JPWO2019039344A1 - Encoder - Google Patents

Abstract

The encoder 10 is an M sensor that detects a plurality of elements indicating angles arranged at predetermined angular intervals on the base body and generates a first signal having periodicity, and the M sensors 31 to 34 include: The predetermined angle is an angle obtained by combining 360 / M × (j−1) (degrees) and 360 / N × MOD [(kj−1) / D] (degrees). Where M is an integer of 2 or more, N is the number of elements, MOD is a function that outputs a value after the decimal point of the input value, D is a divisor of M or M, except for 1 except j Is an integer from 1 to M and takes different values for the M sensors, and kj is an integer from 1 to M. For each of the M sensors and each of the M sensors, Generators 41 to 44 that generate second signals that interpolate the predetermined angular interval based on the first signal, A calculator 50 for summing the second signals for the M sensors to obtain an angular position or a rotation angle.

Description

  The present invention relates to an encoder for detecting a position and an angle.

  The encoder is a device that reads scales written at equal angular intervals written on a scale and measures positions such as a rotation angle and an absolute angle position. Since the accuracy of the scale is naturally limited by the accuracy of writing and the accuracy of the sensor for detecting the scale, the improvement of the resolution by the scale is also limited. Therefore, a sine wave that further divides the minimum graduation interval is generated two analog signals whose phases are shifted from each other by 90 degrees, and the two analog signals are subjected to arctan operation to determine an angle using an interpolation signal representing the angle. To improve the resolution.

  Further, in order to reduce a scale writing error, an encoder mounting error, and the like, a method of arranging a plurality of sensors and averaging interpolation signals obtained from each sensor is used. In addition, a method has been proposed in which a sensor for calibration is further provided to perform self-calibration of an angle error (for example, see Patent Document 1).

JP 2011-99804 A

  An object of the present invention is to provide a new and useful encoder capable of achieving both high resolution and high accuracy.

According to one embodiment of the present invention, there are provided M sensors that detect a plurality of elements indicating angles arranged at predetermined angular intervals on a substrate and generate a first signal having a periodicity. Are arranged at a predetermined angle, and the predetermined angle is an angle obtained by combining 360 / M × (j−1) (degrees) and 360 / N × MOD [(k _j −1) / D]. Where M is an integer of 2 or more, N is the number of elements, MOD is a function that outputs a value after the decimal point of the input value, D is a divisor of M or M, except for 1 , J are integers from 1 to M and take different values for the M sensors, and k _j is an integer from 1 to M, for each of the M sensors and each of the M sensors. A generator for generating a second signal interpolating the predetermined angular interval based on the first signal; An arithmetic unit for calculating an angular position or a rotation angle by adding the second signals to the sensor.

According to the above aspect, M sensors provide 360 / M × (j−1) (degrees) and 360 / N × MOD [ (K _j −1) / D] (degrees), and thereby interpolates the predetermined angular interval generated based on the first signal generated by the sensor. The angular error of the encoder due to the angular error of the second signal can be reduced, and the error due to the eccentricity due to the attachment of the base to the rotating shaft and the error in the formation position of a plurality of elements arranged at equal angular intervals. The angle error of the encoder can be reduced, and as a result, an encoder having both high resolution and high accuracy can be provided.

According to another aspect of the present invention, there are provided M sensors for detecting a plurality of elements indicating positions arranged at predetermined intervals on a base and generating a first signal having periodicity, wherein the M sensors Are spaced apart from each other by a predetermined distance, and the predetermined distance is an integer (m _j ) times the predetermined interval (gl), ie, gl × m _j , and gl × MOD [(k _j −1) / D], where M is an integer greater than or equal to 2, MOD is a function that outputs the fractional part of the input value, and D is a divisor of M or M. _Kj is an integer from 1 to M, excluding 1. For each of the M sensors and each of the M sensors, interpolation is performed between the elements at the predetermined interval based on the first signal. A second signal for generating a second signal for the M sensors; Alternatively, there is provided an encoder including: a calculator for calculating a movement amount.

According to the above aspect, the M sensors provide, for the base on which the plurality of elements indicating the positions at the predetermined intervals are arranged, gl × m _j that is an integer (m _j ) times the predetermined interval (gl). gl × MOD [(k _j −1) / D], the second position interpolating the predetermined interval generated based on the first signal generated by the sensor. The position error of the encoder due to the position error of the signal of the encoder can be reduced, and the error of the encoder due to the position error due to the attachment of the base to the object and the error of the formation position of the plurality of elements arranged at the predetermined interval are also reduced. As a result, it is possible to provide an encoder that achieves both high resolution and high accuracy.

It is a figure showing the angle error of a rotary encoder. FIG. 2 is a diagram showing a discrete Fourier transform (DFT) analysis of the angle error shown in FIG. 1 of the rotary encoder. FIG. 2 is a diagram illustrating an angle error of an interpolation signal included in FIG. 1 of the rotary encoder. FIG. 1 is a diagram illustrating a schematic configuration of an encoder according to a first embodiment of the present invention. FIG. 2 is a diagram illustrating an arrangement position of a sensor of the encoder according to the first embodiment of the present invention. It is a figure showing an example of an arrangement position of each sensor in a 1st embodiment of the present invention. FIG. 3 is a diagram illustrating an angle error of an interpolation signal of the encoder according to the first embodiment of the present invention. FIG. 3 is a diagram illustrating an angle error of the encoder according to the first embodiment of the present invention. FIG. 4 is a diagram illustrating a DFT analysis of an angle error of the encoder according to the first embodiment of the present invention. It is a figure showing the schematic structure of the encoder concerning a 2nd embodiment of the present invention. It is a figure showing an example of an arrangement position of each sensor in a 2nd embodiment of the present invention.

  The inventor of the present application has been conducting research to improve the resolution and accuracy of the rotary encoder, but has encountered the following problem and found a solution to the problem.

  In the rotary encoder, a scale plate having a scale of 360 degrees is read by a sensor, and a sine wave and a cosine wave are generated based on the scale to generate a signal for interpolating between the scales (hereinafter, interpolation). Signal). Then, an angle signal is generated based on the interpolation signal, and the current angle or rotation angle is detected from the angle signal. When a plurality of sensors are provided, the angle is obtained by averaging the angle signals from each sensor. The interpolation signal is used to detect an angle smaller than the minimum scale, that is, for higher resolution.

  The rotary encoder arranges a plurality of sensors at equal angular intervals with respect to the dial, and averages the output multiple angle signals, so that the eccentric error of the rotary encoder and the error of the angular position of each scale of the dial are obtained. Etc. are reduced. However, when the angle error of the rotary encoder is examined, the angle error still remains, which may hinder high accuracy. The inventor of the present application examined an angular error of a rotary encoder in which four sensors were arranged at equal angular intervals of 90 degrees. The number of graduations N on the graduation plate is 360, that is, the graduations are provided at equal intervals every other degree, and are multiplied by 32 by the interpolation signal. Each of the four sensors detects a signal including an angular error generated by the basic scale and the interpolation division according to the rotation of the dial.

  FIG. 1 is a diagram illustrating an angle error of a rotary encoder, and is an angle error when angle signals from four sensors are averaged. Referring to FIG. 1, it can be seen that the angle error has a maximum of ± 30 seconds over 360 degrees (one round).

  FIG. 2 is a diagram showing a discrete Fourier transform (DFT) analysis of the angular error shown in FIG. 1 of the rotary encoder.

  Referring to FIG. 2, it can be seen that the low-order component is small, and is effective in reducing the eccentricity error and the scale angle error. However, it can be seen that the 360, 720, 1080, 1440, and 1800-order components have large angular errors of about 2 to 11 seconds. For these angle error components, the number of sensors N is 360 for the number of sensors M, and the number of sensors M is a divisor of the number of scales 360. Is caused as an angle error. For example, even if the number of sensors is not four, but three, five, or six, it is a divisor of the number of graduations 360, so that an angle error of the interpolation signal similarly occurs.

  As one method for reducing the angle error of the interpolation signal, the number of sensors may be set to 7 or 13 and arranged at equal angular intervals. Since 7 is not a divisor of the number of graduations 360, the angle error of the interpolation signal can be reduced.

  FIG. 3 is a diagram showing the angular error of the interpolation signal included in FIG. 1 of the rotary encoder for each sensor. FIG. 3 shows, for each sensor, only the angle error of the interpolation signal among the angle errors, and the horizontal axis represents the angle (degree), the vertical axis represents the angle error (second), and The position of the triangle (▲) indicates the position of the scale on the dial.

  Referring to FIG. 3, it can be seen that the waveforms of the angular errors of the sensors 1 to 4 are almost the same, and the phases are almost the same. Accordingly, even if the angle signals of the sensors 1 to 4 are averaged, the angle errors of the sensors 1 to 4 do not cancel each other, and the angle error of the interpolation signal remains as shown in FIG. Would.

  Therefore, an object of the present invention is to provide an encoder that achieves both high resolution and high accuracy by reducing the angle error of an interpolation signal by shifting the positions of a plurality of sensors with respect to the scale of a dial. It is to be.

  Hereinafter, an embodiment of the present invention will be described with reference to the drawings. Elements common to a plurality of drawings are denoted by the same reference numerals, and detailed description of the elements will not be repeated.

[First Embodiment]
FIG. 4 is a diagram illustrating a schematic configuration of the encoder according to the first embodiment of the present invention.

  Referring to FIG. 4, an encoder 10 according to the first embodiment is arranged on a rotating shaft 15 to be measured for an angle, and has a graduation plate 20 having graduations 21 formed at equal intervals in a circumferential direction; Four sensors 31 to 34 for detecting the scale 21 and generating a sine wave detection signal having a periodicity and having a phase shift of 90 degrees based on the detection, and a scale based on the detection signal for each sensor 31 to 34 Signal generators 41 to 44 for generating interpolation signals (also referred to as angle signals) for interpolating the intervals of the distances, and adding the interpolation signals for the sensors 31 to 34 based on the interpolation signals to obtain the angular position. Or an arithmetic unit 50 for calculating a rotation angle.

  The graduation plate 20 is mounted concentrically with the rotating shaft 15, and graduations 21 are provided at equal intervals in the circumferential direction, so that the graduation 21 transmits light.

  Each of the sensors 31 to 34 includes a light emitting element 35, a slit 36, and a light receiving element 37. In FIG. 4, the components of the sensors 32 to 34 are not shown in detail, but have the same components as the sensor 31. In the sensors 31 to 34, the light from the light emitting element 35 is transmitted through the scale 21 and received by the light receiving element 37 through the slit 36. The sensors 31 to 34 generate sinusoidal electric signals that are 90 degrees out of phase with each other according to the intensity of the light received by the light receiving element 37 and output the detection signals as detection signals. For example, one of the two sine wave electric signals whose phases are shifted from each other by 90 degrees is a Sin voltage signal, and the other is a Cos voltage signal.

  The input units of the interpolation signal generators 41 to 44 are electrically connected to the output units of the sensors 31 to 34, and generate interpolation signals based on the input detection signals. Specifically, an interpolation signal is generated by obtaining an angle from the Sin voltage signal of the detection signal and the arctan of the Cos voltage signal (the voltage value of the Sin voltage signal / the voltage value of the Cos voltage signal). The interpolation signal is a digital signal. The interpolation signal is a signal obtained by dividing the scale interval at equal intervals, for example, a signal of several tens to several hundreds of times.

  The arithmetic unit 50 is electrically connected to the output units of the interpolation signal generators 41 to 44, respectively, and adds the interpolation signals from the interpolation signal generators 41 to 44. Specifically, for example, by counting the pulses of the interpolation signal generated by the rotation of the rotation shaft 15, adding the obtained pulse numbers, and dividing the result by the number of sensors, the angular position or the rotation angle is obtained. Ask for. The arithmetic unit 50 can cancel the angular error of each of the interpolated signals of the interpolated signal generators 41 to 44 by summing, and can reduce the angle error and improve the accuracy.

  FIG. 5 is a diagram showing the arrangement positions of the sensors of the encoder according to the first embodiment of the present invention.

Referring to FIG. 5, the sensors 31 to 34 are arranged so that their detection positions are at an angle φ (j, k _j ) (degrees) with respect to the scale 20. Although the base point of the angle can be arbitrarily selected, for example, the position of the sensor 31 can be selected. The angle φ (degree) is expressed by Expression 1, θ _j (degree) is expressed by Expression 2, and δ _k is expressed by Expression 3.
φ (j, k _j ) = θ _j + δ _kj (1)
θ _j = 360 / M × (j−1) (j = 1, 2,..., M) (2)
δ _kj = 360 / N × MOD [(k _j −1) / D] (k _j = 1, 2,..., M) (3)
Here, j is assigned an integer of 1 to M to the sensors 31 to 34. D is a divisor of M or M (except for 1). M is the number of sensors, and is 4 in the first embodiment. N is the number of the graduations 21 extending over 360 degrees of the graduation plate 20, which is 360 in the first embodiment.

The MOD in the above equation 3 is a function that outputs a value after the decimal point of the input value. MOD [(k _j -1) / D] is a value (decimal number) smaller than 1; for example, MOD [3.75] = 0.75, MOD [1.25] = 0.25, MOD [0] .25] = 0.25. Accordingly, δ _kj becomes smaller than 360 / N (degrees), that is, becomes smaller than the minimum scale interval.

As a modification of the above formula _{1, φ (j, k j} ) may be = θ _j -δ _kj. That is, Expression 1 may be an angle obtained by combining θ _j in Expression 2 and δ _{kj in} Expression 3.

In FIG. 5, four sensors 31 to 34 are arranged. This is the case where D = M = 4 in Equations 1-3. The sensors 31 to 34 are arranged at angles φ (1, k ₁ ), φ (2, k ₂ ), φ (3, k ₃ ), φ (4, k ₄ ), respectively. Here, k _{j = 1 to 4} = 1, 2,..., 4. The vertex of the triangle △ facing the dial indicates the detection position of the sensor.

  FIG. 6 is a diagram illustrating an example of an arrangement position of each sensor according to the first embodiment of the present invention, and illustrates an enlarged arrangement position of each sensor illustrated in FIG. 5. FIGS. 6A to 6D show the arrangement positions of the sensors 31 to 34, respectively.

Referring to FIGS. 6A to 6D, the sensors 31 to 34 are arranged at angular positions of φ (j, k _j ) = θ _j + δ _kj (j = 1 to an integer of 4). θ _j is an angular position obtained by dividing 360 degrees into four, and δ _kj is an angle obtained by dividing the minimum angle interval of the scale 21 by four. When the number of graduations N = 360, the sensors 31 to 34 respectively have, for example, the following φ (1, k ₁ ), φ (2, k ₂ ), φ (3, k ₃ ), and φ (4, k _4). ).
Sensor 31: φ (1, k ₁ ) = θ ₁ + δ _k1 = 0 + 0 = 0 degrees Sensor 32: φ (2, k ₂ ) = θ ₂ + δ _k2 = 90 + 0.25 = 90.25 degrees Sensor 33: φ (3 , K ₃ ) = θ ₃ + δ _k3 = 180 + 0.50 = 180.50 degrees Sensor 34: φ (4, k ₄ ) = θ ₄ + δ _k4 = 270 + 0.75 = 270.75 degrees

FIG. 7 is a diagram illustrating an angle error of an interpolation signal of the encoder according to the first embodiment of the present invention. Referring to FIG. 7, the waveforms of the angular errors of the interpolation signals of the sensors 11 to 14 are shifted in phase by １ ／ degree (0.25 degree) from each other, and δ _kj of the arrangement of the sensors 31 to 34 is You can see that it is reflected.

  FIG. 8 is a diagram illustrating an angle error of the encoder according to the first embodiment of the present invention.

  Referring to FIG. 8, it can be seen that the angle error of the encoder is ± 16 seconds at the maximum and is almost １ ／ of the angle error of FIG. 1 described above.

  FIG. 9 is a diagram illustrating a DFT analysis of the angle error of the encoder according to the first embodiment of the present invention, and is a result of the DFT analysis of the angle error of FIG.

  Referring to FIG. 9, angular errors of 360, 720, 1080, and 1800-order components, which are multiple orders of the number of graduations 360, are 2 seconds or less. It can be seen that the 720-order component is greatly reduced to 9%. This clearly shows the effect of the present embodiment.

As a modified example (modified example 1) of the arrangement position of the sensors 31 to 34, δ _{kj of the} above equation 1 takes values of 0, 0.25, 0.50, and 0.75 according to the equation 3, but the sensor 31 To 34 may be arbitrarily assigned. For example, (δ _k1 , δ _k2 , δ _k3 , δ _k4 ) = (0, 0.50, 0.25, 0.75), (0, 0.75, 0.25, 0.50), (0 .25, 0, 0.50, 0.75). It is apparent from the principle of the present invention that the effect of the present embodiment described above is similarly obtained by the first modification.

As another modified example (modified example 2) of the arrangement position of the sensors, θ _j in Expression 1 is 0, 90, 180, and 270 according to Expression 2, but the positions of the sensors 31 to 34 are different from each other. May be shifted by an angle that is an integral multiple of 360 / N, but in this case, since errors of low-order components increase, it is preferable to set θ _j at equal angular intervals.

As still another modified example (Modified Example 3), when D in Expression 3 is a divisor of M, since each sensor in Expression 3 is an integer of k _j = 1 to M, the number of sensors M Is 4 and D is 2, then (δ _k1 , δ _k2 , δ _k3 , δ _k4 ) = (0, 0.5, 0, 0.5). In this case, among the angular errors of the encoder caused by the angular error of the interpolation signal, the error of the N-th order component (excluding the (N × D) order component) can be reduced.

According to the present embodiment, the plurality of sensors 31 to 34 are arranged such that, with respect to the scale 20, the term 360 ° / M × (j−1) on the right side of Equation 2 and the term 360 ° / N × on the right side of Equation 3 By being arranged at the position of the angle obtained by combining MOD [(k _j -1) / D], the N-order component (where (( N × D) excluding the following components), and the angle error of the encoder due to the eccentricity due to the mounting of the scale 20 to the rotating shaft 15 and the error of the position of the scale 21 of the scale 20. Can also be reduced. Therefore, according to the present embodiment, it is possible to provide an encoder that achieves both high resolution and high accuracy.

  In the present embodiment, the example using the transmission type optical sensor has been described. However, as an alternative example, for example, a scale is shown on a dial, and the optical contrast between the scale and the other portions is reduced. A reflection type optical sensor that is used may be used. For example, a graduation plate whose graduation portion has a higher or lower reflectance (that is, a higher absorptance) than other portions.

  This embodiment is also applicable to a magnetic sensor and a magnetic encoder that is magnetically scaled, instead of the optical sensor and the scale. A plurality of magnetic sensors for detecting magnetic scales may be arranged in the same manner as the above-described optical sensor.

  The encoder 10 according to the present embodiment can be applied to an incremental encoder that detects a rotation angle and a rotation speed of the rotation shaft 15, and can be applied to an absolute encoder that detects an absolute angular position.

[Second embodiment]
FIG. 10 is a diagram illustrating a schematic configuration of an encoder according to the second embodiment of the present invention.

  Referring to FIG. 10, an encoder 100 according to the first embodiment is arranged on an object (not shown) whose position or amount of movement is to be measured, and is equally spaced in a direction of movement of the object (a direction indicated by an arrow MV). A scale plate 120 having a scale 121 formed on the scale, three sensors 131 to 133 for detecting the scale 121 and generating, based on the detection, sine wave detection signals having a periodicity and having a phase shift of 90 degrees from each other; Interpolation signal generators 141 to 143 for generating interpolation signals for interpolating the intervals of the scales based on the detection signals for the sensors 131 to 133, and interpolation signals for the sensors 131 to 133 based on the interpolation signals And a computing unit 150 for calculating the position or the movement amount by adding

  The scale plate 120 is attached along the moving direction of the object (the direction indicated by the arrow MV), and the scales 121 are provided at equal intervals. The portion of the scale 121 reflects light. Note that the scale 121 may absorb light and the surrounding surface of the scale 120 may reflect the light.

  Each of the sensors 131 to 133 has a light emitting element 135 and a light receiving element 137. In the sensors 131 to 133, the scale 121 reflects the light from the light emitting element 135 and the light receiving element 137 receives the light. The sensors 131 to 133 generate sine-wave electric signals whose phases are shifted by 90 degrees from each other in accordance with the intensity of light received by the light-receiving element 137 and output the detection signals as detection signals. For example, one of the two sine wave electric signals whose phases are shifted from each other by 90 degrees is a Sin voltage signal, and the other is a Cos voltage signal.

  The interpolation signal generators 141 to 143 and the arithmetic unit 150 have the same configurations and operations as the interpolation signal generators 41 to 44 and the arithmetic unit 50 in the first embodiment, respectively. Find the amount of movement. The arithmetic unit 150 can cancel the position error of each of the interpolation signals of the interpolation signal generators 141 to 143, reduce the position error, and improve the accuracy.

  FIG. 11 is a diagram illustrating an example of an arrangement position of each sensor according to the second embodiment of the present invention. (A)-(c) have shown the arrangement position of the sensors 131-133, respectively.

Referring to FIG. 11, the detection positions of the sensors 131 to 133 are arranged at positions p (j, k _j ) with respect to the scale 120. Although the base point of the position can be arbitrarily selected, for example, the position of the sensor 131 can be selected. The position p is expressed by Expression 5, L _j is expressed by Expression 6, and δ _kj is expressed by Expression 7.
p (j, k _j ) = L _j + δ _kj (5)
L _j = gl × m _j (6)
δ _kj = gl × MOD [(k _j −1) / D] (k _j = 1, 2,..., M) (7)
Here, an integer of 1 to M is assigned to j for the sensors 131 to 133. m _j is an integer, and different integers are selected for j. D is a divisor of M or M (except for 1). gl is a scale interval. M is the number of sensors, and is 3 as an example in the second embodiment. MOD is a function for outputting a value after the decimal point of the input value, and is the same as in the first embodiment. As a modification of the above formula _{5, p (j, k j} ) = may be _L j _{-δ kj.} That is, Expression 5 may be any position obtained by combining L _j in Expression 6 and δ _{kj in} Expression 7.

As shown in (a) ~ (c) of FIG. 11, the sensor 131 to 133 will be disposed in _{p (j, k j) =} L j + δ kj (j = 1~3 integer). L _j is an integer multiple (m _j times) of the scale interval gl, and δ _kj is a distance obtained by dividing the scale interval gl into three equal parts. Sensors 131 to 133, respectively, the following _{p (1, k 1),} p (2, k 2), is arranged in the position shown in p _{(3, k} 3).
Sensor 131: p (1, k ₁ ) = L ₁ + δ _k1 = 0 + 0 = 0
Sensor 132: p (2, k ₂ ) = L ₂ + δ _k2 = gl × 10 + gl × 1/3 = (10 + ／) × gl
Sensor 133: p (3, k ₃ ) = L ₃ + δ _k3 = gl × 20 + gl × 2/3 = (20 + 2/3) × gl
By arranging the sensors 131 to 133 in this way, the phase of the position error of the interpolation signal is shifted from each other by 目 of the graduation interval gl. By adding the interpolated signals, an error due to a position error of the interpolated signal is reduced. As a result, the accuracy of the encoder 100 is improved.

As a modification (modification 4) of the arrangement positions of the sensors 131 to 133, δ _kj in Expression 5 takes values of 0, 1/3 and 2/3 according to Expression 7, but is arbitrary with respect to the sensors 131 to 133. May be assigned. It is clear from the principle of the present invention that the above-described effects of the present embodiment can be similarly obtained by this modification.

According to the present embodiment, the plurality of sensors 131 to 133 are provided on the scale 120 by the terms gl × m _{j on} the right side of Equation 6 and the terms gl × MOD [(k _j −1) / on the right side of Equation 7. D], the angle error of the encoder due to the angle error of the interpolation signal can be reduced, and the error due to the alignment of mounting the scale 120 to the object and the scale The position error of the encoder 100 due to the error in the position of the scale 121 at 120 can also be reduced. Therefore, according to the present embodiment, it is possible to provide an encoder that achieves both high resolution and high accuracy.

  In the present embodiment, a transmissive sensor and a scale can be used instead of the reflective sensors 131 to 133 and the scale 120. Furthermore, this embodiment can be applied to a magnetic encoder.

  As described above, the preferred embodiment of the present invention has been described in detail, but the present invention is not limited to the specific embodiment, and various modifications and changes may be made within the scope of the present invention described in the claims. It is possible. For example, of the first embodiment and the second embodiment, the technical ideas and the modifications described in one embodiment may be combined with the other embodiment.

10, 100 Encoder 20, 120 Scale board 21, 121 Scales 31 to 34, 131 to 133 Sensors 41 to 44, 141 to 143 Interpolated signal generator 50, 150 Computing unit

Claims (8)

M sensors for detecting a plurality of elements indicating angles arranged at predetermined angular intervals on the substrate and generating a first signal having periodicity, wherein the M sensors are arranged at a predetermined angle, The predetermined angle is an angle obtained by combining 360 / M × (j−1) (degrees) and 360 / N × MOD [(k _j −1) / D] (degrees), where M is N is the number of elements, N is the number of elements, MOD is a function that outputs a value after the decimal point of the input value, D is a divisor of M or M, except for 1, except that j is 1 to M Taking different values for M sensors with integers of k _j , k _j being an integer from 1 to M;
A generator for generating a second signal for interpolating the predetermined angular interval based on the first signal, for each of the M sensors;
A calculator for summing the second signals for the M sensors to determine an angular position or a rotation angle;
An encoder comprising:   The encoder according to claim 1, wherein the base is a disk-shaped scale, and the elements are arranged in a circumferential direction. M sensors for detecting a plurality of elements indicating positions arranged at predetermined intervals on the base body and generating a first signal having periodicity, wherein the M sensors are separated from each other by a predetermined distance. are arranged, the predetermined distance is a gl × _{m j} is an integer _{(m j)} times the said predetermined constant interval (gl), a position that combines the _{gl × MOD [(k j -1} ) / D], Here, M is an integer of 2 or more, MOD is a function that outputs a value after the decimal point of the input value, D is a divisor of M or M, except for 1, and k _j is 1 to M An integer, the M sensors;
A generator for generating a second signal for interpolating between the elements at the predetermined interval based on the first signal, for each of the M sensors;
A calculator for summing the second signals for the M sensors to determine a position or a movement amount;
An encoder comprising:   The encoder according to claim 3, wherein the plurality of elements are arranged in one direction on the base. The encoder according to any one of claims 1 to 4, wherein the _kj has different values for the M sensors.   The encoder according to any one of claims 1 to 5, wherein D is M. The element is made of a slit that transmits light or a member that reflects or absorbs light,
The encoder according to any one of claims 1 to 6, wherein the plurality of sensors are optical sensors. The element is a convex member or a magnet member made of a ferromagnetic material,
The encoder according to any one of claims 1 to 6, wherein the plurality of sensors are proximity sensors that magnetically detect the convex member or the magnet member.

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