and θ WSME2 of the track parts TR1 and TR2 and the scale element parts PRTSC1 and PRTSC2 may satisfy. θ WSME2 / θ WSME1 =(nm / (n - 1)) (Equation 1) θ WSME2 / θ WSME1 =(nm / (n + 1)) (Equation 2) θ WSME2 / θ WSME1 =((nm + 1) / n) (Equation 3) θ WSME2 / θ WSME1 =((nm - 1) / n) (Equation 4)

[0059] In various implementation forms, the absolute angle measurement range θ ABS is nθ WSME1 or nθ WSME2is equal to any of them. For example, in some implementations, the configuration corresponding to Equation 1 or Equation 2 can satisfy an additional condition that the absolute angle measurement range θ ABS =nθ WSME1 and the configuration corresponding to Equation 3 or Equation 4 can satisfy an additional condition that the absolute angle measurement range θ ABS =nθ WSME2 In various implementations, the configuration corresponding to Equation 1 can satisfy an additional condition that the absolute angle measurement range θ ABS =((n - 1) / m)θ WSME2 and the configuration corresponding to Equation 2 can satisfy an additional condition that the absolute angle measurement range θ ABS =((n + 1) / m)θ WSME2 and the configuration corresponding to Equation 3 can satisfy an additional condition that the absolute angle measurement range θ ABS =(nm + 1)θ WSME1 and the configuration corresponding to Equation 4 can satisfy an additional condition that the absolute angle measurement range θ ABS =(nm - 1)θ WSME1 Based on such relationships, as a method for selecting two signal modulation element angular space steps, it can be understood that the absolute angle measurement range θ ABS is set to include an angular space step of an integer n (for example, either θ WSME2 or θ WSME1 ), and the other signal modulation element angular space step (for example, either θ WSME2 or θ WSME1 ) is determined according to the relationships as described above.

[0060] In various implementations, the first scale element part PRTSC1 has an arc length ARC1 and is arranged at a first radius distance RD1 from the rotating part PPN, and the second scale element part PRTSC2 has an arc length ARC2 and is arranged at a second radius distance RD2 from the rotating part PPN (for example, as shown in FIG. 4), and ARC2 / ARC1 = RD2 / RD1. In various implementations, the second signal modulation element angular space step θ WSME2 is larger than the first signal modulation element angular space step θ WSME1 (for example, in a configuration where m is 2 or more, the angular space step θ WSME2is close to an integer multiple of the angular space step θ WSME1 ).

[0061] As described above, the first signal modulation element pattern PATSME1 of the first scale element part PRTSC1 in the first track part TR1 includes a first half pattern part FHPP1 and a second half pattern part SHPP1, and each half pattern part includes a column of the first signal modulation element SME1. In each scale column, the first signal modulation element SME1 is arranged according to the first signal modulation element angular space step θ WSME1 (e.g., arranged at intervals / spatially). For two adjacent scale columns of the half pattern part, the spatial phase of the scale column of the second half pattern part is shifted by 1 / 2 of the first signal modulation element angular space step θ WSME1 from the spatial phase of the adjacent scale column of the first half pattern part. Therefore, in this example, the signal modulation element spatial phase offset is 1 / 2 of the first signal modulation element angular space step θ WSME1 (e.g., this may correspond to a 180-degree spatial phase shift / difference between adjacent scale rows).

[0062] As described above, the second signal modulation element pattern PATSME2 of the second scale element part PRTSC2 in the second track part TR2 includes a first half pattern part FHPP2 and a second half pattern part SHPP2, and each half pattern part includes a column of the second signal modulation element SME2. In each scale column, the second signal modulation element SME2 is arranged according to the second signal modulation element angular space step θ WSME2 (e.g., arranged at intervals / spatially). For two adjacent scale columns of the half pattern part, the spatial phase of the scale column of the second half pattern part is shifted by 1 / 2 of the second signal modulation element angular space step θ WSME2 from the spatial phase of the adjacent scale column of the first half pattern part. Therefore, in this example, the signal modulation element spatial phase offset is 1 / 2 of the second signal modulation element angular space step θ WSME2 (e.g., this may correspond to a 180-degree spatial phase shift / difference between adjacent scale rows).

[0063] In various implementation forms, in the first sensing element unit PRTSEN1, the first set SET1SEN1 and the second set SET2SEN1 of the first sensing elements are at different angular space phase positions so as to be separated by the first sensing element angular space phase offset. In various implementation forms, the first sensing element angular space step θ of the first sensing element unit PRTSEN1 (for example, each of the sets SET1SEN1 and SET2SEN1 of the first sensing elements) WSEN1 may correspond to (for example, may be equal to) the first signal modulation element angular space step θ of the first scale element unit PRTSC1. WSME1 In various implementation forms, the first sensing element angular space phase offset may be equal to approximately 1 / 4 of the first sensing element angular space step θ (for example, according to an orthogonal configuration as understood by those skilled in the art). WSEN1

[0064] Similarly, in various implementation forms, in the second sensing element unit PRTSEN2, the first set SET1SEN2 and the second set SET2SEN2 of the second sensing elements are at different angular space phase positions so as to be separated by the second sensing element angular space phase offset. In various implementation forms, the second sensing element angular space step θ of the second sensing element unit PRTSEN2 (for example, each of the sets SET1SEN2 and SET2SEN2 of the second sensing elements) WSEN2 may correspond to (for example, may be equal to) the second signal modulation element angular space step θ of the second scale element unit PRTSC2. WSME2 In various implementation forms, the second sensing element angular space phase offset may be equal to approximately 1 / 4 of the second sensing element angular space step θ (for example, according to an orthogonal configuration as understood by those skilled in the art). WSEN2

[0065] In an example of one implementation form, θ WSME1 = 0.0300 radians and θ WSME2 = 0.625 radians. Regarding the above values, 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. Further, in various implementation forms, θ ABS is, θ ABS = nθ WSME1 = 25(0.0300 radians) = 0.75 radians or 25(1.72 degrees) = 43 degrees and 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 can be determined according to these. According to these relationships, within the absolute angle measurement range θ ABS there are 25 θ WSME1 (corresponding to 25 SME1s) and 12 θ WSME2 (corresponding to 12 SME2s). The relational expression of this configuration can also be described based on Equation 3 instead. When n = 12 and m = 2, θ WSME2 / θ WSME1 = ((nm + 1) / n) = 25 / 12 = 0.0625 radians / 0.0300 radians or 3.58 degrees / 1.72 degrees. Also, 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.

[0066] As another example, for the absolute angle measurement range θ ABS (continuing to be 0.75 radians = 43 degrees) including 25 θ WSME1 (corresponding to 25 SME1s), where θ WSME1 remains 0.0300 radians = 1.72 degrees, and further including 13 θ WSME2 (corresponding to 13 SME2s), in an alternative configuration where θ WSME2 = 0.75 radians / 13 = 0.0577 radians or 43 degrees / 13 = 3.31 degrees, it should be noted that these relationships can be expressed by Equation 2 or Equation 4. More specifically, according to Equation 2, when n = 25 and m = 2, θ WSME2 / θ WSME1 =(nm / (n + 1)) = 50 / 26 = 0.0577 radian / 0.0300 radian = 3.31 degrees / 1.72 degrees. θ ABS = nθ WSME1 = ((n + 1) / m)θ WSME2 In the case of, within the absolute angle measurement range, there are 25 θ WSME1 (corresponding to 25 SME1s) and 13 θ WSME2 (corresponding to 13 SME2s). Or, according to Equation 4, when n = 13 and m = 2, θ WSME2 / θ WSME1 = ((nm - 1) / n) = 25 / 13 = 0.0577 radian / 0.0300 radian = 3.31 degrees / 1.72 degrees. θ ABS = nθ WSME2 = (nm - 1)θ WSME1 In the case of, within the absolute angle measurement range, there are 13 θ WSME2 (corresponding to 13 SME2s) and 25 θ WSME1 (corresponding to 25 SME1s). As yet another alternative example, when n = 12 and m = 2, according to Equation 4, θ WSME2 / θ WSME1 = ((nm - 1) / n) = 23 / 12 = 0.0625 radian / 0.0326 radian = 3.58 degrees / 1.87 degrees. θ ABS = nθ WSME2 = (nm - 1)θ WSME1 In the case of, within the absolute angle measurement range, there are 12 θ WSME2 (corresponding to 12 SME2s) and 23 θ WSME1 (corresponding to 23 SME1s).

[0067] In the transducers of FIGS. 3A and 4, the first scale element portion PRTSC1 is within a first scale track ST1 having a first scale track width STW1 (for example, the upper and lower ends 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 within a second scale track ST2 having a second scale track width STW2 (for example, the upper and lower ends 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 and second scale tracks ST1 and ST2. The separation region SEPA is shown between the first and second scale tracks ST1 and ST2 (for example, having a radial width defined by the separation distance SEP12 and defined by the lower boundary of the first scale track ST1 and the upper boundary of the second scale track ST2, etc.). Note that the separation region SEPA is shown as being empty (for example, not including a scale element portion such as would be disposed in an encoder track portion having a sensing element portion). The differential distance D12 is shown as the difference in the distance between the center reference point REF1 and the center reference point REF2 and correspondingly is also the difference between the first radial distance RD1 and the second radial distance RD2. As an example of some specific dimensions, in one implementation, the first scale track width STW1 may be 4.0 mm, the second scale track width STW2 may be 2.75 mm, the separation distance SEP12 may be 8.25 mm, the first radial distance RD1 may be 37.125 mm, the second radial distance may be 25.5 mm, and the differential distance D12 may be 11.625 mm. In various implementations, such dimensions may result in certain desirable operating characteristics, as will be described in more detail below.

[0068] FIG. 5 is a diagram showing some signals 500 resulting from the operation of the transducer TDR of FIG. 3A with an arcuate motion between the detection unit 167 and the scale unit 170. As shown in FIG. 5, graph 510A shows the SEN1 signal as a function of the angular position. In various implementations, the signal of graph 510A may correspond to the detection signals SIG1A and SIG1B of the transducer unit PRTTDR1 of the first track unit TR1. Similarly, graph 520A illustrates the SEN2 signal as a function of the angular position. In various implementations, the signal of graph 520A may correspond to the detection signals SIG2A and SIG2B of the transducer unit PRTTDR2 of the second track unit TR2. Graphs 510B and 520B show the phase signals of the SEN1 and SEN2 signals of graphs 510A and 520A, respectively (e.g., from the calculation of arctan(SIGxB / SIGxA) such as arctan(SIG1B / SIG1A) and arctan(SIG2B / SIG2A)).

[0069] Graph 530 illustrates the absolute ABS phase signal (generated as a result of combining other signals, including those of graphs 510B and 920B). In various implementations, the absolute ABS phase signal may be Φ ABS = Φ SIG1 - mΦ SIG2 (Equation 5) represented according to.

[0070] As shown in graph 530, the absolute angle measurement range θ ABSextends over a range from -21.5 degrees to +21.5 degrees (i.e., from -0.375 radians to +0.375 radians) so as to correspond to an absolute angle range of 43 degrees (i.e., 0.75 radians). Correspondingly, in graphs 510A and 510B, there are 25 cycles / periods (e.g., corresponding to 25 SME1s in the first scale element part PRTSC1 of the first track part TR1) illustrated within the angle range from -21.5 degrees to +21.5 degrees (i.e., from -0.375 radians to +0.375 radians), and in graphs 520A and 520B, 12 cycles / periods (e.g., corresponding to 12 SME2s in the second scale element part PRTSC2 of the second track part TR2) are shown within the angle range from -21.5 degrees to +21.5 degrees (i.e., from -0.375 radians to +0.375 radians).

[0071] According to the principles described herein, the absolute angle measurement range θ ABS can be adjusted / configured according to a specific maximum angle movement range θ MAX in a particular application. It will be understood that the above specific numerical examples show an arrangement in which the absolute angle measurement range θ ABS is configured to be 43 degrees (i.e., 0.75 radians), but according to the principles described above, other arrangements configured with larger or smaller absolute angle measurement ranges are also possible. In some implementations, a smaller absolute angle measurement range may be utilized for a particular application (e.g., a range less than 15 degrees, or 10 degrees, or 5 degrees).

[0072] The absolute angle measurement range θ for a particular application ABSIt will be appreciated that being able to adjust has certain advantages. For example, in the case of a multi-track transducer, designing for a longer absolute angle measurement range generally requires a certain resolution and accuracy (e.g., obtaining an appropriate and distinct signal level over the entire range, and in particular, with respect to the relationship between multiple track portions (e.g., TR1 and TR2), having a high information accuracy necessary for each increment to be distinguishable over the entire range). In contrast, in the case of a multi-track transducer having a relatively short absolute angle measurement range (e.g., such as those formed according to the principles described herein), a higher resolution can be achieved within a smaller range (e.g., using smaller or different increments / space steps between multiple tracks, which may be too fine and / or cause other problems over a longer range), and / or sufficient accuracy can be achieved within a smaller range by implementing with lower complexity, cost, power requirements, etc.

[0073] In some implementations, the comparison may be made against an absolute rotary encoder having an integer number of angular space steps for each track portion over a complete 360-degree absolute range (e.g., to effectively function for continuously measuring the angular position in implementations where complete 360-degree rotations and rotations beyond can be performed). According to such a principle, when a portion of such a rotary encoder is utilized in an application of circular arc motion (e.g., when 1 / 4 or 1 / 8 of such a rotary encoder is utilized for a 90-degree or 45-degree measurement range), the angular space steps in each track portion are still correspondingly evenly divided into 360 degrees. For example, when a portion of such a rotary encoder is utilized, for each track portion within the transducer, dividing 360 degrees by the angular space steps of that track portion within the transducer results in an integer value.

[0074] It should be noted that such an implementation form that utilizes a part of the rotary encoder has specific drawbacks (as described above, in the design of a relatively long measurement range such as a 360-degree angle measurement range, generally, in order to achieve the entire 360-degree range, especially in the relationship between track parts, a certain level of resolution and accuracy is required to distinguish each increment). In contrast, as described above, when the absolute angle measurement range is relatively small (that is, less than 360 degrees, and in some implementation forms, it may be even smaller, such as less than 45 degrees, less than 15 degrees, or less than 5 degrees), an arc motion encoder having certain advantages as described above can be formed according to the principles described in this specification.

[0075] FIG. 6 is a diagram of a partial implementation form of a transducer TDR'''', which is configured to be used with the arc motion between a detection unit 167'''' and a scale unit 170'''' that can be used in the measuring instrument of FIG. 2 and has a relatively small separation of scale tracks ST1 and ST2'''' compared to the implementation form of FIG. 3A. FIG. 7 is a diagram showing some dimensions and features of the measuring instrument of FIG. 2 and the transducer of FIG. 6. It should be noted that the implementation forms of FIGS. 6 and 7 are similar to the implementation forms of FIGS. 3A and 4 in some respects, as will be described in more detail below.

[0076] The first encoder track part TR1 in the implementation forms of FIGS. 6 and 7 is the same as the first encoder track part TR1 in the implementation forms of FIGS. 3A and 4, and it should be noted that it will be understood based on the above description of the first encoder track part TR1. The second encoder track part TR2'''' in FIGS. 6 and 7 is configured to generate signals similar to the second encoder track part TR2 in FIGS. 3A and 4. FIG. 5 represents the signals resulting from the operation of the implementation forms of FIGS. 6 and 7, as well as the signals resulting from the operation of the implementation forms of FIGS. 3A and 4. In this regard, during operation, the signals SIG2A'''' and SIG2B'''' of the implementation form of FIG. 6 may be similar to the signals SIG2A and SIG2B of the implementation form of FIG. 3A.

[0077] Also, it will be understood that each of the components of the second encoder track portion TR2 of FIG. 3A has corresponding components in the second encoder track portion TR2'''' of FIG. 6 (such as may be designated by quadruple prime). Thus, the components of the transducer TDR'''' will be understood by those skilled in the art based on the corresponding components of the transducer TDR, except where otherwise described below. Thus, a complete description of the components of the transducer TDR'''' is not provided herein, but for reference, a brief description is provided below. This numbering scheme (including the use of different numbers of prime designations such as XX, XX', XX'', etc.) for indicating elements having similar designs and / or functions is also applied to other figures described herein.

[0078] Generally, the components of the second encoder track portion TR2'''' of FIG. 6 may be larger than the corresponding components of the second encoder track portion TR2 of FIG. 3A along the arc movement direction ARCD. In various implementations, the larger size of the components corresponds to the fact that, as will be understood by those skilled in the art, the radius distance RD2'''' is larger compared to the radius distance RD2 and the corresponding arc length ARC2'''' is larger compared to the arc length ARC2, so as to be required to generate similar signals. For generating similar signals, 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 WSME2 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 WSEN2 of the second sensing element.

[0079] Similar to the implementation forms of FIGS. 3A and 4, in the implementation forms of FIGS. 6 and 7, the first scale element part PRTSC1 is within the first scale track ST1 having the first scale track width STW1 (for example, the upper and lower ends of the first scale element part PRTSC1 may correspond to the upper and lower boundaries of the first scale track ST1). The second scale element part PRTSC2'''' is within the second scale track ST2'''' having the second scale track width STW2'''' (for example, the upper and lower ends of the second scale element part 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 scale track ST2''''. The separation region SEPA'''' is shown between the first scale track ST1 and the second scale track ST2'''' (for example, it has a radial width defined by the separation distance SEP12'''' and 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 empty (for example, it does not include the scale element part arranged in the encoder track part having the sensing element part).

[0080] As shown in FIG. 7, the first and second scale element parts PRTSC1 and PRTSC2'''' of the first and second track parts TR1 and TR2'''' are arc-shaped and parallel to each other (for example, they form concentric arcs). The second track part TR2'''' is closer to the rotating part PPN than the first track part TR1 (for example, the radial distance RD2'''' of the second center reference point REF2'''' of the second track part TR2'''' is smaller than the radial distance RD1 of the first center reference point REF1 of the first track part TR1). In various implementation forms, the reference point REF1 may be on the center line CL1, and the reference point REF2'''' may be on the center line CL2''''. The differential distance D12'''' is shown as the difference in the distance between the center reference point REF1 and the center reference point REF2'''', and correspondingly, it is also the difference between the first radial distance RD1 and the second radial distance RD2''''.

[0081] The first scale element part PRTSC1 has a first angular range θ RG1 and a corresponding arc length ARC1, and the second scale element part PRTSC2’’’’ has a second angular range θ RG2 and a corresponding arc length ARC2’’’’. The angular ranges θ RG1 and θ RG2 are shown as being nominally equal, and in the examples of FIGS. 6 and 7, the absolute angle measurement range θ ABS and the maximum angle movement range θ MAX are shown as being nominally equal.

[0082] As some specific exemplary dimensions, in one implementation form, the first scale track width STW1 may be 4.0 mm, the second scale track width STW2 may be 2.75 mm, the separation distance SEP12 may be 1.25 mm, the first radius distance RD1 may be 37.125 mm, the second radius distance RD2 may be 32.5 mm, and the differential distance D12 may be 4.625 mm. In various implementation forms, such dimensions may result in some less desirable operating characteristics (for example, compared with those of the implementation forms of FIGS. 3A and 4) as will be described in more detail below.

[0083] Note that the implementation forms of FIGS. 6 and 7 have a smaller overall size of the corresponding transducer TDR’’’’ compared with the implementation forms of FIGS. 3A and 4 where the overall size of the corresponding transducer TDR is relatively large. This is the main reason why conventional encoders have generally been designed with a relatively small spacing between encoder tracks in order to limit the overall size. According to such prior art design principles, it may have been considered counterintuitive and / or surprising that implementation forms such as those of FIGS. 3A and 4 (i.e., with a relatively large separation of the encoder / scale tracks) result in some more desirable operating characteristics as will be described in more detail below.

[0084] Generally, in the case of a transducer using circular arc motion, it should be noted that the signal periodicity depends on the spatial step in the scale track section and also on the radial distance of the scale section and / or the detection section from the rotating section. This is in contrast to a standard transducer that uses only linear motion, where the signal periodicity depends only on the spatial step of the scale track section. Since the circular arc motion transducer depends on the radial distance of the scale section and / or the detection section from the rotating section, some problems may occur if there is an offset / misalignment. For example, the transducer may be designed to operate ideally with the scale section and the detection section centered and aligned radially with each other, and as a result, the designed signal periodicity may be obtained. However, if there is a radial offset / misalignment (e.g., of the scale section with respect to the detection section), due to the dependence on the radial distance, the signal periodicity may be different from the design, and as a result, the position determined by the operation of the transducer may have a linear error (e.g., as the measured position moves away from the reference point, the error may increase linearly with further circular arc motion of the transducer).

[0085] As an example of how a radial offset / misalignment can occur, during the manufacture / assembly of a measuring instrument as shown in FIG. 2, a movable encoder unit MEP (for example, consisting of a printed circuit board on which a scale unit or a detection unit is fabricated) may be coupled to a support member MEPSM (for example, attached, affixed, etc.). During such manufacture / assembly, a certain amount of radial offset / misalignment of the movable encoder unit MEP may occur (for example, due to manufacturing tolerances such as the positioning of the movable encoder unit MEP on the support member MEPSM, etc.). As a result, the radial offset / misalignment of the movable encoder unit MEP (i.e., coupled to the support member MEPSM) may correspond to the radial offset / misalignment of the scale unit with respect to (for example, the detection unit). As described above, such a radial offset / misalignment may introduce an error in the determined position of the transducer. As will be described in more detail below, to address such a problem, in accordance with the principles described herein, an offset value corresponding to such a radial offset may be determined at least partially based on a signal from the transducer, and the determined offset value may be used to correct one or more values used to determine the relative position between the detection unit and the scale unit.

[0086] In various implementations, the following concepts may be related to determining an offset value at least partially based on a signal from a transducer. With respect to the signal of FIG. 5, the SEN1 signal and the SEN1 phase (for example, corresponding to the signal phase Φ SIG1 corresponds to the first signal modulation element angular spatial step θ of the first scale element part PRTSC1 of the first scale track ST1. WSME1 Similarly, the SEN2 signal and the SEN2 phase (for example, corresponding to the signal phase Φ SIG2 corresponds to the second signal modulation element angular spatial step θ of the second scale element part PRTSC2 of the second scale track ST2. WSME2 As described above, the first signal modulation element angular spatial step θ WSME1 is the second signal modulation element angular spatial step θ WSME2is smaller than this, and in contrast, the first signal modulation element angular space step θ WSME1 is characterized as a finer or more minute space step (e.g., of the fine track ST1), while the second signal modulation element angular space step θ WSME2 can be characterized as a coarser space step (e.g., of the sub-track ST2).

[0087] As illustrated and described, the space step of the first scale element part PRTSC1 of the first scale track ST1 can provide the finest measurement resolution, and thus can be referenced and utilized as a part for determining a high-precision absolute measurement position. However, as part of determining the overall absolute measurement position, a determination must be made as to whether the current absolute measurement position is within which period / interval of the SEN1 phase (i.e., corresponding to the signal phase Φ SIG1 ), or otherwise corresponding (e.g., corresponding to the generated integer space step and may be added to the position indicated by the SEN1 phase / signal phase Φ SIG1 ). For example, in the illustration of FIG. 5, corresponding to 25 signal modulation elements SME1 (within the first scale element part PRTSC1 of the first track part TR1 of FIG. 6), there are 25 periods / intervals of the SEN1 phase (i.e., corresponding to the signal phase Φ SIG1 ), and there are 25 space steps corresponding within the absolute range (i.e., within the absolute range θ ABS indicated with respect to the absolute phase). It should also be noted that there are 12 periods / intervals of the SEN2 phase (i.e., corresponding to the signal phase Φ ABS ), corresponding to 12 signal modulation elements SME2 and corresponding 12 space steps within the absolute range. Further with respect to FIG. 5, in various implementations, the absolute ABS phase (i.e., corresponding to the signal phase Φ SIG2 ), can have sufficient accuracy to be used to determine which period / interval the current absolute measurement position corresponds to. In various implementations, such processing may be referred to as phase unwrapping processing, or chain down processing, etc. ABS ).

[0088] In one implementation, the absolute ABS phase (i.e., corresponding to the signal phase Φ ABS corresponding thereto) is considered accurate enough to be used to determine which period / interval (e.g., out of 25 periods / intervals in the example of FIG. 5) of the current absolute measurement position corresponding to the SEN1 phase (i.e., the signal phase Φ SIG1 corresponding thereto). Such corresponding processing may be referred to as direct chain-down processing (i.e., only a single chain-down step is executed). Alternatively, as part of a more robust process (e.g., more robust against some types of encoder errors or other accuracy issues), the absolute ABS phase (i.e., the signal phase Φ ABS corresponding thereto) may first be used to determine which period / interval (e.g., out of 12 periods / intervals in the example of FIG. 5) of the current absolute measurement position corresponding to the SEN2 phase (i.e., the signal phase Φ SIG2 corresponding thereto), and the result of such a first determination may be used to determine which period / interval (e.g., out of 25 periods / intervals in the example of FIG. 5) of the current absolute measurement position corresponding to the SEN1 phase (i.e., the signal phase Φ SIG1 corresponding thereto). Such corresponding processing may be referred to as double chain-down processing (i.e., two chain-down steps are executed).

[0089] As part of such chain-down processing, a rounding process may be executed (e.g., for the absolute ABS phase / signal phase Φ ABSRegarding the case where it may be executed in the first step of direct chain - down processing or double chain - down processing. The rounded amount (for example, between - 0.5 and 0.5) may be referred to as the chain - down value and may represent the difference in cumulative position values. In a complete configuration (for example, without a radial offset), the chain - down value may be close to zero or zero. However, in an actual practical configuration (for example, during manufacturing / assembly, when there are some manufacturing / assembly tolerances), there may be a certain radial offset (for example, such that it can result in a specific chain - down value). As will be described in more detail below, in various implementations, a chain - down gradient (that is, corresponding to the chain - down curve plot of the chain - down value) may be determined, associated with the offset value, and / or used to determine the offset value (for example, corresponding to the radial offset of the scale part with respect to the detection part or the radial offset of the detection part with respect to the scale part). In various implementations, the determined offset value may be used to correct one or more values (for example, those of a spatial step or other spatial dimensions) used to determine the relative position between the detection part and the scale part.

[0090] As part of the following chain - down processing, the absolute phase Φ ABS is within the range of [0,1], the signal phase Φ SIG1 and Φ SIG2 are within the range of [- 0.5,+0.5], Φ SIG1 =(1 / 2π)arctan(SIG1B / SIG1A) (Equation 6) Φ SIG2 =(1 / 2π)arctan(SIG2B / SIG2A) (Equation 7) may be represented according to.

[0091] The relationship of the absolute phase Φ ABS is Φ ABS =(Φ SIG1 -mΦ SIG2 +Φ0)%1 (Equation 8) It may be represented according to. Here, Φ0 is the buffer ABS signal phase included in some implementations to avoid jumps in the ABS spatial range / step, %1 indicates a modulo / modulus operation, which returns the remainder or signed remainder after dividing a numerical value by a specified divisor. In this case, since the specified divisor is 1, the result generally becomes a non-integer value (for example, if the value is 1.2, applying this operation returns 0.2, etc.).

[0092] In the case of direct chain down processing, the next determination is n AWSME1 =round((Φ ABS (θ ABS / θ WSME1 )-Φ SIG1 +Φ1)(Equation 9) It may be represented according to. Here, n AWSME1 is an integer of the first signal modulation element space step for absolute measurement distance determination, "round" indicates a rounding operation (for example, for determining the integer of n AWSME1 ), Φ1 minimizes the first chain down value in some implementations, and θ WSME1 is included to avoid jumps in the space step. Note that θ ABS / θ WSME1 results in the number of the first signal modulation element angle space steps θ ABS in the absolute angle measurement range θ WSME1 (for example, as in the above example, when θ ABS =0.75 radians and θ WSME1 =0.03 radians, θ ABS / θ WSME1 =25). After the integer first signal modulation element space step n AWSME1 is determined according to Equation 9, the absolute measurement value can be determined according to Equation 12 as described in more detail below.

[0093] As an alternative to direct chain down processing, in the case of double chain down processing, as part of the first chain down step, the next determination after Equation 8 is n AWSME2=round((Φ ABS (θ ABS / θ WSME2 )-Φ SIG2 +Φ1)(Equation 10) may be represented according to. Here, n AWSME2 is an integer of the second signal modulation element space step for absolute measurement distance determination, "round" indicates a rounding operation (for example, for determining the integer of n AWSME2 ), and Φ1 minimizes the first chain down value in some implementations and is included to avoid jumps in the θ WSME2 space step. Note that θ ABS / θ WSME2 is the number of second signal modulation element angular space steps θ ABS in the absolute angle measurement range θ WSME2 resulting in (for example, when θ ABS =0.75 radians and θ WSME2 =0.0625 radians, θ ABS / θ WSME2 =12). As a further part of the double chain down process, the second / next chain down step is n AWSME1 =round(((n AWSME2 +Φ SIG2 )(θ WSME2 / θ WSME1 ))-Φ SIG1 +Φ2)(Equation 11) may be represented according to. Here, n AWSME1 is an integer of the first signal modulation element space step for absolute measurement distance determination, "round" indicates a rounding operation (for example, for determining the integer of n AWSME1 ), and Φ2 minimizes the second chain down value in some implementations and is included to avoid jumps in the θ WSME1 space step, and θ WSME2 / θ WSME1 is a ratio value (for example, in the above example, a value corresponding to 0.0625 / 0.03 = 2.0833).

[0094] The integer first signal modulation element space step n AWSME1After being determined according to Equation 9 (e.g., as part of direct chain - down processing) or according to Equation 11 (e.g., as part of double chain - down processing), the absolute measurement value is MEAS ANG =θ WSME1 (n AWSME1 +Φ SIG1 ) - θ0 (Equation 12) and may be expressed as follows. Here, MEAS ANG is the absolute angle measurement value (e.g., in radians), and θ0 is the angle origin position. In some implementations, the absolute measurement value may be expressed in terms of arc distance, and the arc distance is related to the first signal modulation element angular space step θ WSME1 and the radius distance RD1 of the first scale element part PRTSC1 of the first scale track ST1, MEAS ARC =(MEAS ANG )RD1 (Equation 13) and may be expressed like this.

[0095] Note that this corresponds to the arc distance along the first scale track ST1. As described above, the amount to be rounded (e.g., in either direct or double chain - down processing) may be referred to as the chain - down value. Regarding direct chain - down processing and Equation 9, the chain - down value is chain - down value=(Φ ABS (θ ABS / θ WSME1 ) - Φ SIG1 +Φ1) - n AWSME1 (Equation 14) and may be expressed as follows.

[0096] Regarding double chain - down processing and Equation 10, the chain - down value is chain - down value=(Φ ABS (θ ABS / θ WSME2 ) - Φ SIG2 +Φ1) - n AWSME2 (Equation 15) and may be expressed as follows.

[0097] In various implementations, such chain-down values may be included in a chain-down plot and / or may be otherwise utilized to determine a chain-down gradient and, as will be described in more detail below, can be utilized to correct for linear errors. Briefly, with respect to Equation 12 (and some of the other equations above), the signal periodicity of the first scale element portion PRTSC1 of the first scale track ST1 (e.g., due to a radial offset of a scale portion or a detection portion) does not match θ WSME1 (e.g., or its equivalent arc distance), an error will accumulate in the determined measurement value. The determined chain-down gradient may be utilized to determine an offset value corresponding to a radial offset of a scale portion or a detection portion (e.g., relative to each other), and this determined offset value may be utilized to correct a value that can be used to determine a relative position between the detection portion and the scale portion (e.g., to determine a correction value θ WSME1C ).) may be utilized (e.g., such as in Equation 12).

[0098] More generally, transducers that utilize circular arc motion are typically sensitive to radial offset / misalignment (e.g., of a scale portion relative to a sensing portion), and such radial offset / misalignment causes a linear long-range-error (LRE) (e.g., having a gradient approximately equal to the radial offset divided by the radial distance of a scale track in some implementations). One way to correct such LRE is to calibrate against a known standard (e.g., a reference encoder or gauge block, etc.), but in some implementations, such a process can be prohibitively complex, difficult, and expensive. Alternatively, and according to certain principles described herein, a two-track arc encoder (i.e., having a transducer that utilizes circular arc motion) can be configured to “self-correct” such problems (e.g., at least in part by essentially utilizing a known separation of first and second scale tracks, and / or by correcting values in other ways). Stated another way, in embodiments as described herein, when the first and second scale track portions have different radial distances from a rotating portion, a radial offset results in a gradient in the chain-down plot of chain-down values (i.e., the chain-down gradient), which can be measured (e.g., without requiring an external reference standard) and used to correct values (e.g., to correct for linear errors). As will be described in more detail below, in various implementations, when the separation / difference in radial distances of the two scale tracks is relatively large, it may be possible to more / fully accurately determine an offset value (e.g., corresponding to the radial offset) that can be utilized for value correction (e.g., correction of linear errors).

[0099] According to the above principles, the following equations show some corresponding relationships. LRE gradient = OFF / (RD - OFF) ≈ OFF / RD (Equation 16) Here, OFF is the radial offset, and RD is the radial distance of the corresponding scale track / scale element portion. It should be noted that the radial offset OFF is generally sufficiently small with respect to the radial distance RD, and RD - OFF can be approximated sufficiently well by RD. In the case of direct chain-down processing, the chain-down gradient is CDSLOPE DIR ≈ -OFF((1 / RD2) - (1 / RD1))(n) (Equation 17) when expressed as follows. Here, CDSLOPE DIR is the chain-down gradient of the direct chain-down processing, and RD1 and RD2 are the radial distances of the first and second scale element portions and the corresponding first and second scale tracks, respectively. In some implementations, Equation 17 may be modified as further specified below. CDSLOPE DIR ≈ -OFF((1 / RD2) - (1 / RD1))(n - 1) (Equation 18)

[0100] In the case of double chain-down processing, the chain-down gradient may be characterized as follows. CDSLOPE DBL ≈ -OFF((1 / RD2) - (1 / RD1))(n / m) (Equation 19) Here, CDSLOPE DBL is the chain-down gradient of the double chain-down processing. Note that Equation 19 can be used to solve for the offset according to -OFF ≈ CDSLOPE DBL / (((1 / RD2) - (1 / RD1))(n / m)). In some implementations, Equation 19 may be modified as further specified below. CDSLOPE DBL ≈ -OFF((1 / RD2) - (1 / RD1))((n - 1) / m) (Equation 20)

[0101] Note that Equation 20 is -OFF ≈ CDSLOPE DBLIt can be used to solve the offset according to / (((1 / RD2)-(1 / RD1))((n - 1) / m)). In various implementation forms, the self - correction / correction process may be characterized as follows. θ WSME1C = θ WSME1 (1 - (OFF D / RD1)) (Equation 21) Here, θ WSME1C is the correction value of θ WSME1 , and OFF D is the determined radial offset (determined, for example, based on the chain - down slope CDSLOPE). The above principles and some related examples (related to, for example, the above - mentioned equations, etc.) will be described in more detail below with respect to FIGS. 8A - 21.

[0102] FIGS. 8A - 8B show the offsets related to some features of FIGS. 6 and 7 (for example, the radial offset of the scale part or the detection part). FIG. 8A is compared with a figure representing a part of the vertical center line of FIG. 7 and is generally corresponding. In the figure of FIG. 8A (in various implementation forms, it may correspond to the condition where the radial offset is zero), the first center reference point REF1 Z (arranged, for example, at the center x and / or y - axis positions such as the center line CL1 of the first scale element part PRTSC1 and / or the first sensing element part PRTSEN1 of the first scale track ST1) is at a radial distance RD1 Z from the rotating part PPN. The second center reference point REF2 Z ’’’’ (arranged, for example, at the center x and / or y - axis positions such as the center line CL2’’’’ of the second scale element part PRTSC2’’’’ and / or the second sensing element part PRTSEN2’’’’ of the second scale track ST2’’’’) is at a radial distance RD2 Z ’’’’ from the rotating part PPN.

[0103] The differential distance D12’’’’ is shown as the difference in the distance between the center reference point REF1 Z and the center reference point REF2 Z ’’’’, and correspondingly, the first radial distance RD1 Z and the second radial distance RD2Z is also the difference from "". As some specific numerical examples, the illustration in FIG. 8A shows that the first radius distance RD1 Z may be 37.125 mm, and the second radius distance RD2 Z "" may be 32.5 mm (for example, corresponding to the numerical examples described above with respect to FIGS. 6 and 7), and correspondingly, it shows that the differential distance D12"" may be 4.625 mm. As described above, in the illustration of FIG. 7, the numerical example may further include that the first scale track width STW1 may be 4.0 mm, the second scale track width STW2"" may be 2.75 mm, and the separation distance SEP12"" may be 1.25 mm.

[0104] FIG. 8B shows the condition having an offset OFF P (for example, the radial offset of the scale portion or the detection portion). In the figure of FIG. 8B (for example, in various implementation forms, corresponding to the condition of a positive radial offset OFF P ), the first center reference point REF1 P (for example, of the first scale element portion PRTSC1 of the first scale track ST1) is shifted upward by the offset OFF P so as to be at a radius distance RD1 P from the rotating portion PPN. The second center reference point REF2 P "" (for example, of the second scale element portion PRTSC2"" of the second scale track ST2"") is also shifted upward correspondingly by the offset OFF P (for example, because the first and second scale element portions and the corresponding scale tracks may be fabricated on a single PCB that can be coupled to the support member MEPSM in FIG. 2 so that the scale portion as a whole may have a radial offset OFF P ) and is at a radius distance RD2 PIt is in the “”. Note that the differential distance D12’’’’ is shown to be the same as in FIG. 8A in FIG. 8B (for example, in some implementations, a certain known differential distance D12’’’’ and / or corresponding characteristics may be considered to be used as internal references for performing the self-correction described herein).

[0105] Also, in this example, the scale part may have a radial offset as shown, but the detection part including the sensing part has the central reference points REF1 Z and REF2 Z ’’’’ with it. It should be noted that it may remain so. Therefore, the radial offset of the scale part may be referred to as being related to the detection part including the sensing part in some implementations (for example, in some implementations, the detection part including the sensing part may be further or alternatively referred to as having a radial offset with respect to the scale part). In an alternative example, at the position shown in FIG. 8A, the scale part is the central reference point REF1 Z and REF2 Z ’’’’, and at the position shown in FIG. 8B, the sensing part may be switched to be the central reference point REF1 P and REF2 P ’’’’ (for example, it may be described that the sensing part has a radial offset with respect to the scale part and / or the scale part has a radial offset with respect to the sensing part). As some specific numerical examples, the illustration in FIG. 8B shows that the first radial distance RD1 P may be 37.225 mm, and the second radial distance RD2 P ’’’’ may be 32.6 mm (for example, corresponding to a positive radial offset OFF P that may be 0.1 mm). A certain differential distance D12’’’’ can continue to be 4.625 mm.

[0106] Figures 9A to 9C are diagrams of graphs 910 to 930 showing specific data resulting from the operation and correction processing of the transducers of FIGS. 6 and 7 having the offset as shown in FIGS. 8A and 8B. The x-axis of graphs 910 to 930 is the arc distance along the first scale track TR1 (for example, in various implementations, Equation 13 or a similar calculation may be used to convert an angular value to an arc distance or vice versa, and the calculation can be utilized according to a known equation associating the angular value and the arc distance). In relation to the graphed values in millimeters plotted in FIGS. 9A and 9C, in various implementations, the equation associating the chain-down value in millimeters may be as follows. Chain-down (in millimeters) = Chain-down × θ WSME1 × RD1 (Equation 22)

[0107] Note that θ WSME1 × RD1 term is common to both axes and is canceled out in the calculation of the gradient. This technique as applied to FIGS. 9A and 9B is also applicable to FIGS. 11A, 11B, 14A, 14B, 17A, and 19A. Further, some or all of the plots / curve plots of FIGS. 9A to 9C, FIGS. 11A to 11C, FIGS. 14A to 14C, FIGS. 17A to 17B, and FIGS. 19A to 19B, and the corresponding calculations described below may follow the -OFF technique, and in an alternative technique using +OFF, the plot / curve plot is horizontally inverted and the sign of the calculated value may be reversed.

[0108] FIG. 9A is a graph 910 of a chain-down curve plot 911 of chain-down values for direct chain-down processing. FIG. 9B is a graph 920 of a chain-down curve plot 921 of chain-down values for double chain-down processing. In accordance with including an m variable (e.g., equal to 2 in this example) in the denominator of the formula for the chain-down gradient of double chain-down processing, the chain-down gradient in FIG. 9B (i.e., for double chain-down processing) may be 1 / 2 of the chain-down gradient in FIG. 9A (i.e., for direct chain-down processing), as will be understood (e.g., as shown by equations 17 to 20).

[0109] FIG. 9C is a graph 930 showing long-distance error curve plots 931 and 933, where the long-distance error curve plot 931 represents data before correction processing, and the long-distance error curve plot 933 represents data after correction processing is performed in accordance with the principles described herein (e.g., in accordance with equations 21 and / or other processing). More specifically, in various implementations, the chain-down gradient may be determined based on data as shown in either graph 910 or graph 920. As an example, in one particular implementation, determining the chain-down gradient may include applying a least-squares linear fit to the data.

[0110] The determined chain-down gradient can be used to determine an offset value (e.g., corresponding to the radial offset of the scale part or the detection part) according to, for example, an equation (e.g., one of Equations 17 to 20) that enables determining the offset value based on the determined chain-down gradient, or other calculations or methods, or based on chain-down data. The determined offset value may be used to correct one or more values used to determine the relative position between the detection part and the scale part. For example, the determined offset value may be used to correct the spatial step value or other spatial values of the scale part according to Equation 21 or other calculations, and the corrected value may be used in one or more equations (e.g., Equation 12) or other calculations for determining a measured value (i.e., corresponding to the relative position between the detection part and the scale part).

[0111] As described above, the long-distance error curve plot 933 represents the data after such correction processing. The plot 933 with correction applied (i.e., there remains a gradient of error of approximately -0.67 μm per 1 mm of measurement) shows that it is somewhat improved compared to the original error plot 931 (i.e., there remains a gradient of error of approximately -2.67 μm per 1 mm of measurement). However, for some practical applications, the remaining error (i.e., -0.67 μm per mm) may be too high. In various implementations, this can be characterized as being at least partially due to the difficulty of accurately determining the chain-down gradient from the data as shown in Graph 910 or Graph 920.

[0112] For example, when the data includes a certain degree of dispersion / variation caused by various factors (such as noise, amplitude variation, misalignment, etc.) as indicated by the dispersion / vibration in plots 911 and 921, considering the nature of such data in actual applications, the accuracy of determining the chain-down gradient may be affected. When the accuracy of determining the chain-down gradient is limited, the accuracy of determining the offset value (for example, corresponding to the radial offset of the scale part or the detection part) is also limited, and correspondingly, the accuracy of the correction process that results in the error curve plot 933 showing the remaining error may also be restricted. Such characteristics may be at least partially due to specific dimensional relationships in the implementations of FIGS. 6 and 7. On the other hand, the implementations of FIGS. 3A and 4 may be able to achieve improved characteristics that provide sufficient accuracy for specific practical applications, as will be described in more detail below.

[0113] FIGS. 10A - 10B are diagrams showing offsets (for example, radial offsets of the scale part or the detection part) related to some features of FIGS. 3A and 4. Note that FIGS. 10A and 10B have some similarities with FIGS. 8A and 8B. FIG. 10A is compared with a diagram representing a part of the vertical center line of FIG. 4 and is generally corresponding. In the diagram of FIG. 10A (for example, in various implementations, it can correspond to the condition where the radial offset is zero), the first center reference point REF1 Z (for example, arranged at the center x and / or y-axis positions such as the center line CL1 of the first scale element part PRTSC1 and / or the first sensing element part PRTSEN1 of the first scale track ST1) is at a radial distance RD1 from the rotating part PPN Z The second center reference point REF2 Z (for example, arranged at the center x and / or y-axis positions such as the center line CL2 of the second scale element part PRTSC2 and / or the second sensing element part PRTSEN2 of the second scale track ST2) is at a radial distance RD2 from the rotating part PPN Z Therein.

[0114] The differential distance D12 is between the center reference point REF1 Z and REF2Z shown as the difference in distance between, and correspondingly, a first radius distance RD1 Z and a second radius distance RD2 Z which is also the difference between. As some specific numerical examples, the diagram of FIG. 10A shows that the first radius distance RD1 Z may be 37.125 mm, and the second radius distance RD2 Z may be 25.5 mm (e.g., corresponding to the numerical examples described above with respect to FIGS. 3A and 4), and correspondingly, the differential distance D12 may be 11.625 mm. As described above, in the illustration of FIG. 4, the numerical examples may further include that the first scale track width STW1 may be 4.0 mm, the second scale track width STW2 may be 2.75 mm, and the separation distance SEP12 may be 8.25 mm.

[0115] FIG. 10B shows the condition having an offset OFF P (e.g., a radial offset of the scale portion or the detection portion). In the diagram of FIG. 10B (e.g., in various implementation forms, corresponding to the condition of a positive radial offset OFF P ), the first center reference point REF1 P (e.g., of the first scale element portion PRTSC1 of the first scale track ST1) is shifted upward by the offset OFF P such that it is at a radius distance RD1 P from the rotating portion PPN. The second center reference point REF2 P (e.g., of the second scale element portion PRTSC2 of the second scale track ST2) is also correspondingly shifted upward by the offset OFF P (e.g., the first and second scale element portions and the corresponding scale tracks may be fabricated on a single PCB coupled to the support member MEPSM of FIG. 2 such that the scale portion as a whole may have a radial offset OFF P ) and is at a radius distance RD2 PIt is in [the relevant situation]. Note that in FIG. 10B, the differential distance D12 is shown to be the same as in FIG. 10A (for example, in some implementations, a certain known differential distance D12 and / or corresponding characteristics may be regarded as an internal reference for performing the self-correction described herein).

[0116] Also, in this example, the scale part may have a radial offset as shown, but the detection part including the sensing part may have the central reference points REF1 Z and REF2 Z while remaining as shown in FIG. 10A. It should be noted that, thus, the radial offset of the scale part may be referred to as being related to the detection part including the sensing part in some implementations (for example, in some implementations, the detection part including the sensing part may be further or alternatively referred to as having a radial offset with respect to the scale part). In an alternative example, at the position shown in FIG. 10A, the scale part may be the central reference points REF1 Z and REF2 Z while remaining unchanged, and at the position shown in FIG. 10B, the sensing part may be the central reference points REF1 P and REF2 P while remaining unchanged, and may be switched (for example, it may be described that the sensing part has a radial offset with respect to the scale part and / or the scale part has a radial offset with respect to the sensing part). As some specific numerical examples, the illustration in FIG. 10B shows that the first radial distance RD1 P may be 37.225 mm, and the second radial distance RD2 P may be 25.6 mm (for example, corresponding to a positive radial offset OFF P which may be 0.1 mm). A certain differential distance D12 can continue to be 11.625 mm.

[0117] Figures 11A to 11C are diagrams of graphs 1110 to 1130 showing some data resulting from the operation and correction processing of the transducers of FIGS. 3A and 4 having an offset as shown in FIGS. 10A to 10B. The x-axis of graphs 1110 to 1130 relates to the arc distance along the first scale track TR1. Graphs 1110 to 1130 have a certain similarity to graphs 910 to 930 of FIGS. 9A to 9C and will be understood at least in part based on the description of FIGS. 9A to 9C, except as otherwise described below.

[0118] FIG. 11A is graph 1110 of chain-down curve plot 1111 of the chain-down values of the direct chain-down process. FIG. 11B is graph 1120 of chain-down curve plot 1121 of the chain-down values of the double chain-down process. In accordance with including the m variable (for example, equal to 2 in this example) in the denominator of the formula for the chain-down gradient of the double chain-down process, the chain-down gradient in FIG. 11B (i.e., in the case of the double chain-down process) may be 1 / 2 of the chain-down gradient in FIG. 11A (i.e., in the case of the direct chain-down process), as will be understood (for example, as shown by Equations 17 to 20). As a specific numerical example regarding Equation 17, when the determined offset OFF is approximately 0.1 mm, RD1 = 37.125 mm, RD2 = 25.5 mm, and n = 25, Equation 17 should be DIR ≈ 0.03, which is approximately the same as the chain-down gradient observed in chain-down curve plot 1111 and can thus be used to approximately determine the offset OFF.

[0119] FIG. 11C is a graph 1130 showing long-distance error curve plots 1131 and 1133, where the long-distance error curve plot 1131 represents data before correction processing, and the long-distance error curve plot 1133 represents data after correction processing is executed according to the principles described herein (e.g., according to Equation 21 and / or other processing). More specifically, in various implementations, the chain-down gradient can be determined based on data as shown in either graph 1110 or graph 1120. As an example, in one particular implementation, determining the chain-down gradient may include applying a least-squares linear fit to the data.

[0120] The determined chain-down gradient may be used to determine an offset value OFF (e.g., corresponding to the radial offset of the scale part or the detection part), and this determination is made according to an equation (e.g., one of Equations 17 to 20), the determined chain-down gradient, or other calculation methods or techniques for obtaining the offset value based on the chain-down data. The determined offset value may be used to correct one or more values used to determine the relative position between the detection part and the scale part. For example, the determined offset value may be used to correct the spatial step value or other spatial value of the scale part according to Equation 21 or other calculations, and the corrected value may be used in one or more equations (e.g., Equation 12) or other calculations for determining the measured value (i.e., corresponding to the relative position between the detection part and the scale part).

[0121] As described above, the long-distance error curve plot 1133 represents the data after such correction processing. The corrected plot 1133 (i.e., there remains a gradient of error of approximately -0.2 μm per 1 mm of measurement) shows that it has been somewhat improved compared to the original error plot 1131 (i.e., there remains a gradient of error of approximately -2.67 μm per 1 mm of measurement). This can be sufficient or more for some practical applications (e.g., in contrast to the results shown in FIGS. 9A - 9C where a significantly high error level remained even after the correction processing). Such improved characteristics in FIGS. 11A - 11C may be at least partially due to some dimensional relationships in the implementation forms of FIGS. 3A and 4 compared to the implementation forms of FIGS. 6 and 7.

[0122] As described above, an important aspect of the implementation forms of FIGS. 3A and 4 is the large separation of the scale tracks. For some relationships (e.g., those shown by Equations 17 - 20), the large separation of the scale tracks in some examples can be represented by the relationship of (1 / RD2)-(1 / RD1). For the exemplary values RD2 = 25.5 mm and RD1 = 37.125 mm in the implementation forms of FIGS. 3A and 4, (1 / RD2)-(1 / RD1)=0.01228 mm -1 which corresponds to the desirable results in FIGS. 11A - 11C. This is in contrast to the implementation forms of FIGS. 6 and 7 which, for the exemplary values RD2 = 32.5 mm and RD1 = 37.125 mm, (1 / RD2)-(1 / RD1)=0.00383 mm -1 It can be contrasted. Note that the 0.01228 mm -1 coefficient is approximately 3.2 times better than the 0.00383 mm -1 coefficient with respect to the correction processing. In a specific implementation form, it may be desirable for the (1 / RD2)-(1 / RD1) coefficient to be at least 0.01 mm -1

[0123] ​Another way to represent / characterize a large separation of the scale tracks is by the ratio of RD1 / RD2. In the embodiments of FIGS. 3A and 4, RD1 / RD2 = 1.456. This can be contrasted with the implementations of FIGS. 6 and 7 where RD1 / RD2 = 1.142. In some implementations, it may be desirable for the ratio of RD1 / RD2 to be at least 1.4.

[0124] Another way to represent / characterize a large separation of the scale tracks is by the separation distance SEP12 between the first and second scale tracks, such as being related to the widths of the first and / or second scale tracks. In the implementations of FIGS. 6 and 7, the separation distance SEP12 is 1.25 mm, and it should be noted that this is smaller than the widths of the first and second scale tracks of 4.0 mm and 2.75 mm respectively. In contrast, in the implementations of FIGS. 3A and 4, the separation distance SEP12 is 8.25 mm, which is larger than the width of the first and / or second scale tracks. In various implementations, it may be desirable for the separation distance SEP12 to be larger than the width of the first scale track and larger than the width of the second scale track. In various implementations, it may be desirable for the separation distance SEP12 to be larger than the combined widths of the first and second scale tracks. In various implementations, it may be desirable for the separation distance SEP12 to be larger than a multiple of the width of the second scale track, such as larger than twice the width of the second scale track. In various implementations, the separation region between the first scale track and the second scale track has a width defined by the separation distance SEP12, and it may be further desirable for the separation region to be relatively empty (e.g., not including a scale element portion disposed in a track portion having a sensing element portion).

[0125] FIG. 12 shows some dimensions and features of i) the measuring instrument of FIG. 2 and ii) a part of a transducer TDR' that may be used in the measuring instrument of FIG. 2 and is configured to correspond to the arcuate motion between the detection part and the scale part and has a second large separation of the scale track. The transducer TDR' of FIG. 12 is configured to generate signals similar to those of the transducers TDR of FIGS. 3A and 4. FIG. 5 represents the signals resulting from the operation of the implementation form of FIG. 12 and also represents the signals resulting from the operation of the implementation forms of FIGS. 3A and 4. In this regard, during operation, the signals of the implementation form of FIG. 12 may be similar to the signals SIG1A, SIG1B, SIG2A, and SIG2B of the implementation form of FIG. 3A.

[0126] Also, it will be understood that each of the components of the transducer TDR of FIG. 3A has a corresponding component (such as may be designated with a prime symbol ') of the transducer TDR' of FIG. 12. Thus, the components of the transducer TDR' will be understood by those skilled in the art based on the corresponding components of the transducer TDR, except where otherwise described below. Thus, a complete description of the components of the transducer TDR' is not provided herein. The main differences between the transducer TDR' and the transducer TDR are some dimensional relationships, some of which are described in more detail below.

[0127] In the transducer of FIG. 12, the first scale element portion PRTSC1' is within a first scale track ST1' having a first scale track width STW1' (for example, the upper and lower ends 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 within a second scale track ST2' having a second scale track width STW2' (for example, the upper and lower ends 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 scale track ST2'. A separation region SEPA' is shown between the first scale track ST1' and the second scale track ST2' (for example, having a radial width defined by the separation distance SEP12' and 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 (for example, not including a scale element portion arranged in an encoder track portion having a sensing element portion).

[0128] The second scale element portion PRTSC2' of the second scale track ST2', which is included as part of the second encoder track portion, is closer to the rotating portion PPN than the first scale element portion PRTSC1' of the first scale track ST1', which is included as part of the first encoder track portion (for example, the radial distance RD2' of the second center reference point REF2' of the second scale element portion PRTSC2' of the second scale track portion ST2' of the second encoder track portion is smaller than the radial distance RD1' of the first center reference point REF1' of the first scale element portion PRTSC1' of the first scale track portion ST1' of the first encoder track portion). In various implementations, the reference point REF1' may be on the center line CL1', and the reference point REF2' may be on the center line CL2'. The differential distance D12' is shown as the difference in the distance between the center reference point REF1' and the center reference point REF2', and correspondingly, is also the difference between the first radial distance RD1' and the second radial distance RD2'.

[0129] 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 shown as being nominally equal, and in the example of FIG. 12, the nominal absolute angle measurement range θ ABS and the maximum angle movement range θ MAX are shown as being equal. In these examples, the arc lengths can be determined according to standard arc length formulas such as ARC1’ = RD1’(θ ABS ) and ARC2’ = RD2’(θ ABS ) (for example, θ ABS has a value in radians). As some specific exemplary dimensions, in one implementation, the first scale track width STW1’ may be 4.0 mm, the second scale track width STW2’ may be 2.75 mm, the separation distance SEP12’ may be 13.85 mm, the first radius distance RD1’ may be 38.725 mm, the second radius distance RD2’ may be 21.5 mm, and the differential distance D12’ may be 17.225 mm. In various implementations, such dimensions can provide some desirable operating characteristics, as will be described in more detail below.

[0130] FIGS. 13A - 13B show offsets (e.g., radial offsets of the scale portion or the detection portion) related to some features of FIG. 12. Note that FIGS. 13A and 13B are similar to FIGS. 10A and 10B and will be understood based on the description of FIGS. 10A and 10B, except where otherwise described below. The main difference between FIGS. 13A and 13B is the numerical example of the dimensions, which will be described in more detail below. In the illustration of FIG. 13A (for example, in various implementations, it may correspond to the condition where the radial offset is zero), the first central reference point REF1 Z ’ is at a radial distance RD1 Z ’ from the rotating portion PPN. The second central reference point REF2 Z ’ is at a radial distance RD2 from the rotating portion PPNZ is at

[0131] As some specific numerical examples, the diagram of FIG. 13A shows that the first radius distance RD1 Z ’ may be 38.725 mm, and the second radius distance RD2 Z ’ may be 21.5 mm (for example, corresponding to the numerical examples described above with respect to FIG. 12), and correspondingly, it shows that the differential distance D12’ may be 17.225 mm. As described above, in the diagram of FIG. 12, the numerical examples may further include that the first scale track width STW1’ may be 4.0 mm, the second scale track width STW2’ may be 2.75 mm, and the separation distance SEP12’ may be 13.85 mm.

[0132] In the diagram of FIG. 13B (for example, this may correspond to the condition of a positive radial offset OFF P in various implementation forms), the first central reference point REF1 P ’ (for example, the first scale element part PRTSC1’ of the first scale track ST1’) is shifted upward by an offset OFF P such that it is at a radius distance RD1 P ’ from the rotating part PPN. The second central reference point REF2 P ’ (for example, the second scale element part PRTSC2’ of the second scale track ST2’) is also shifted upward by the offset OFF P correspondingly and is at a radius distance RD2 P ’ from the rotating part PPN. Note that in FIG. 13B, the differential distance D12’ is shown as the same as that in FIG. 13A (for example, in some implementation forms, a certain known differential distance D12’ and / or corresponding characteristics may be regarded as being utilized as an internal reference for performing the self-correction described in this specification).

[0133] Also, in this example, the scale part may have a radial offset as shown, but the detection part including the sensing part has the central reference points REF1 Z ’ and REF2 ZIt should be noted that it may remain with '. Therefore, the radial offset of the scale part may be referred to as related to the detection part including the sensing part in some implementation forms (for example, in some implementation forms, the detection part including the sensing part may further or alternatively be referred to as having a radial offset with respect to the scale part). In an alternative example, at the position as shown in FIG. 13A, the scale part is the central reference point REF1 Z ’ and REF2 Z ’ remains, and at the position as shown in FIG. 13B, the sensing part may be switched such that it remains the central reference point central reference point REF1 P ’ and REF2 P ’ remains (for example, it may be described that the sensing part has a radial offset with respect to the scale part and / or the scale part has a radial offset with respect to the sensing part). As some specific numerical examples, the illustration in FIG. 13B shows that the first radial distance RD1 P ’ may be 38.825 mm, and the second radial distance RD2 P ’ may be 21.6 mm (for example, corresponding to a positive radial offset OFF P that can be 0.1 mm). A certain differential distance D12’ can continue to be 17.225 mm.

[0134] FIGS. 14A to 14C are schematic views of graphs 1410 to 1430 showing specific data resulting from the operation and correction processing of the transducer of FIG. 12 having the offset as shown in FIGS. 13A to 13B. The x-axis of graphs 1410 to 1430 relates to the arc distance along the first scale track TR1. Graphs 1410 to 1430 have some similarities with graphs 1110 to 1130 of FIGS. 11A to 11C and will be understood based at least in part on the description of FIGS. 11A to 11C, except as otherwise described below.

[0135] FIG. 14A is a graph 1410 of a chain-down curve plot 1411 of chain-down values for direct chain-down processing. FIG. 14B is a graph 1420 of a chain-down curve plot 1421 of chain-down values for double chain-down processing. As a specific numerical example regarding Equation 17, when the determined offset OFF is approximately 0.1 mm, RD1 = 38.725 mm, RD2 = 21.5 mm, and n = 25, Equation 17 should be DIR ≈ 0.05, which is approximately the same as the chain-down gradient observed in the chain-down curve plot 1411 and can thus be used to approximately determine the offset OFF.

[0136] FIG. 14C is a graph 1430 showing long-distance error curve plots 1431 and 1433, where the long-distance error curve plot 1431 represents data before correction processing, and the long-distance error curve plot 1433 represents data after correction processing is performed according to the principles described herein (e.g., according to Equation 21 and / or other processing). More specifically, in various implementations, the chain-down gradient can be determined based on data as shown in either graph 1410 or graph 1420. As an example, in one particular implementation, determining the chain-down gradient may include applying a least-squares linear fit to the data.

[0137] The determined chain-down gradient may be used to determine an offset value OFF (e.g., corresponding to the radial offset of the scale part or the detection part), and this determination is made according to an equation (e.g., one of Equations 17 to 20), the determined chain-down gradient, or other calculation methods and techniques for obtaining the offset value based on the chain-down data. The determined offset value may be used to correct one or more values used to determine the relative position between the detection part and the scale part. For example, the determined offset value may be used to correct the spatial step value or other spatial value of the scale part according to Equation 21 or other calculations, and the corrected value may be used in one or more equations (e.g., Equation 12) or other calculations for determining the measured value (i.e., corresponding to the relative position between the detection part and the scale part).

[0138] As described above, the long-distance error curve plot 1433 represents the data after such correction processing. The corrected plot 1433 (i.e., a gradient of about -0.1 μm error remains per 1 mm of measurement) shows that it is somewhat improved compared to the original error plot 1431 (i.e., a gradient of about -2.67 μm error remains per 1 mm of measurement). This may be sufficient or more for some practical applications (e.g., in contrast to the results shown in FIGS. 9A to 9C where a significantly high error level still remained after the correction processing). Such improved characteristics in FIGS. 14A to 14C may be at least partially due to some dimensional relationships in the implementation forms of FIGS. 12 to 13B compared to the implementation forms of FIGS. 6 and 7.

[0139] According to the principles described in this specification, an important aspect of the implementation forms of FIGS. 12 to 13B is the large separation of the scale tracks. For some relationships (e.g., those shown by Equations 17 to 20), the large separation of the scale tracks in some examples can be represented by the relationship of (1 / RD2)-(1 / RD1). For the exemplary values RD2 = 21.5 mm and RD1 = 38.725 mm of the implementation forms of FIGS. 12 to 13B, (1 / RD2)-(1 / RD1)=0.0269 mm -1 and this corresponds to the desirable results of FIGS. 14A to 14C. For the exemplary values RD2 = 32.5 mm and RD1 = 37.125 mm, (1 / RD2)-(1 / RD1)=0.00383 mm -1 which may be in contrast to the implementation forms of FIGS. 6 and 7 where it is. In some implementation forms, the (1 / RD2)-(1 / RD1) coefficient is at least 0.01 mm -1 or at least 0.015 mm -1 may be desirable.

[0140] Another way to represent / characterize the large separation of the scale tracks is by the ratio of RD1 / RD2. In the implementation forms of FIGS. 12 to 13B, RD1 / RD2 = 1.801. This may be in contrast to the implementation forms of FIGS. 6 and 7 where RD1 / RD2 = 1.142. In some implementation forms, it may be desirable for the ratio of RD1 / RD2 to be at least 1.4, or at least 1.5.

[0141] Another way to represent / characterize a large separation of the scale tracks is by the separation distance SEP12 between the first and second scale tracks, such as related to the widths of the first and / or second scale tracks. In the implementations of FIGS. 6 and 7, the separation distance SEP12 is 1.25 mm, which is smaller than the widths of the first and second scale tracks of 4.0 mm and 2.75 mm, respectively. In contrast, in the implementations of FIGS. 12 to 13B, the separation distance SEP12 is 13.85 mm, which is larger than the width of the first and / or second scale tracks. In various implementations, it may be desirable for the separation distance SEP12 to be larger than the width of the first scale track and larger than the width of the second scale track. In various implementations, it may be desirable for the separation distance SEP12 to be larger than the combined widths of the first and second scale tracks. In various implementations, it may be desirable for the separation distance SEP12 to be larger than a multiple of the width of the second scale track, such as larger than twice the width of the second scale track or larger than three times the width of the second scale track.

[0142] FIG. 15 shows some dimensions and features of i) the measuring instrument of FIG. 2 and ii) a part of the transducer TDR'' that may be used in the measuring instrument of FIG. 2 and is configured to correspond to the circular arc motion between the detection part and the scale part and has a second large separation of the scale tracks. The transducer TDR'' in FIG. 15 may have some different design features (e.g., n = 60 and m = 2, and the corresponding spatial step relationship according to Equation 1), but otherwise may be configured to operate substantially the same as the transducer TDR in FIGS. 3A and 4. Therefore, the components of the transducer TDR'' will be understood by those skilled in the art based on the corresponding components of the transducer TDR, except where otherwise explained below. Therefore, a complete description of the components of the transducer TDR'' is not provided herein. Some differences between the transducer TDR'' and the transducer TDR are some dimensional relationships, some of which are described in more detail below.

[0143] In the transducer of FIG. 15, the first scale element portion PRTSC1’’ is within a first scale track ST1’’ having a first scale track width STW1’’ (for example, the upper and lower ends 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 within a second scale track ST2’’ having a second scale track width STW2’’ (for example, the upper and lower ends 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 scale track ST2’’. A separation region SEPA’’ is shown between the first scale track ST1’’ and the second scale track ST2’’ (for example, having a radial width defined by the separation distance SEP12’’ and 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 (for example, not including a scale element portion arranged in an encoder track portion having a sensing element portion).

[0144] The second scale element part PRTSC2’’ of the second scale track ST2’’’, which is included as part of the second encoder track part, is closer to the rotating part PPN than the first scale element part PRTSC1’’ of the first scale track ST1’’’, which is included as part of the first encoder track part (for example, the radius distance RD2’’ of the second center reference point REF2’’ of the second scale element part PRTSC2’’ of the second scale track ST2’’ of the second encoder track part is smaller than the radius distance RD1’’ of the first center reference point REF1’’ of the first scale element part PRTSC1’’ of the first scale track part ST1’’ of the first encoder track part). In various implementations, the reference point REF1’’ may be on the center line CL1’’, and the reference point REF2’’ may be on the center line CL2’’. The differential distance D12’’ is shown as the difference in the distance between the center reference point REF1’’ and the center reference point REF2’’, and correspondingly, it is also the difference between the first radius distance RD1’’ and the second radius distance RD2’’.

[0145] The first scale element part PRTSC1’’ has a first angular range θ RG1 and a corresponding arc length ARC1’’, and the second scale element part PRTSC2’’’ has a second angular range θ RG2 and a corresponding arc length ARC2’’. The angular ranges θ RG1 and θ RG2 2 are shown as being nominally equal, and in the example of FIG. 15, they are shown as being equal to the nominal absolute angular measurement range θ ABS and the maximum angular movement range θ MAX . In these examples, the arc lengths are ARC1’’ = RD1’’(θ ABS ) and ARC2’’ = RD2’’(θ ABS ) (for example, θ ABSIt can be determined according to the formula of standard arc length (which has a value in radians). As some specific exemplary dimensions, in one implementation, the first scale track width STW1’’ may be 4.0 mm, the second scale track width STW2’’ may be 2.75 mm, the separation distance SEP12’’ may be 16.625 mm, the first radius distance RD1’’ may be 40 mm, the second radius distance RD2’’ may be 20 mm, and the differential distance D12’’ may be 20 mm. In various implementations, such dimensions can bring about some desirable operating characteristics, as will be described in more detail below.

[0146] Figures 16A - 16B show an offset in the first direction (e.g., the positive direction) (e.g., the radial offset of the scale part) related to some features of Figure 15. Figures 16A and 16B are similar to Figures 10A and 10B and will be understood based on the description of Figures 10A and 10B, except as otherwise described below. The main difference between Figures 16A and 16B is the numerical example of the dimensions, which will be described in more detail below. In the illustration of Figure 16A (e.g., in various implementations, it may correspond to the condition where the radial offset is zero), the first central reference point REF1 Z ’’ is at a radial distance RD1 Z ’’ from the rotating part PPN. The second central reference point REF2 Z ’’ is at a radial distance RD2 Z ’’ from the rotating part PPN.

[0147] As some specific numerical examples, the illustration of Figure 16A shows that the first radius distance RD1 Z ’’ may be 40 mm, and the second radius distance RD2 Z’’ may be 20 mm (for example, corresponding to the numerical example described above with respect to FIG. 15), indicating that the differential distance D12’’ may also be 20 mm correspondingly. As described above, in the illustration of FIG. 15, the numerical example may further include that the first scale track width STW1’’ may be 4.0 mm, the second scale track width STW2’’ may be 2.75 mm, and the separation distance SEP12’’ may be 16.625 mm.

[0148] In the diagram of FIG. 16B (for example, in various implementation forms, it may correspond to the condition of the positive radial offset OFF P ), the first center reference point REF1 P ’’ (for example, one of the first scale element parts PRTSC1’’ of the first scale track ST1’’) is shifted upward by the offset OFF P ’’ so as to be at a radial distance RD1 P ’’ from the rotating part PPN. The second center reference point REF2 P ’’ (for example, of the second scale element part PRTSC2’’ of the second scale track ST2’’) is also shifted upward by the offset OFF P ’’ so as to be at a radial distance RD2 P ’’ from the rotating part PPN correspondingly. Note that in FIG. 16B, the differential distance D12’’ is shown as the same as that in FIG. 16A (for example, in some implementation forms, a certain known differential distance D12’’ and / or the corresponding characteristics may be regarded as being utilized as an internal reference for performing the self-correction described in this specification).

[0149] Also, in this example, the scale part may have a radial offset as shown, but the detection part including the sensing part has the center reference points REF1 Z ’’ and REF2 ZIt should be noted that it may remain with ''. Therefore, the radial offset of the scale part may be referred to as related to the detection part including the sensing part in some implementation forms (for example, in some implementation forms, the detection part including the sensing part may be further or alternatively referred to as having a radial offset with respect to the scale part). In an alternative example, at the position as shown in FIG. 16A, the scale part is the central reference point REF1 Z '' and REF2 Z '' remains, and at the position as shown in FIG. 16B, the sensing part may be switched so that it remains the central reference point REF1 P '' and REF2 P '' remains (for example, it may be described that the sensing part has a radial offset with respect to the scale part, and / or it may be described that the scale part has a radial offset with respect to the sensing part). As some specific numerical examples, the figure of FIG. 16B shows that the first radius distance RD1 P '' may be 40.1 mm, and the second radius distance RD2 P '' may be 20.1 mm (for example, corresponding to a positive radial offset OFF P that can be 0.1 mm). A certain differential distance D12'' can continue to be 20 mm.

[0150] FIGS. 17A and 17B are respectively schematic views of graphs 1720 and 1730 showing specific data resulting from the operation and correction processing of the transducer of FIG. 15 having the offsets as shown in FIGS. 16A - 16B. The x - axes of graphs 1720 and 1730 relate to the arc distance along the first scale track TR1. Graphs 1720 and 1730 have some similarities with graphs 1120 and 1130 of FIGS. 11B and 11C and will be understood at least in part based on the description of FIGS. 11B and 11C, except as otherwise described below.

[0151] FIG. 17A is a graph 1720 of a chain-down curve plot 1721 of chain-down values in a double chain-down process. As a specific numerical example regarding Equation 19, when the determined offset OFF is approximately 0.1 mm, RD1 = 40 mm, RD2 = 20 mm, n = 60, and m = 2, Equation 19 should be DIR CDSLOPE

[0152] ≒ 0.075, which is approximately the same as the chain-down gradient observed in the chain-down curve plot 1721, and thus can be used to approximately determine the offset OFF. FIG. 17B is a graph 1730 showing long-distance error curve plots 1731, 1732, and 1733. The long-distance error curve plot 1731 represents data from the first scale track before correction processing. The long-distance error curve plot 1732 represents data from the second scale track before correction processing. The long-distance error curve plot 1733 represents data after correction processing is performed according to the principles described herein (e.g., according to Equation 21 and / or other processing). More specifically, in various implementations, the chain-down gradient can be determined based on data such as that shown in graph 1720. As an example, in one particular implementation, determining the chain-down gradient may include applying a least-squares linear fit to the data.

[0153] The determined chain-down gradient may be used to determine an offset value OFF (for example, corresponding to the radial offset of the scale part or the detection part), and this determination is made according to an equation (for example, one of Equations 19 to 20), the determined chain-down gradient, or other calculation methods and techniques for obtaining the offset value based on the chain-down data. The determined offset value may be used to correct one or more values used to determine the relative position between the detection part and the scale part. For example, the determined offset value may be used to correct the spatial step value or other spatial value of the scale part according to Equation 21 or other calculations, and the corrected value may be used in one or more equations (for example, Equation 12) or other calculations for determining the measured value (that is, corresponding to the relative position between the detection part and the scale part).

[0154] As described above, the long-distance error curve plot 1733 represents the data after such correction processing. The plot 1733 with correction applied (that is, a gradient of about -0.1 μm error remains per 1 mm of measurement) shows that it is somewhat improved compared to the original error plot 1731 (that is, a gradient of about -2.5 μm error remains per 1 mm of measurement). This may be sufficient or more for some practical applications (for example, in contrast to the results shown in FIGS. 9A to 9C where a significantly high error level still remained after the correction processing). Such improved characteristics in FIGS. 17A to 17B may be at least partially due to some dimensional relationships in the implementation forms of FIGS. 15 to 16B compared to the implementation forms of FIGS. 6 and 7.

[0155] According to the principles described in this specification, an important aspect of the implementations of FIGS. 15 to 16B is the large separation of the scale tracks. For some relationships (e.g., those shown by Equations 19 to 20), the large separation of the scale tracks in some examples can be represented by the relationship of (1 / RD2) - (1 / RD1). For the exemplary values of RD2 = 20 mm and RD1 = 40 mm in the implementations of FIGS. 15 to 16B, (1 / RD2) - (1 / RD1) = 0.02500 mm -1 which corresponds to the desired results of FIGS. 17A to 17B. This is, for the exemplary values of RD2 = 32.5 mm and RD1 = 37.125 mm, (1 / RD2) - (1 / RD1) = 0.00383 mm -1 and can be contrasted with the implementations of FIGS. 6 and 7 which is (1 / RD2) - (1 / RD1). In some implementations, the (1 / RD2) - (1 / RD1) coefficient is at least 0.01 mm -1 or at least 0.015 mm -1 or at least 0.017 mm -1 or at least 0.020 mm -1 may be desirable in some cases.

[0156] Another way to represent / characterize the large separation of the scale tracks is by the ratio of RD1 / RD2. In the implementations of FIGS. 15 to 16B, RD1 / RD2 = 2.0. This can be contrasted with the implementations of FIGS. 6 and 7 where RD1 / RD2 = 1.142. In some 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.

[0157] Another way to represent / characterize a large separation of the scale tracks is by the separation distance SEP12 between the first and second scale tracks, such as related to the widths of the first and / or second scale tracks. In the implementations of FIGS. 6 and 7, note that the separation distance SEP12 is 1.25 mm, which is smaller than the first and second scale track widths of 4.0 mm and 2.75 mm, respectively. In contrast, in the implementations of FIGS. 15 - 16B, the separation distance SEP12 is 16.625 mm, which is larger than the width of the first and / or second scale track. In various implementations, the separation distance SEP12 may desirably be larger than the width of the first scale track and larger than the width of the second scale track. In various implementations, the separation distance SEP12 may desirably be larger than the combined widths of the first and second scale tracks. In various implementations, the separation distance SEP12 may desirably be larger than a multiple of the width of the second scale track, such as more than twice the width of the second scale track, or more than three times the width of the second scale track, or more than four times the width of the second scale track.

[0158] FIGS. 18A - 18B are related to some features of FIG. 15 and show an offset in the second direction (e.g., negative direction) (e.g., a radial offset of the scale portion). FIGS. 18A and 18B are similar to FIGS. 16A and 16B and will be understood based on the description of FIGS. 16A and 16B, except that they have an offset OFFn in the negative direction and except as otherwise described below. In the illustration of FIG. 18A (e.g., in various implementations, it may correspond to the condition where the radial offset is zero), the first center reference point REF1 Z ’’ is at a radial distance RD1 Z ’’ from the rotating part PPN. The second center reference point REF2 Z ’’ is at a radial distance RD2 Z ’’ from the rotating part PPN. Note that FIG. 18A is the same as FIG. 16A and will be understood based on the above description of FIG. 16A.

[0159] In the illustration of FIG. 18B (e.g., in various implementations), the first central reference point REF1n’’ (e.g., of the first scale element portion PRTSC1’’ of the first scale track ST1’’) is shifted downward by an offset OFFn such that it is at a radial distance RD1n’’ from the rotating portion PPN. The second central reference point REF2n’’ (e.g., of the second scale element portion PRTSC2’’ of the second scale track ST2’’) is also shifted downward by the offset OFFn accordingly and is at a radial distance RD2n’’ from the rotating portion PPN. Note that in FIG. 18B, the differential distance D12’’ is shown as the same as in FIGS. 16A and 18A (e.g., in some implementations, a certain known differential distance D12’’ and / or corresponding characteristics may be considered to be utilized as an internal reference for performing the self-correction described herein).

[0160] Also, in this example, the scale portion may have a radial offset as shown, but the detection portion including the sensing portion may have the central reference points REF1 Z ’’ and REF2 Z ’’ remaining as shown in FIGS. 16A and 18A. It should be noted that thus, the radial offset of the scale portion may, in some implementations, be referred to as being related to the detection portion including the sensing portion (e.g., in some implementations, the detection portion including the sensing portion may further or alternatively be referred to as having a radial offset with respect to the scale portion). In an alternative example, at the position as shown in FIG. 18A, the scale portion has the central reference points REF1 Z ’’ and REF2 Z’’ remains as it is, and may be switched so that the sensing unit remains at the central reference points REF1n’’ and REF2n’’ as shown in FIG. 18B (for example, it may be described that the sensing unit has a radial offset with respect to the scale unit, and / or the scale unit has a radial offset with respect to the sensing unit). As some specific numerical examples, the figure of FIG. 18B shows that the first radial distance RD1n’’ may be 39.9 mm, and the second radial distance RD2n’’ may be 19.9 mm (for example, corresponding to a positive radial offset OFFn that can be 0.1 mm). The constant differential distance D12’’ can continue to be 20 mm.

[0161] FIGS. 19A and 19B are schematic views of graphs 1920 and 1930 showing specific data resulting from the operation and correction processing of the transducer of FIG. 15 having the offsets as shown in FIGS. 18A to 18B, respectively. The x - axes of graphs 1920 and 1930 relate to the arc distance along the first scale track TR1. Graphs 1920 and 1930 have a certain similarity to graphs 1720 and 1730 of FIGS. 17A and 17B, but are different in that they correspond to the condition of a negative offset instead of a positive offset. It will be understood that any of the implementations as described herein may similarly operate with a negative offset (for example, such an operation may be equivalent to the operation in the case of a positive offset, as shown by comparing the operations of FIGS. 19A and 19B with those of FIGS. 17A and 17B).

[0162] FIG. 19A is graph 1920 of the chain - down curve plot 1921 of the chain - down values of the double - chain - down process. As a specific numerical example for Equation 19, when the determined offset OFF is about - 0.1 mm (i.e., corresponding to a negative offset), RD1 = 40 mm, RD2 = 20 mm, n = 60, and m = 2, Equation 19 gives CDSLOPE DIRIt should be approximately -0.075, which is approximately the same as the chain-down gradient observed in the chain-down curve plot 1921, and thus can be used to approximately determine the offset OFF.

[0163] FIG. 19B is a graph 1930 showing long-distance error curve plots 1931, 1932, and 1933. The long-distance error curve plot 1931 represents data from the first scale track before correction processing. The long-distance error curve plot 1932 represents data from the second scale track before correction processing. The long-distance error curve plot 1933 represents data after correction processing is performed according to the principles described herein (e.g., according to Equation 21 and / or other processing). More specifically, in various implementations, the chain-down gradient can be determined based on data such as that shown in graph 1920. As an example, in one particular implementation, determining the chain-down gradient may include applying a least-squares linear fit to the data.

[0164] The determined chain-down gradient may be used to determine an offset value OFF (e.g., corresponding to the radial offset of the scale portion or the detection portion). This determination is made according to an equation (e.g., one of Equations 19 - 20), the determined chain-down gradient, or other calculation methods or techniques for obtaining the offset value based on the chain-down data. The determined offset value may be used to correct one or more values used to determine the relative position between the detection portion and the scale portion. For example, the determined offset value may be used to correct the spatial step value or other spatial value of the scale portion according to Equation 21 or other calculations, and the corrected value may be used in one or more equations (e.g., Equation 12) or other calculations for determining a measured value (i.e., corresponding to the relative position between the detection portion and the scale portion).

[0165] As described above, the long-distance error curve plot 1933 represents the data after such correction processing. The corrected plot 1933 (i.e., there remains a gradient of error of approximately 0.1 um per 1 mm of measurement) shows that it has been somewhat improved compared to the original error plot 1931 (i.e., there remains a gradient of error of approximately 2.5 um per 1 mm of measurement). This may be sufficient or more for some practical applications (e.g., in contrast to the results shown in FIGS. 9A - 9C where a significantly high error level remained even after the correction process). Such improved characteristics in FIGS. 19A - 19B may be at least partially due to some dimensional relationships in the implementation forms of FIGS. 15 - 16B compared to the implementation forms of FIGS. 6 and 7.

[0166] According to the principles described herein, an important aspect of the implementation forms of FIGS. 15 - 16B is the large separation of the scale tracks. Various aspects and relationships regarding the large separation of the scale tracks in the implementation forms of FIGS. 15 - 16B are described above following the description of FIGS. 17A and 17B.

[0167] FIG. 20 is a flowchart showing an operating method 2000 of a measuring instrument with an arc motion for measuring the relative position between a detection unit and a scale unit. Block 2010 includes receiving a detection signal from the detection unit 167, and the detection signal includes: i) a detection signal from a first set SET1SEN1 of first detection elements operating in conjunction with the first signal modulation scale element SME1; and ii) a detection signal from a first set SET1SEN2 of second sensing elements operating in conjunction with the second signal modulation scale element SME2. The maximum movement range of the arc motion of the movable encoder unit is less than 360 degrees. The first scale element unit is arranged with a central reference point at a first radius distance RD1 from the rotating part, the second scale element unit is arranged with a central reference point at a second radius distance RD2 from the rotating part, and the ratio of RD1 / RD2 is at least 1.4. Block 2030 includes determining the relative position between the detection unit 167 and the scale unit 170 based at least in part on the detection signal input from the detection unit 167.

[0168] In connection with the operation in block 2030 that determines the relative position between the detection unit (167) and the scale unit (170) based at least in part on the detection signal from the detection unit, various processing and / or signal synthesis techniques may be utilized (e.g., as will be understood by those skilled in the art and at least in part in accordance with the teachings of the incorporated references). Briefly, in various implementations, two driving operations may be utilized for the generation and processing of the signal from the detection unit. In various implementations, the two driving operations may be performed simultaneously or at different timings.

[0169] Specifically, as part of the first driving operation, the first magnetic field generating element unit PRTFGE1 can be driven (e.g., by a corresponding driving signal from the signal processing configuration 166). When the first magnetic field generating element unit PRTFGE1 is driven, corresponding signals (e.g., signals SIG1A, SIG1B) from the first sensing element SEN1 of the first sensing element unit PRTSEN1 of the detection unit are read out (e.g., received, processed, etc.). As part of the second driving operation, the second magnetic field generating element unit PRTFGE2 can be driven (e.g., by a corresponding driving signal from the signal processing configuration 166). When the second magnetic field generating element unit PRTFGE2 is driven, corresponding signals (e.g., signals SIG2A and SIG2B) from the second sensing element SEN2 of the second sensing element unit PRTSEN2 of the detection unit can be read out (e.g., received, processed, etc.). The detection signals generated during the first and second driving operations (i.e., from the detection unit) may be utilized to determine the relative position (e.g., the absolute position between the detection unit and the scale unit). In various implementations, the detection signals may include four signals (e.g., SIG1A, SIG1B, SIG2A, SIG2B) such as the signals SIG1A and SIG1B of the first driving operation and the signals SIG2A and SIG2B of the second driving operation, which may be utilized to determine the relative position.

[0170] FIG. 21 is a flowchart showing a correction processing method 2100 of a measuring instrument with an arc motion. Block 2110 includes providing a drive signal that causes the magnetic field generation unit PRTFGE to generate a changing magnetic flux. Block 2120 includes receiving, from the detection unit 167, a detection signal including i) a detection signal from a first set SET1SEN1 of first detection elements operating in conjunction with the first signal modulation scale element SME1, and ii) a detection signal from a first set SET1SEN2 of second sensing elements operating in conjunction with the second signal modulation scale element SME2. Block 2130 includes determining an offset value corresponding to a radial offset of a scale unit including the first signal modulation scale element and the second signal modulation scale element, based at least in part on the received detection signal. Block 2140 includes correcting one or more values used to determine a relative position between the detection unit and the scale unit, using the determined offset value. For example, the determined offset value can be used according to Equation 21 or the spatial step value of the scale unit or other calculations for correcting other spatial values, and can be used in one or more equations (e.g., Equation 12, etc.) or other calculations for determining a measurement value (i.e., corresponding to the relative position between the detection unit and the scale unit).

[0171] In various implementations, the determination of the offset value in block 2130 includes determining a differential gradient (e.g., a chain down gradient). In various implementations, the differential gradient can correspond to a gradient of a difference between an absolute position signal and at least one of the following: i) a first position signal corresponding at least in part to a detection signal from a first sensing element (e.g., as part of the direct chain down processing described herein), or ii) a second position signal corresponding at least in part to a detection signal from a second sensing element (e.g., as part of the first step of the double chain down processing described herein). In various implementations, the difference between the absolute position signal and at least one of the first position signal or the second position signal corresponds at least in part to a phase difference between the respective signals (e.g., as shown by Equations 9, 10, 14, and 15).

[0172] In various implementation forms, correcting one or more values using the offset value determined at block 2140 includes, at least in part, dividing the determined offset value by the radial distance of the first scale element sub - part. For example, as shown by Equation 21, the correction value is obtained by dividing the determined offset value OFF D by the radial distance RD1 of the first scale element part and multiplying by the spatial step of the first scale element part (e.g., θ WSME1 ). The correction value (i.e., corresponding to - θ WSME1 (OFF D / RD1)) is added to the spatial step value of the first scale element part (e.g., added to θ WSME1 ) to determine the corrected spatial step value θ WSME1C , and the corrected spatial step value θ WSME1C is then used (e.g., in Equation 12 or other calculations) to determine the relative position between the detection part and the scale part (e.g., as part of a measurement operation). In various implementation forms, method 2100 (e.g., configured to be executed by a signal processing configuration) further includes determining the absolute relative position between the detection part and the scale part based at least in part on a detection signal input from the detection part, and the detection signal includes a detection signal from a first set of first sensing elements and a detection signal from a second set of second sensing elements (e.g., similar to block 2030 in FIG. 20 and may correspond to entering a normal measurement mode to perform a normal measurement operation after the calibration process is completed).

[0173] Generally, in an implementation configured such that there is a relatively large difference between the first radial distance of the first scale element portion and the corresponding first scale track, and the second radial distance of the second scale element portion and the corresponding second scale track, in accordance with the principles described herein (for example, or otherwise, if there is a large difference in the position of the scale tracks), the influence of the radial offset / misalignment (e.g., of the scale portion with respect to the sensing portion of the detection unit) is also relatively large. This effect / difference can be confirmed or detected through a process of determining an integer value of the spatial step (e.g., corresponding to the integer of the signal modulation element in the scale element portion of the scale track) as part of the determination of the absolute measurement value. For example, as part of the chain-down process, a rounding process is included when determining the integer value of the spatial step, and the rounded amount is referenced as the chain-down value. A chain-down gradient (e.g., determined from the chain-down curve plot of the chain-down value or determined from the chain-down value) can be determined for use in determining an offset value (e.g., corresponding to the radial offset of the scale portion in relation to the sensing portion of the detection unit and / or in relation to the rotating portion or other reference, or corresponding to the radial offset of the sensing portion of the detection unit in relation to the scale portion and / or in relation to the rotating portion or other reference). The determined offset value may be used to correct one or more values used to determine the relative position between the detection unit and the scale portion. For example, a value (e.g., corresponding to the spatial step or absolute measurement range or other spatial value of the first scale element portion and the corresponding first scale track, used as part of the determination of the absolute measurement value) is corrected (e.g., as part of the correction and / or calibration process) and subsequently can be used as part of the determination of the absolute measurement value (e.g., corresponding to the determination of the relative position between the detection unit and the scale portion).

[0174] In various implementation forms, the correction process can be executed as part of a calibration procedure (i.e., a calibration process). As part of such a process, the measuring instrument can be put into a calibration mode (for example, when the measuring device is first assembled, after the movable encoder part MEP is coupled to the support member MEPSM, or when calibration is carried out at any other arbitrary timing). Measurement data (for example, corresponding to the detection signal received from the detection unit) can be collected in the memory as the measuring instrument moves in an arc motion over a range of positions (for example, involving relative movement between the scale part and the detection part). The measurement data can be analyzed to calculate an offset value (for example, a value corresponding to the radial offset of the movable encoder part MEP, corresponding to the radial offset of the scale part with respect to the detection unit, or corresponding to the radial offset of the detection unit with respect to the scale part, etc.). The determination of the offset value can include determining a differential gradient (for example, a chain-down gradient). In various implementation forms, when the differential gradient is very large, the data set may wrap around (for example, jump from -0.5 to +0.5 or from +0.5 to -0.5), and in this case, a de-wrapping process is executed or enabled to calculate the overall differential gradient. In various implementation forms, the offset value can be determined from the differential gradient. The determined offset value can then be used to correct one or more values used to determine the relative position between the detection unit and the scale part. When the calibration is completed, the measuring instrument can be put into, or may enter, a normal operating mode (for example, while accurate measurement values can be determined based on the fact that the calibration has been carried out). It will be understood that such calibration helps to ensure the accuracy of the measuring instrument, particularly with respect to the radial offset (for example, regarding the coupling of the movable encoder part MEP to the support member MEPSM, regarding the assembly and / or manufacturing tolerances of the components, regarding the radial offset that can occur in the relative position between the scale part and the detection part, etc.).

[0175] Some of the examples described herein are primarily related to an electronic position encoder having an arcuate motion and an arcuate encoder track portion. However, some similar or identical principles may be applied to an electronic position encoder having an arcuate motion and a linear encoder track portion, and it will be understood that the techniques described herein may be similarly applicable. Some examples of electronic position encoders having an arcuate motion and a linear encoder track portion are described in U.S. Patent Application No. 18 / 391,275, filed December 20, 2023, which is hereby incorporated by reference in its entirety. Some examples of electronic position encoders having an arcuate motion and an arcuate encoder track portion are described in U.S. Patent Application No. 18 / 391,294, filed December 20, 2023, which is hereby incorporated by reference in its entirety. Each of these applications describes specific design principles that can be utilized in combination with the teachings described herein to form an electronic position encoder having the characteristics and operations as described herein.

[0176] As used herein, the term "nominal" encompasses variations in one or more parameters that fall within an acceptable tolerance. By way of example, in one implementation, terms such as "nominal" may correspond to a minimum variance from a specified value (e.g., less than 5%, or less than 2%, or less than 1% variance, etc., according to an acceptable tolerance).

[0177] The principles disclosed and claimed in this specification will be understood to be capable of being readily and desirably combined with the various features disclosed in the incorporated references. The various implementations described above may be combined to provide further implementations. All of the U.S. patents and U.S. patent applications referred to in this specification are hereby incorporated by reference in their entirety. Aspects of the embodiments may be modified, as necessary, to employ concepts of various patents and applications to provide further embodiments. These and other changes can be made in implementation in light of the above detailed description. Generally, in the following claims, the terms used should not be construed as limiting the claims to the specific implementations disclosed in this specification and the claims, but rather the claims should be construed to include all possible implementations along with the full scope of equivalents to which such claims are entitled.

Claims

1. a movable part configured to rotate in an arc motion about a pivot part, the movable part including a movable encoder part; an electronic position encoder configured to measure an absolute relative position between a detector portion and a scale portion, the movable encoder portion of the movable portion having one of the detector portion or the scale portion; Equipped with The electronic position encoder comprises: A scale portion, a first scale element portion including a first signal modulating scale element; and a second scale element portion including a second signal modulating scale element; a scale portion having a scale direction and extending along the scale direction; A detection unit, A magnetic field generating unit configured to generate a magnetic flux that changes in response to a drive signal; A sensing unit, a first sensing element portion including a first set of first sensing elements and disposed in a first track portion with the first scale element portion; and a second sensing element portion including a first set of second sensing elements and disposed in a second track portion with the second scale element portion; A sensing unit having a detection unit configured to approach the scale unit by a relative movement between the detection unit and the scale unit caused by the arcuate motion of the movable encoder unit; Equipped with a maximum range of movement of the arcuate motion of the movable encoder portion is less than 360 degrees; the first scale element portion is disposed with a central reference point at a first radial distance RD1 from the pivot portion, and the second scale element portion is disposed with a central reference point at a second radial distance RD2 from the pivot portion, the ratio RD1 / RD2 being at least 1.4; Measuring instrument.

2. The ratio of RD1 / RD2 is at least 1.5; The measuring device of claim 1 .

3. the first and second scale element portions are in first and second scale tracks having first and second scale track widths, respectively, and a separation distance SEP12 between the first and second scale tracks is greater than the first scale track width and greater than the second scale track width; The measuring device of claim 1 .

4. the separation distance SEP12 is greater than the combined first and second scale track widths; The measuring device according to claim 3.

5. a separation region between the first scale track and the second scale track has a width defined by the separation distance SEP12, and the separation region does not include a scale element portion disposed in a track portion having a sense element portion. The measuring device according to claim 3.

6. a signal processing arrangement operatively connected to the detection portion for providing the drive signal, the signal processing arrangement being configured to determine an absolute relative position between the detection portion and the scale portion based at least in part on detection signals input from the detection portion, the detection signals including detection signals from the first set of the first sensing elements and detection signals from the first set of the second sensing elements; The measuring device of claim 1 .

7. a first magnetic field generating element portion disposed on 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; a second magnetic field generating element portion disposed on the second track portion and configured to operate in conjunction with second signal modulating scale elements of the second scale element portion and the second sensing elements of the second sensing element portion; The measuring device of claim 1 , comprising:

8. the first and second scale element portions of the first and second track portions are arcuate and parallel to each other, the second track portion being closer to the pivot portion than the first track portion; The first signal modulating scale element has a first signal modulating element angular spatial step θ ＷＳＭＥ１ and the second signal modulating scale elements are arranged along the first scale element portion according to the first signal modulating element angular spatial step θ ＷＳＭＥ１ The second signal modulation element angle space step θ ＷＳＭＥ２ and arranged along the second scale element portion according to The first and second scale element portions correspond to an absolute angular range θ ＡＢＳ To define The measuring device of claim 1 .

9. The signal modulating element angular space step θ ＷＳＭＥ２ / θ ＷＳＭＥ１ The ratio of may be expressed according to being equal to at least one of the following formulas: (nm / (n-1)), (nm / (n+1)), ((nm+1) / n), ((nm-1) / n), n is a positive integer and m is a positive integer that is at least 2; The measuring device according to claim 8.

10. The absolute angle range θ ＡＢＳ is nθ ＷＳＭＥ１ Or nθ ＷＳＭＥ２ where n is a positive integer and the absolute angle range θ ＡＢＳ is less than 360 degrees, 9. The measuring device of claim 8.

11. the first scale element portion has an arc length ARC1 at the first radial distance RD1 from the pivot portion, and the second scale element portion has an arc length ARC2 at the second radial distance RD2 from the pivot portion, where ARC2 / ARC1=RD2 / RD1. The measuring device of claim 1 .

12. operation of the first track portion comprises a first set of the first sensing elements providing detection signals responsive to a local effect on a changing magnetic flux provided by a first signal modulating scale element of the first scale element portion; Operation of the second track portion comprises a first set of the second sensing elements providing detection signals responsive to a local effect on a changing magnetic flux provided by a second signal modulating scale element of the second scale element portion. The measuring device of claim 1 .

13. the first sensing element portion further comprising one or more additional sets of first sensing elements, each additional set of first sensing elements having a spatial phase offset relative to the first set of first sensing elements; the second sensing element portion further comprising one or more additional sets of second sensing elements, each additional set of second sensing elements having a spatial phase offset relative to the first set of second sensing elements. The measuring device of claim 1 .

14. the first and second signal modulating scale elements comprise conductive plates and the first and second sensing elements comprise conductive loops. The measuring device of claim 1 .

15. 1. A method of operating a meter, comprising: The measuring instrument is a movable part that rotates in an arc motion around a rotating part, the movable part including a movable encoder part; an electronic position encoder configured to measure an absolute relative position between a detector portion and a scale portion, the movable encoder portion of the movable portion having one of the detector portion or the scale portion; Equipped with The electronic position encoder comprises: A scale portion, a first scale element portion including a first signal modulating scale element; and a second scale element portion including a second signal modulating scale element; a scale portion having a scale direction and extending along the scale direction; A detection unit, A magnetic field generating unit configured to generate a magnetic flux that changes in response to a drive signal; A sensing unit, a first sensing element portion including a first set of first sensing elements and disposed in a first track portion with the first scale element portion; and a second sensing element portion including a first set of second sensing elements and disposed in a second track portion with the second scale element portion; A sensing unit having having a detection unit configured to approach the scale unit by a relative movement between the detection unit and the scale unit caused by the arcuate motion of the movable encoder unit; Equipped with The method comprises: Supplying a drive signal to the magnetic field generating unit to generate a varying magnetic flux; receiving a detection signal from the detection unit, the detection signal comprising: a detection signal from the first set of first sensing elements operatively associated with the first signal modulating scale element; a detection signal from the first set of second sensing elements operatively associated with the second signal modulating scale elements; Equipped with receiving a detection signal from the detection unit; a maximum range of movement of the arcuate motion of the movable encoder portion is less than 360 degrees; the first scale element portion is disposed with a central reference point at a first radial distance RD1 from the pivot portion, and the second scale element portion is disposed with a central reference point at a second radial distance RD2 from the pivot portion, the ratio RD1 / RD2 being at least 1.4; How to operate the instrument.

16. the first and second scale element portions are in first and second scale tracks having first and second scale track widths, respectively, and a separation distance SEP12 between the first and second scale tracks is greater than the first scale track width and greater than the second scale track width; The method of claim 15.

17. determining a relative position between the detection unit and the scale unit based at least in part on the detection signal input from the detection unit. The method of claim 15.

18. Operating the first set of first sensing elements in conjunction with the first signal-modulating scale elements includes the first set of first sensing elements providing detection signals responsive to a local effect on a changing magnetic flux provided by a first signal-modulating scale element of the first scale element portion, Operating the first set of second sensing elements in conjunction with the second signal-modulating scale elements includes the first set of second sensing elements providing detection signals responsive to a local effect on a changing magnetic flux provided by the second signal-modulating scale elements of the second scale element portion. The method of claim 15.

19. 1. An electronic position encoder configured to measure an absolute relative position between a detection portion and a scale portion, for use in a measuring instrument having a movable portion configured to rotate in an arc motion, the electronic position encoder comprising: A scale portion, a first scale element portion including a first signal modulating scale element; and a second scale element portion including a second signal modulating scale element; a scale portion having a scale direction and extending along the scale direction; A detection unit, A magnetic field generating unit configured to generate a magnetic flux that changes in response to a drive signal; A sensing unit, a first sensing element portion including a first set of first sensing elements and disposed in a first track portion with the first scale element portion; and a second sensing element portion including a first set of second sensing elements and disposed in a second track portion with the second scale element portion; A sensing unit having having a detection unit configured to approach the scale unit by a relative movement between the detection unit and the scale unit caused by the arcuate motion of the movable encoder unit; Equipped with a maximum range of movement of the arcuate motion of the movable encoder portion is less than 360 degrees; the first scale element portion is disposed with a central reference point at a first radial distance RD1 from the pivot portion, and the second scale element portion is disposed with a central reference point at a second radial distance RD2 from the pivot portion, the ratio RD1 / RD2 being at least 1.4; Electronic position encoder.

20. the first and second scale element portions are in first and second scale tracks having first and second scale track widths, respectively, and a separation distance SEP12 between the first and second scale tracks is greater than the first scale track width and greater than the second scale track width; 20. An electronic position encoder according to claim 19.

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