JP2012237633A - Device for detecting multi-turn absolute rotation angle - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method for highly accurately calculating a multi-turn absolute rotation angle of a motor rotating shaft connected to a motor output shaft.SOLUTION: In the rotation angle detection device using a calculation method according to the present invention, a rotation angle θof the rotation angle of an n-th rotating shaft satisfies θ=(-(m±1)/m)×θwith respect to a rotation angle θof the motor rotating shaft. In a gear mechanism satisfying the relationship, a multi-turn rotation angle of a first rotating shaft is developed to a detection value pfor the first rotating shaft, which is the rotation angle of the first rotating shaft and R×m+R×m+...R×mwhich corresponds to the number of rotations of the first rotating shaft, coefficients Rto Rare determined on the basis of the detection value from an angle detector for each shaft, and the multi-turn rotation angle for the first rotating shaft is calculated. A detection error generated by the angle detector of the second and subsequent rotating shafts can be effectively suppressed, and high-precision multi-turn rotation angles can be calculated. A plurality of systems of gear mechanisms are juxtaposed and, on the basis of the detection values obtained from the gear mechanisms, a wider rotation angle detection range can be attained.

Description

  The present invention relates to a device for detecting a rotation angle of a rotating shaft and a method for calculating the rotation angle, and more specifically, an improvement capable of detecting a multi-rotation absolute rotation angle without using a means such as a battery backup. The present invention relates to a rotation angle detection device and a method for calculating the rotation angle.

  The rotation angle detection device detects, for example, the rotation angle of the motor rotation shaft, and controls the position of a moving body such as a machine tool driven by the motor in response to the detected value. In order to control the position of the moving body over a wide range and with high accuracy, it is desirable that the rotation angle detection device can detect the motor rotation shaft with multiple rotations and absolute rotation angles.

  As such a rotation angle detection device, Japanese Patent Application Laid-Open No. 2010-44055 (corresponding to US Patent Application No. 12 / 168,151) discloses an inductive multi-turn encoder. The inductive multi-turn encoder 10 includes geared circular disks 41-46 connected in series and in multiple stages, and detects the rotation angle of the disks 42, 44, 46 among them to perform multiple rotations. Realize angle detection. The range in which the multi-rotation angle in this prior art document can be detected is determined by the reduction ratio of the final stage disk 46 with respect to the input rotation axis. The rotary shaft 20 as an input rotary shaft is mechanically connected to the circular disk 41 with a gear reduction ratio of 1: 4, and the subsequent circular disks 41 and 42, 42 and 43, 43 and 44, 44 and 45 with gears. , And 45 and 46 are also mechanically connected with a gear reduction ratio of 1: 4, respectively. By executing six stages of such 1: 4 gear reduction, the multi-turn encoder 10 can obtain a multi-rotation detection range of 4096 rotations.

JP 2010-440558 A JP 2002-107178 A Japanese Patent No. 3967963 Japanese Patent Publication No. 05-38243

Koichi Hayashi and four others, “Development of a batteryless multi-rotation detection ultra-high resolution small absolute encoder”, Journal of Precision Engineering, 2000, Vol. 66, no. 8, p1177-1180

  Since the inductive multi-turn encoder 10 described above directly determines the multi-rotation rotation angle from the rotation angle of the decelerated circular disc, it is necessary to increase the reduction ratio in order to set a wide multi-rotation detection range. As a result, the inductive multi-turn encoder 10 has a problem that the mechanism is complicated and large, and the cost is increased.

  In order to improve the above problem, it was introduced in "Development of a battery-less multi-rotation detection ultra-high resolution small absolute encoder" (Journal of the Japan Society for Precision Engineering, Vol. 66, No. 8, p1177-1180) The encoder and the resolver disclosed in Japanese Patent Application Laid-Open No. 2002-107178 are each provided with an angle detector for detecting the rotation angle of the rotating shaft connected in parallel to the rotating input shaft at different speed ratios, The multi-rotation absolute position is detected based on the rotation angle information obtained from them.

  However, in the method of obtaining multi-rotation information from the relationship between the rotation angles of a plurality of axes connected in parallel at different gear ratios, the multi-rotation angle detection range is generally a period obtained by processing the angle detection signal of each axis. Determined by the least common multiple of the signal. In the method of detecting the multi-rotation absolute rotation angle as described in the above-mentioned prior document, it is necessary to select a gear shift that is relatively prime in order to widen the multi-rotation angle detection range. There is a problem of increasing. In addition, since the number of prime numbers is limited, there is a problem that the degree of freedom of the multi-rotation angle detection range that can be designed is limited. Furthermore, since the multi-rotation angle detection range that can be adapted to other applications varies, the multi-rotation angle detection range that can be actually realized is limited to a special value that is the least common multiple of prime values. Remains. Furthermore, in the above-described method, the absolute position of multiple rotation is obtained from the rotation angle information of each axis, but there is a problem that the calculation is complicated.

  In order to cope with the above-mentioned problem that the calculation for obtaining the multi-rotation absolute position is complicated, Japanese Patent Laid-Open No. 2002-107178 discloses the relationship between the value obtained from the rotation angle of each rotation axis and the rotation speed of the main rotation axis. An absolute position detection method is disclosed in which a table (FIG. 9) is stored in advance in a memory, and the number of rotations of the main rotation shaft corresponding to the value obtained from the rotation angle of each rotation shaft is selected from the table. However, in order to increase the multi-rotation detection range, there is a problem that a lot of memory corresponding to the multi-rotation detection range (0 to 20357) is consumed.

  Japanese Patent No. 3967963 discloses a calculation method that saves memory consumption by storing the calculation result of only one of the two periods in the memory. However, this method also has the same problem as the above-described detection method regarding the use of the memory.

  Further, regarding the calculation method for obtaining the multi-rotation absolute rotation angle, Japanese Patent Publication No. 05-38243 discloses a relational expression of detection values from a plurality of rotation angle detectors with respect to the rotation angle of the shaft, Using a program for substituting and discriminating the rotation angle of the shaft that is satisfactory, the multi-rotation absolute rotation angle is searched. When the multi-rotation detection range becomes wide, there is a problem that it takes time to calculate because there are many combinations to search for.

の関係を満たす伝達機構を具備する多回転アブソリュート回転角検出装置に適用されることを特徴とする。ここで、ｎｍａｘ及びｍは３以上の整数であり、かつｎは１≦ｎ≦ｎｍａｘである。 The present invention is made in order to solve the above-described problem, and is a transmission mechanism that transmits rotation from the first rotation shaft to the nmax rotation shaft, and the nth rotation with respect to the rotation angle θ ₁ of the first rotation shaft. The rotation angle θ _{n of the} shaft is

The present invention is applied to a multi-rotation absolute rotation angle detection device having a transmission mechanism that satisfies the above relationship. Here, nmax and m are integers of 3 or more, and n is 1 ≦ n ≦ nmax.

上記回転角計算式の数値ｎを２からｎｍａｘまで繰り返すことにより、係数Ｒ_０から係数Ｒ_{ｎｍａｘ−２}までの値を順次決定し、第１回転軸の多回転アブソリュート回転角計算値θ_１（ｍ^ｎ−１）’を求める。ここで、係数Ｒ_０〜Ｒ_{ｎｍａｘ−２}は０およびｍ−１を含む０からｍ−１の整数、ｕは基本単位量、および回転角計算値θ_１（ｍ^０）’は第１回転軸の角度検出値ｐ_１である。 Multiple rotation absolute rotational angle detecting apparatus according to the present invention detects an angle detection value p _n in one rotation of the first n rotation axis by the angle detector attached to each rotation shaft. Detected angle detected value p _n coefficients based R a _n-2 was determined, the determined coefficient R _n-2 are substituted into the following rotation angle calculation formula rotation angle calculated value θ _{¹ (m n-1} ) ' The calculated rotation angle θ ₁ (m ⁿ⁻¹ ) ′ represents the multi-rotation rotation angle of the first rotation axis, and the rotation angle detection range is 0 to m ⁿ⁻¹ rotation.

By repeating the numerical value n of the rotation angle calculation formula from 2 to nmax, values from the coefficient R ₀ to the coefficient R _nmax−2 are sequentially determined, and the multi-rotation absolute rotation angle calculation value θ ₁ (m ^n-1 ) ′. Here, the coefficients R _{0 to} R _nmax-2 are integers from 0 to m−1 including 0 and m−1, u is the basic unit amount, and the calculated rotation angle θ ₁ (m ⁰ ) ′ is the first rotation axis. is the angle detected value _{p 1.}

により求めることができ、ここで、ｋ_１，ｋ_２，・・・ｋ_ｎは、（ｘ＋１）^ｎ−１の展開式ｋ_１×ｘ^０＋ｋ_２×ｘ^１＋ｋ_３×ｘ^２・・・ｋ_ｎｘ^ｎ−１におけるｘのｎ−１次項の係数であり、ｍｏｄ（ｘ，ａ）は、ｘをａで割ったときの余りを求める剰余演算であり、Ｊは、隣接する回転軸間の変速比が−（ｍ−１）／ｍのとき、Ｊ＝１であり、変速比が−（ｍ＋１）／ｍのとき、Ｊ＝−１である符号調整項である。また角度補正値ｐ_ｎ’は、計算された回転角計算値θ_１（ｍ^ｎ−１）’を、次式の角度補正値計算式、

に代入して計算することができる。 The coefficient R _n−2 is calculated from the calculation result of the rotation angle calculation formula for obtaining the rotation angle calculation value θ ₁ (m ⁿ⁻¹ ) ′ of the first rotation axis when the number of rotation axes is n. It is determined so as to approximate the rotation angle detection value θ ₁ (m ⁿ⁻¹ ) of one rotation axis. Rotation angle detection value θ ^{₁ (m _n-1)} is the ^{m n-1} to the periodic signal is determined by the following formula from the detected angle value _p 1 ~p _n up to the n rotation axis S ^{(m n-1)} It is calculated by multiplying. The rotation angle detection range of the rotation angle detection value θ ₁ (m ⁿ⁻¹ ) is 0 to m ⁿ⁻¹ rotations.

It can be obtained by, _{where, k 1, k 2, ···} k n is, (x + ¹⁾ expansions of ^{_{n-1 k 1 × x 0}} + k 2 × x 1 + k 3 × x 2 ··· k _n x ⁿ⁻¹ is the coefficient of the n−1 order term of x, mod (x, a) is a remainder operation for calculating the remainder when x is divided by a, and J is the value between adjacent rotation axes. This is a sign adjustment term in which J = 1 when the gear ratio is − (m−1) / m and J = −1 when the gear ratio is − (m + 1) / m. In addition, the angle correction value p _n ′ is calculated by using the calculated rotation angle calculation value θ ₁ (m ⁿ⁻¹ ) ′ and the following angle correction value calculation formula:

Can be calculated by substituting

の計算結果に最も近似した整数を決定することより求めることができる。 The coefficient R _n−2 is

It can be obtained by determining an integer that most closely approximates the result of the calculation.

を演算することにより求めることができ、ＩＮＴ（ｘ）は、数値ｘの小数点以下を切り捨てる演算である。 Further, the coefficient R _n-2 is

INT (x) is an operation for rounding down the decimal point of the numerical value x.

上記角度補正値計算式の数値ｎを２からｎｍａｘまで繰り返すことにより、係数Ｒ_０から係数Ｒ_{ｎｍａｘ−２}までの値が順次決定される。 In the present invention, the coefficient R _n−2 is determined so that the angle correction value _pn ′ represented by the following formula is closest to the detected angle value pn of the _n- th rotation axis, and the calculated rotation angle θ _1. (M ^n-1 ) ′ is obtained.

By repeating the numerical value n of the angle correction value calculation formula from 2 to nmax, values from the coefficient _R0 to the coefficient _Rnmax-2 are sequentially determined.

に代入して第１回転軸の多回転アブソリュート回転角計算値θ_１（ｍ^{ｎｍａｘ−１}）’を求める。ここで、係数Ｒ_０〜Ｒ_{ｎｍａｘ−２}は０およびｍ−１を含む０からｍ−１の整数、ｕは基本単位量、および角度補正値ｐ_１’は第１回転軸の角度検出値ｐ_１である。 These determined coefficients R _{0 to} R _nmax−2 are _expressed by the following rotation angle calculation formula:

To obtain the calculated value of the multi-rotation absolute rotation angle θ ₁ (m ^nmax−1 ) ′ of the first rotation axis. Here, the coefficients R _{0 to} R _nmax-2 are integers from 0 to m−1 including 0 and m−1, u is the basic unit amount, and the angle correction value p ₁ ′ is the detected angle value p of the first rotation axis. ₁ .

の計算結果に最も近似した整数を決定することにより求めることができる。 The coefficient R _n-2 is

It can be obtained by determining an integer that is closest to the calculation result of.

を演算することにより求めることができ、ＩＮＴ（ｘ）は、数値ｘの小数点以下を切り捨てる演算である。 Further, the coefficient R _n-2 is

INT (x) is an operation for rounding down the decimal point of the numerical value x.

  Furthermore, the present invention is a method and apparatus for providing a plurality of transmission mechanisms as described above, obtaining a periodic signal and an angle correction value from each series, and calculating a multi-rotation absolute rotation angle. In particular, m is set so that the periods of the periodic signals are relatively prime.

  According to the present invention, even if the detection value of the angle detector includes an error, the detection error generated by the angle detector can be suppressed, and a highly accurate multi-rotation rotation angle detection value can be calculated. In particular, this calculation can cancel the detection error caused by the angle detector attached after the second rotation axis, and keep it within the detection error caused by the angle detector of the first rotation axis. As a result, even if the detection range of the multi-rotation rotation angle is expanded by increasing the rotation axis, the calculated multi-rotation rotation angle detection value can be suppressed within the detection error of the first rotation axis.

In addition, the accuracy required for the angle detector of the present invention only needs to have the accuracy necessary for the determination of the coefficient Rn _-2 . Compared with directly calculating the detection value of each axis to obtain the multi-rotation angle, the accuracy can be lowered, so that the cost of the multi-rotation angle detection device can be reduced.

  Furthermore, since the multi-rotation angle detection device to which the present invention is used does not require a gearshift that is a prime relationship, fewer types of gears are used. In addition, the detection range of the multi-rotation rotation angle can be designed freely. Further, since the memory reference is not required in the multi-rotation cycle calculation, a large amount of memory is not consumed, and the cost and size of the memory component are not increased.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings. However, the drawings and descriptions corresponding to the drawings are merely exemplary descriptions for carrying out the present invention, and the claimed invention is not limited to the present invention. It is not intended to be limited to the examples. In addition, the present invention is construed only by the terms defined in the claims, and the terms follow their general interpretation.

It is a block diagram of the transmission mechanism of the rotation angle detection device for explaining the principle of obtaining the multi-rotation absolute rotation angle according to one embodiment of the present invention. It is a block diagram of the rotation angle detection apparatus for detecting the multi-rotation absolute rotation angle which is one Example of this invention. In one Example of this invention, the block diagram of the rotation angle detection apparatus for calculating the multi-rotation absolute rotation angle of a motor rotating shaft is shown. In one Example of this invention, it is a graph which shows the relationship between the rotation angle of a 1st rotating shaft, and the 1st-4th rotation angle. In one embodiment of the present invention, it is a graph showing the relationship between the detection value _{p 1, p 2, p 3} , p 4 of the rotation angle and the axis of the first rotary shaft. In one Example of this invention, it is a graph which shows the relationship of the periodic signal with respect to the rotation angle of a 1st rotating shaft. In one Example of this invention, it is a graph which shows the relationship between the rotation angle of a 1st rotating shaft, and the rotating angle of each axis | shaft. In one Example of this invention, the angle detection value output from the angle detector of each axis | shaft with respect to the rotation angle of a 1st rotating shaft is shown. In one Example of this invention, it is a graph which shows the relationship of the periodic signal with respect to the rotation angle of a 1st rotating shaft. In one embodiment of the present invention, it is a graph showing the relationship between the rotation angle and the coefficient R ₀ to R ₂ of the first rotating shaft. In one Example of this invention, it is a graph for demonstrating the structure of the integer part in the rotation angle calculation value of a 1st rotating shaft. 5 is a flowchart showing a procedure for calculating a rotation angle calculated value of a first rotating shaft in the first embodiment of the present invention. It is a flowchart which shows the procedure which calculates the rotation angle calculated value of a 1st rotating shaft in 2nd Example of this invention. It is a block diagram of the configuration of the transmission mechanism of the rotation angle detection device according to the third embodiment of the present invention.

With reference to FIG. 1, the principle of obtaining the multi-rotation absolute rotation angle according to the first embodiment of the present invention will be described. In the configuration block diagram of the transmission mechanism 10 of the rotation angle detection device shown in FIG. 1, the first rotation shaft 11 coupled to the motor output shaft is connected to the angle detector S <b> 1 and within one rotation of the first rotation shaft 11. The detected value p ₁ corresponding to the rotation angle θ ₁ indicating the angle is detected. Similarly, the angle detector S2-Sn detects a detection value _p 2 ~p _n corresponding to the rotation angle theta ₂ through? _N that indicates the angle of the second to n-th rotary shaft 12-15, respectively. Gears with the number of teeth m−1 (or m + 1) and the number of teeth m are respectively fixed to the first to n-th rotation shafts 11 to 15, and the gear 11 a of the first rotation shaft 11 is a second rotation shaft 12. Is engaged with the gear 12b. Further, the gear 12 a fixed to the second rotating shaft 12 is engaged with the gear 13 b of the third rotating shaft 13. Thus, the transmission mechanism 10 forms a gear mechanism in which a gear having the number of teeth m−1 (or m + 1) meshes with a gear having the number of teeth m between adjacent rotating shafts.

Although the embodiment according to the present invention will be described using a gear mechanism as a transmission means, the transmission mechanism according to the present invention is not limited to a gear, and any element capable of transmitting the rotational force of a rotating shaft. including. In the gear mechanism arranged as described above, the multi-rotation absolute rotation angle of the first rotation shaft 11 is detected values p _{1 to} p of the _first to n-th rotation shafts 11 to 15 detected by the angle detectors S2 to Sn. It is calculated by executing the following calculation formula from _n .

In FIG. 1, assuming that the gears having the number of teeth m−1 and the number of teeth m are meshed with the first to n-th rotation shafts 11 to 15, the gear transmission ratio is (m−1) / m. It is represented by In the gear mechanism arranged in series from the first rotating shaft 11 to the n-th rotating shaft 15, the meshed gear pairs have the same gear speed ratio (m−1) / m. When the angle is θ ₁ , the rotation angle θ _n of the n-th rotation shaft 15 is expressed by Expression (1).

なお、式（１）において（ｍ−１）／ｍの前のマイナス記号は、第１回転軸１１の回転方向をプラス（正）で表現し、その回転と逆の回転方向をマイナス（負）で表現する。

In Equation (1), the minus sign before (m−1) / m expresses the rotation direction of the first rotating shaft 11 as positive (positive), and the rotation direction opposite to the rotation is negative (negative). Express with

The transmission mechanism shown in FIG. 1 is a gear mechanism formed by a first rotation shaft to a fourth rotation shaft, and assuming that the rotation angle of the first rotation shaft coupled to the motor output shaft is θ ₁ , The rotation angle θ ₂ , the rotation angle θ ₃ of the third rotation axis, and the rotation angle θ ₄ of the fourth rotation axis are obtained from the equation (1) as follows.

ここで、式ｙ＝ｍｏｄ（ｘ，ａ）は、一般にｘをａで割ったときの余りｙを算出する剰余演算と定義される。すなわち、ある回転軸の回転角の単位を度（°）とし、１周期の回転角を表す数値（基本単位量）であるｕを３６０（°）とする場合、検出値ｐ_ｎは、回転角に応じて０から３６０（°）の値を示す。たとえば、回転角θ_ｎが９０（°），５１０（°）である場合、検出値ｐ_ｎは、それぞれ９０（°），１５０（°）となる。なお、回転角θ＝−１（°）とする場合は、検出値ｐは−１（°）ではなく、３５９（°）として扱う。回転角θ_ｎとｕは、単位が一致してればどのような単位を採用してもよい。たとえば、単位量を１（回転）とすると、検出値ｐ_ｎは、回転角に応じて０から１の値を示す。 The angle detectors S1 to Sn are detectors that detect the rotation angles of the first to nth rotation shafts 11 to 15 (for example, detection values representing 0 (°) to 360 (°)). When n rotary shaft rotates by theta _n, the detection value p _n of an angle detector Sn can be expressed by equation (6).

Here, the expression y = mod (x, a) is generally defined as a remainder operation for calculating a remainder y when x is divided by a. That is, when the unit of the rotation angle of a certain rotation axis is degrees (°) and u that is a numerical value (basic unit amount) representing the rotation angle of one cycle is 360 (°), the detected value _pn is the rotation angle. Depending on, values from 0 to 360 (°) are shown. For example, if the rotation angle theta _n is 90 (°), 510 (° ), the detection value _{p n,} respectively 90 (°), the 150 (°). When the rotation angle θ = −1 (°), the detected value p is handled as 359 (°) instead of −1 (°). Any unit may be adopted for the rotation angles θ _n and u as long as the units match. For example, if the unit weight and 1 (rotation), the detection value p _n denotes a value from 0 to 1 in accordance with the rotation angle.

  If the detection value of the angle detector is further extended, the angle detectors S1 to Sn for detecting the rotation angle of the first rotation shaft 11 to the n-th rotation shaft 15 output a detection value for one cycle when the rotation shaft makes one rotation. . For example, the angle detectors S1 to Sn monotonically increase from the detection value 0 to the detection value u according to the rotation angle of the rotation shaft, where u is the unit amount of one cycle, and the detection value 0 when the rotation shaft makes one rotation. A sawtooth detection signal is output. The unit amount u is a numerical value representing the rotation angle per cycle, and as described above, any unit may be used as long as it is the same as the rotation angle unit.

Next, when the rotation angles θ ₁ to θ ₄ represented by the equations (2) to (5) are substituted into the equation (6), the detection values p _{1 to} p ₄ of the angle detectors S1 to Sn are the first rotation. from the rotation angle theta ₁ of the shaft is calculated by the equation (7) to (10).

と表現できるので、ｍｏｄ（ａ＋ｂ，ｕ）＝ｍｏｄ（ｍｏｄ（ａ，ｕ）＋ｍｏｄ（ｂ，ｕ），ｕ）の関係から、第１回転軸の検出値ｐ_１、及び、第２回転軸の検出値ｐ_２を用いて、上記周期信号を表す剰余式を式（１１）のように変形することができる。

Now, assuming a periodic signal with one cycle of m rotation of the first rotating shaft, the remainder equation representing the periodic signal S (m ¹ ) is

From the relationship of mod (a + b, u) = mod (mod (a, u) + mod (b, u), u), the detected value p ₁ of the first rotation axis and the second rotation axis using the detection value p _2, the remainder equation representing the periodic signal can be transformed into the equation (11).

と表現できるので、第１〜３回転軸の検出値ｐ_１，ｐ_２，ｐ_３を用いて上記周期信号Ｓ（ｍ^２）を表す剰余式を式（１２）のように変形することができる。

Further, assuming a periodic signal having one cycle of m ² rotation of the first rotating shaft, the remainder equation representing the periodic signal S (m ² ) is

Therefore, the remainder equation representing the periodic signal S (m ² ) using the detected values p ₁ , p ₂ , and p ₃ of the _{first to} third rotation axes can be transformed as shown in Equation (12). .

と表現できるので、第１〜４回転軸の検出値ｐ_１，ｐ_２，ｐ_３，ｐ_４を用いて上記周期信号Ｓ（ｍ^３）を表す剰余式を式（１３）のように変形することができる。

Furthermore, assuming a periodic signal having one cycle of m ³ rotations of the first rotating shaft, the remainder equation representing the periodic signal S (m ³ ) is

Therefore, using the detected values p ₁ , p ₂ , p ₃ , and p ₄ of the _{first to} fourth rotation axes, the remainder equation that represents the periodic signal S (m ³ ) is transformed as shown in Equation (13). be able to.

と表現できるので、式（１１）から式（１３）を演繹すると、周期信号Ｓ（ｍ^ｎ−１）は、式（１４）の周期信号計算式として表すことができる。ここで、ｎは、回転軸の数である。

ただし、ｋ_１，ｋ_２，・・・，ｋ_ｎは、（ｘ＋１）^ｎ−１の展開式の係数に対応する。すなわち、二項定理から、（ｘ＋１）^ｎ−１は、ｋ_１×ｘ⁰＋ｋ_２×ｘ^１＋・・・＋ｋ_ｎ×ｘ^ｎ−１に展開される。 In general, assuming a periodic signal having one cycle of ^mn-1 rotations of the first rotating shaft, the remainder equation representing the periodic signal is

Therefore, when the equations (11) to (13) are deduced, the periodic signal S (m ^n-1 ) can be expressed as the periodic signal calculation equation of the equation (14). Here, n is the number of rotation axes.

_{However, k 1, k 2, ···} , k n corresponds to the coefficients of expansion formula of ^{(x + 1) n-1} . That is, from the binomial theorem, (x + 1) ⁿ⁻¹ is expanded to k ₁ × x ⁰ + k ₂ × x ¹ +... + K _n × x ⁿ⁻¹ .

式（１５）に示されるように、各回転軸の角度検出器の検出値ｐ_１〜ｐ_ｎを代入することにより、第１軸の多回転回転角検出値θ_１（ｍ^ｎ−１）を求めることができる。ｎは、回転軸の軸数である。 Therefore, the multi-rotation absolute rotation angle detection value θ ₁ (m ⁿ⁻¹ ) of the first rotation axis is calculated by multiplying the periodic signal of equation (14) by m ⁿ⁻¹ and expressed as equation (15). The

As shown in Expression (15), by substituting the detection values p _{1 to pn} of the angle detectors of the respective rotation axes, the multi-rotation rotation angle detection value θ ₁ (m ⁿ⁻¹ ) of the first axis is obtained. Can be sought. n is the number of rotation axes.

  The above calculation assumes a gear mechanism having a gear transmission ratio of (m−1) / m. However, the present invention also applies to a gear mechanism having a gear transmission ratio of (m + 1) / m. Applicable. The periodic functions described above can be distinguished by introducing a sign adjustment term as described below.

従って、第１〜４回転軸の角度検出値ｐ_１〜ｐ_４は、次のように求められる。

Similarly to the above, the periodic function in the case of a gear mechanism having a gear speed ratio of (m + 1) / m is obtained as follows. That is, the detected angle value pn of the _n- th rotation axis is expressed as follows.

Thus, the angle detection value _p 1 ~p ₄ of the first to fourth rotary shaft is determined as follows.

上式において、ｐ_１＋ｐ_２の演算結果が−（１／ｍ）となるので、−１が乗じられる。

Next, the periodic functions S (m ¹ ) to S (m ³ ) are obtained as follows.

In the above equation, since the calculation result of p ₁ + p ₂ is − (1 / m), −1 is multiplied.

ここで、Ｊは、隣接する回転軸間の変速比が−（ｍ−１）／ｍのとき、Ｊ＝１であり、前記変速比が−（ｍ＋１）／ｍのとき、Ｊ＝−１である。 In the above equation, since the calculation result of p ₁ + 3p ₂ + 3p ₃ + p ₄ is − (1 / m ³ ), −1 is multiplied. Thus, when the gear speed ratio is (m + 1) / m, when n is an even number, the calculation result in the remainder equation is negative, so the sign adjustment term J ⁿ⁻¹ with J as −1 is a periodic function. Introduced in. That is, the periodic function S (m ^n-1 ) is expressed as the following equation.

Here, J is J = 1 when the gear ratio between adjacent rotating shafts is − (m−1) / m, and J = −1 when the gear ratio is − (m + 1) / m. is there.

となり、第１回転軸の回転角検出値θ_１（ｍ^３）は、式（１６）により求められる。

Here, in the gear mechanism shown in FIG. 1, for example, the number of axes of the rotating shaft is 4, the number of teeth m is 32 (the number of teeth on the driving side rotating shaft is m−1, and the number of teeth on the passive side rotating shaft is m. Assuming that the unit quantity u is 131072 (u corresponds to the detection value p ₁ of the angle detector S1 having a resolution of 17 bits (= 2 ¹⁷ )), the equation (14) is

Thus, the rotation angle detection value θ ₁ (m ³ ) of the first rotation shaft is obtained by Expression (16).

Accordingly, by detecting the detection values p _{1 to} p ₄ indicating the rotation angles of the first to fourth rotating shafts, the first rotating shaft that makes one cycle in 32768 (= 32 ³ ) rotations from the above equation (16). Can be detected with a resolution of 131072.

  An embodiment for detecting the multi-rotation absolute rotation angle based on the above-described principle will be described in detail below.

  FIG. 2 is a configuration diagram of a rotation angle detection device 20 for detecting a multi-rotation absolute rotation angle according to the first embodiment of the present invention. An optical absolute encoder 22 is connected to a first rotating shaft 23 provided on the opposite side of an output rotating shaft (not shown) of the servo motor 21 and a gear 23a having 31 teeth is fixed. . The gear 23 a is meshed with a gear 24 b having the number of teeth 32 fixed to the second rotating shaft 24. Further, the gear 24 a having the number of teeth 31 fixed to the second rotating shaft 24 is engaged with the gear 25 b having the number of teeth 32 fixed to the third rotating shaft 25. Further, the gear 25 a having 31 teeth fixed to the third rotating shaft 25 is meshed with a gear 26 b having 32 teeth fixed to the fourth rotating shaft 26. The gear 24a and the gear 24b, the gear 25a and the gear 25b, and the gear 26a and the gear 26b are integrally formed resin gears having the same shape, and may be integrally formed with the rotating shaft. As described above, the rotation angle detection device 20 has a structure in which the rotation of the servo motor 21 is transmitted from the first rotation shaft 23 to the fourth rotation shaft 26 via the gear mechanism connected in series.

The optical absolute encoder 22 detects the absolute angle θ ₁ within one rotation of the first rotating shaft 23 with a resolution of 17 bits (2 ¹⁷ = 131072P / Rev). The optical absolute encoder 22 is electrically connected to a signal processing circuit 28 mounted on the printed circuit board 27 and is detected as rotation angle information of the first rotary shaft 23 detected by the optical absolute encoder 22. The value p ₁ is sent to the signal processing circuit 28.

  In addition, magnets 29a, 29b, 29c having two poles magnetized in the same direction as the radial direction of the gears 24a, 25a, 26a are attached to the shaft ends of the second to fourth rotating shafts 24, 25, 26, respectively. Rotate with shaft rotation. MR rotation angle sensors 30a, 30b, 30c using MR elements are mounted on the substrate 27 at positions facing the magnets 29a, 29b, 29c. When the magnets 29a, 29b, and 29c rotate once, the MR sensors 30a, 30b, and 30c output two sinusoidal voltages that are 90 ° out of phase for one period. The detection voltages detected by the MR sensors 30a, 30b, and 30c are sent to the signal processing circuit 28, respectively.

  The resin structure 32 formed using the spacer 31 holds the second to fourth rotating shafts 24 to 26 described above. The first to fourth rotating shafts 23 to 26 shown in FIG. 2 are linearly held in the structure 32 for the sake of simplicity of explanation, but the space in the structure 32 is effectively used. Therefore, the central axes of the first to fourth rotating shafts 23 to 26 may be arranged on a curve.

Next, FIG. 3 shows a block diagram of the rotation angle detection device 20 for calculating the multi-rotation absolute rotation angle θ _{1 (} m ⁿ⁻¹ ₎ of the servo motor 21. 3, elements that are the same as or similar to the elements shown in FIG. 2 are given the same reference numerals.

In FIG. 3, a detection value p ₁ indicating the rotation angle of one cycle of the first rotation shaft 23 that is the rotation shaft of the servo motor 21 is detected by the encoder 22, and communication within the signal processing circuit 28 is performed via the signal line 33. Sent to port 34. The detection value p ₁ output from the encoder 22 has a resolution of 17 bits. The detection value p ₁ received by the communication port 34 is further sent to the multi-rotation arithmetic circuit 35 in order to calculate the absolute angle of the first rotation shaft 23.

The rotation of the first rotating shaft 23 is transmitted to the second to fourth rotating shafts 24 to 26 by a gear mechanism. Rotation angle theta ₁ through? ₄ of the first to fourth rotating shafts 23 to 26, for example, m is 32, and assuming to represent the rotation angle in the rotational speed, the first to the rotational speed of the first rotary shaft 4 the relationship between the rotation angle theta ₁ through? ₄ is a as shown in FIG. Here, the horizontal axis of FIG. 4 represents the rotation speed of the first rotation axis, and the vertical axis represents the rotation angles θ _{1 to} θ ₄ of each axis. A minus sign on the vertical axis indicates that the rotational direction of the shaft is opposite to the first rotational axis. For example, if the number of rotations of the first rotation axis is 32, the second rotation axis is θ ₂ = −31, and it can be seen that 31 rotations are performed opposite to the first rotation axis. These relationships are as shown in equations (2) to (5).

Returning to FIG. 3, the rotation angles of the first to fourth rotation shafts 23 to 26 are detected by the MR element angle detectors 30a, 30b, and 30c, respectively, and are detected by two sinusoidal detection voltages (sin). Component, cosin component) are sent to the AD converter 37 via signal lines 33a, 33b, 33c, respectively. The two detection voltages are converted from analog values into, for example, 12-bit digital values by the AD converter 37 and sent to the RD conversion arithmetic circuit 38, respectively. The RD conversion arithmetic circuit 38 calculates an angle from the two received digital values (sin component and cosin component). This angle has a resolution of 12 bits, but detection values p ₂ , p ₃ , and p ₄ extended to 17 bits in order to match the resolution of the detection value p ₁ of the encoder 22 are obtained. Specifically, 0 is added to 5 bits in the lower order of 12 bits to obtain a detection value of 17 bits. The detection voltages of the MR element angle detectors 30a, 30b, and 30c include errors due to various factors such as variations in the MR element itself and magnetic / circuit / mechanical accuracy. Therefore, the detection voltage is directly converted into an angle. Instead, offset correction and amplitude correction of the voltage signal are performed, and various accuracy corrections such as error correction with respect to the actual rotation angle and correction related to the detection value of each rotation axis are performed. The detection values p ₂ , p ₃ and p ₄ subjected to such processing are sent to the multi-rotation arithmetic circuit 35. FIG. 5 shows changes in the detected values p ₁ , p ₂ , p ₃ , and p ₄ obtained as described above with respect to the rotation speed of the first rotation shaft. Since the detection values p ₁ , p ₂ , p ₃ , and p ₄ received by the multi-rotation arithmetic circuit 35 have a resolution of 17 bits, as shown on the vertical axis in FIG. It changes between 0 and 131072 for each rotation of each axis.

The multi-rotation arithmetic circuit 35 receives the detection values p ₁ , p ₂ , p ₃ , and p ₄ from the communication port 34 and the RD conversion arithmetic circuit 38 and substitutes these values into the equation (16), so that m is 32 The multi-rotation absolute rotation angle when the resolution is 17 bits (2 ¹⁷ = 131072) and the multi-rotation range is 15 bits (2 ¹⁵ = 32768) can be calculated and output.

FIG. 6 is a graph showing each periodic signal obtained by the equations (11) to (13). Here, the horizontal axis represents the number of rotations of the first rotation shaft 23 and ranges from the number of rotations 0 to 32768, but a part of the middle is omitted for simplicity. The lower graph in FIG. 6 corresponds to the equation (11), and is a periodic signal having 32 cycles as one cycle. The periodic signal obtained by substituting the detected values p ₁ and p ₂ of the _first and second rotary shafts 23 and 24 into the equation (11) indicates the absolute rotation angle from 0 to 32 of the first rotary shaft 23. Indicates that it can be detected. The graph in the middle of FIG. 6 corresponds to the equation (12), and is a periodic signal with 1024 rotations as one cycle. A periodic signal obtained by substituting the detected values p ₁ , p ₂ , and p ₃ of the _first to third rotating shafts 23 to 25 into the equation (12) is an absolute value in which the rotational speed of the first rotating shaft 23 is from 0 to 1024. It shows that the rotation angle can be detected. Further, the upper graph in FIG. 6 corresponds to the equation (13), and is a periodic signal having 32768 rotations as one cycle. The periodic signal obtained by substituting the detected values p ₁ , p ₂ , p ₃ , and p ₄ of the first to fourth rotating shafts 23 to 26 into the equation (13) indicates that the rotational speed of the first rotating shaft 23 is 0 to 32768. The absolute rotation angle up to can be detected.

The above-described multi-rotation absolute rotation angle detection device can achieve a wide multi-rotation detection range by increasing the rotation axis. However, in order to calculate an accurate multi-rotation rotation angle detection value as described below, Therefore, high accuracy is required for each angle detector that measures the detection value of the rotating shaft. In general, the detection value measured by each angle detector includes an error. Therefore, in order to keep the calculated value of the multi-rotation rotation angle of the first rotation axis with a certain accuracy, the following will examine how much error each angle detector can tolerate. For example, the rotation angle detection value θ ₁ (m ⁿ⁻¹ ) of the first rotation axis of the multi-rotation absolute rotation angle detection device configured with n axes is expressed by the number of rotation axes n as shown in Expression (15). In the case of 2, 3 and 4, the periodic signals S (m) to S (m ³ ) represented by the equations (11) to (13) are respectively multiplied by the rotation angle detection ranges m ¹ , m ² and m ^3. And is expressed by equations (17) to (19).

軸数が３である場合

軸数が４である場合

ここで、ｍは第１回転軸の歯数であり、式（１１）〜（１３）中の単位量ｕは、１とする。すなわち、各周期関数は、第１回転軸の回転角に応じて、０から１の値をとる。 When the number of axes is 2

When the number of axes is 3

When the number of axes is 4

Here, m is the number of teeth of the first rotating shaft, and the unit amount u in the formulas (11) to (13) is 1. That is, each periodic function takes a value from 0 to 1 according to the rotation angle of the first rotation axis.

軸数３の場合

軸数４の場合

In order to maintain the accuracy of the rotation angle detection value θ ₁ (m ⁿ⁻¹ ) of the first rotation axis equal to or less than one rotation (± 0.5 rev), where e _n is the absolute value of the detection error of each rotation axis, It is necessary to satisfy the following expressions (20) to (22).
When the number of axes is 2

When the number of axes is 3

For 4 axes

軸数３の場合

軸数４の場合

Assuming that the detection error of each rotation axis is substantially equal, the detection error must fall within the following range.
When the number of axes is 2

In case of 3 axes

For 4 axes

式（２６）から理解されるように、軸数ｎが増加すると、多回転検出範囲は広くなるが、その増加に伴って各検出軸の角度検出器に対して要求される検出精度も指数的の高くなる。要求される高い検出精度を角度検出器に求めることは、多回転検出装置のコストを上昇させる原因となる。そこで、各回転軸の角度検出器に対して要求される検出精度を抑えつつ、角度検出器の検出誤差に起因する影響を低減させる多回転回転角を求めるための演算処理が必要となる。 From the equations (23) to (25), when the error range in the case of the number of axes n is deduced, the following equation (26) is obtained.

As understood from the equation (26), when the number of axes n is increased, the multi-rotation detection range is widened, but with the increase, the detection accuracy required for the angle detector of each detection axis is also exponential. Will be higher. Obtaining the required high detection accuracy from the angle detector causes an increase in the cost of the multi-rotation detection device. Therefore, it is necessary to perform arithmetic processing for obtaining a multi-rotation rotation angle that reduces the influence caused by the detection error of the angle detector while suppressing the detection accuracy required for the angle detector of each rotation axis.

Therefore, a calculation method for obtaining a calculated multi-rotation angle value that reduces the influence caused by the detection error of the angle detector using the transmission mechanism 10 shown in FIG. 1 will be described below. In general, the integer I can be expanded into the column of power m ⁿ of m. Specifically, if k is an integer from 0 to n and a _i is an integer of 0 ≦ a _k <n,
I = a ₀ m ⁰ + a ₁ m ¹ + a ₂ m ² +... A _i m ⁱ +... + A _n m ⁿ
It can be expressed as For example, if m is 10, the integer 1056 can be expanded as 6 × 10 ⁰ + 5 × 10 ¹ + 0 × 10 ² + 1 × 10 ³ . This representation is called a decimal number. In the following description, the rotation number portion of the multi-rotation absolute rotation angle uses such m-adic expansion.

ここで、ｍは第１回転軸の歯数に対応し、ｎは軸数であり、係数Ｒ_０〜Ｒ_ｎ−２は、０およびｍ−１を含む０からｍ−１の整数であり（０≦Ｒ_０〜Ｒ_ｎ−２＜ｍ）、そしてｕは、基本単位量とする。図１に示される伝達機構１０の構造では、回転軸が１軸増加する毎に多回転を検出することのできる範囲がｍ倍拡大するので、ｍ進数を用いて式（２７）の多回転回転数部を表現すると都合が良い。 In FIG. 1, the multi-rotation absolute rotation angle of the first rotation shaft 11 is mathematically calculated by the sum of the angle detection value p ₁ within one rotation of the first rotation shaft 11 and the multi-rotation rotation speed of the first rotation shaft 11. Can be expressed. Then, when this multi-rotation rotational speed is represented by an m-adic number (the reason will be described below), the multi-rotation rotational angle calculated value θ ₁ (m ⁿ⁻¹ ) ′ of the first rotational axis is expressed by the following equation (27). It can be expressed by a rotation angle calculation formula.

Here, m corresponds to the number of teeth of the first rotation axis, n is the number of axes, and the coefficients R _{0 to} R _n-2 are integers from 0 to m−1 including 0 and m−1 ( 0 ≦ R _{0 to} R _n−2 <m), and u is a basic unit amount. In the structure of the transmission mechanism 10 shown in FIG. 1, the range in which multiple rotations can be detected is increased by a factor of m each time the rotation axis is increased by one axis. It is convenient to express several parts.

The multi-rotation rotation angle detection value θ ₁ (m ⁿ⁻¹ ) of the first rotation shaft 11 can be obtained by substituting the detection values p _{1 to pn} detected by the rotation shafts into the equation (15). Essentially, the detected rotation angle value θ ₁ (m ⁿ⁻¹ ) and the calculated rotation angle value θ ₁ (m ⁿ⁻¹ ) ′ are approximately equal by appropriately selecting the coefficients R _{0 to} R _n−2. can do. That is, the coefficient R ₀ to the coefficient R ₀ to the rotation speed calculation value θ ₁ (m ⁿ⁻¹ ) ′ so that the multi-rotation rotation speed portion becomes equal to the rotation angle detection value θ ₁ (m ⁿ⁻¹ ). If R _n−2 is appropriately selected, the error of the rotation angle calculation value included in the rotation angle calculation value θ ₁ (m ⁿ⁻¹ ) ′ is only the detection error caused by the detection value p ₁ of the first rotation axis. can do. Hereinafter, a method for calculating coefficients R _{0 to} R _n-2 in order to obtain a rotation angle calculated value θ ₁ (m ⁿ⁻¹ ) ′ from detection values p _{1 to pn} detected by the detectors of the respective rotation axes. explain.

上記の条件の下で、係数Ｒ_０〜Ｒ_２の算出方法について説明する。 In order to simplify the explanation, in the transmission mechanism 10 shown in FIG. 1, when it is assumed that the number of rotation axes nmax is 4, the number of teeth m of the first rotation axis is 4, and the basic unit amount u is 1, the first rotation The calculated rotation angle value θ ₁ (m ⁿ⁻¹ ) ′ of the shaft can be expressed by the following equation (28) from equation (27).

A method for calculating the coefficients R _{0 to} R ₂ will be described under the above conditions.

したがって、第１回転軸の回転角θ_１に対する第２，第３，第４回転軸の回転角θ_２，θ_３，θ_４は、図７に示される。 First, the rotation angle θ ₁ of the _first rotation axis and the rotation angles θ ₂ , θ ₃ , θ ₄ of the second, third, and fourth rotation axes are as follows from the relationship shown in the equation (1). Each has the relationships shown in equations (29) to (31).

Accordingly, the rotation angles θ ₂ , θ ₃ , and θ ₄ of the second, third, and fourth rotation shafts with respect to the rotation angle θ ₁ of the _first rotation shaft are shown in FIG.

したがって、第１回転軸の回転角θ_１に対する各回転軸の検出値ｐ_１，ｐ_２，ｐ_３，ｐ_４は、図８に示される。 Then, since the detection value p _n indicates the detection value within one revolution in the n rotation shaft (in this example, since the base unit quantity u is 1, 0 and 1 or less), the rotation of said n rotary shaft Strictly speaking, the angle θ _n and the detected value _pn are shown in the equation (6). However, since the angle detector actually includes an error, _pn has a relationship substantially equal to mod (θ _n , u). . Therefore, the detected values p ₁ , p ₂ , p ₃ , and p ₄ of each rotation axis are obtained by substituting the above formulas (29) to (31) for the rotation angles θ ₂ , θ ₃ , and θ ₄ of each rotation axis. The relationship between the rotation angle θ ₁ of one rotation axis and the detected values p ₁ , p ₂ , p ₃ , and p _{4 of} each rotation axis is expressed by the following equations (32) to (35).

Therefore, the detected values p ₁ , p ₂ , p ₃ , and p ₄ of each rotation axis with respect to the rotation angle θ ₁ of the first rotation axis are shown in FIG.

Periodic signal S ^{(m n-1),} if the detected angle value _{p n} contains no error, it has a relationship represented by the formula (14). When obtaining the periodic signal S (m ^n-1) by using the detected angle value p _n, which includes an error, these errors affect the operation to expand. Therefore, the rotation angle calculation value θ ₁ (m ⁿ⁻¹ ) ′ obtained by Expression (27) does not include an error in terms other than the angle detection value p ₁ of the first rotation axis, and therefore includes an angle including an error. Instead of the detection value _pn, the angle correction value _pn ′ not including an error calculated by the angle correction value calculation formula of the following formula (36) is used to calculate the periodic signal S (m ⁿ⁻¹ ). .

ここで、角度補正値ｐ_２’〜ｐ_ｎ−１’は、角度検出値ｐ_２〜ｐ_ｎ−１に対する補正値であり、Ｊは、隣接する回転軸間の変速比が−（ｍ−１）／ｍのとき、Ｊ＝１とし、変速比が−（ｍ＋１）／ｍのとき、Ｊ＝−１とする符号調整項である。 The relationship between the angle correction value of each rotating shaft and the periodic signal is expressed by the following equation (37).

Here, the angle correction values p ₂ ′ to p _n−1 ′ are correction values for the angle detection values p _{2 to pn−1} , and J is a gear ratio between adjacent rotating shafts − (m−1). ) / M is a sign adjustment term in which J = 1, and when the speed ratio is − (m + 1) / m, J = −1.

Periodic signals S (m), S (m ² ), S (m ³ ) each having 4 (= m ¹ ), 16 (= m ² ), and 64 (= m ³ ) rotations of the first rotation axis as one period, respectively. Is calculated from the equations (11) to (13) in consideration of the angle correction value p _n ′, and is expressed as the following equations (38) to (41). The periodic signal S (m ⁰ ) of the first rotating shaft is the detected angle value p ₁ itself. Further, in the remainder calculation, the relationship of mod (a, c) + mod (b, c) = mod ((a + b), c) and b × mod (a, c) = mod (a × b, c) is established. Therefore, the periodic signals S (m ¹ ) to S (m ³ ) are transformed as the following equations (38) to (41).

Therefore, the relationship between the periodic functions S (m ¹ ), S (m ² ), S (m ³ ) and the rotation angle θ ₁ of the first rotating shaft is shown in FIG. As shown in FIG. 9, the periodic signal S (m ¹ ) has a periodic signal S (m ¹ ) that is further rotated every 4 rotation angles of the first rotation axis, and the periodic signal S (m ² ) is further rotated every 16 rotation angles. ³ ) becomes a sawtooth wave that monotonously increases from 0 to 1 every 64 rotation angles.

従って、ｎが１から４である場合の周期関数と第１回転軸の回転角θ_１（ｍ^ｎ−１）との関係は、式（４３）〜（４６）によって表される。

Due to the property of the periodic signal described above, when the periodic function S ( ^mn-1 ) is multiplied by ^mn-1 as shown in the following equation (42), the rotation angle detection value of the first rotating shaft up to ^mn-1 is obtained. S (m ^n-1 ) can be calculated.

Therefore, the relationship between the periodic function when n is 1 to 4 and the rotation angle θ ₁ (m ⁿ⁻¹ ) of the first rotation axis is expressed by equations (43) to (46).

  Equation (44) shows a sawtooth wave that changes from 0 to 4 every four rotations of the first rotation axis. Equation (45) represents a sawtooth wave that changes from 0 to 16 every 16 rotations of the first rotation axis. Furthermore, Formula (46) shows a sawtooth wave that monotonously increases from 0 to 64 every 64 rotations of the first rotation axis.

が成立する。 Next, a calculation method for calculating the coefficients R _{0 to} R _n−2 shown in Expression (27) from the above-described relational expression will be described. The rotation angle calculation value θ ₁ (m ⁿ⁻¹ ) ′ represented by the equation (27) and the rotation angle detection value θ ₁ (m ⁿ⁻¹ ) represented by the equation (42) are the coefficient R ₀ in the equation (42). Since ~ Rn _-2 takes only natural numbers, they do not match completely, but are approximated. That is, the following formula (47)

Is established.

ｎが１〜４の場合、回転角計算値θ_１（ｍ^０）’，θ_１（ｍ^１）’，θ_１（ｍ^２）’，θ_１（ｍ^３）’は、それぞれ次式（４９）〜（５２）のように表される。

Substituting equation (27) into the calculated rotation angle θ ₁ (m ⁿ⁻¹ ) ′ of equation (47) yields the following equation (48).

When n is 1 to 4, rotation angle calculation values θ ₁ (m ⁰ ) ′, θ ₁ (m ¹ ) ′, θ ₁ (m ² ) ′, and θ ₁ (m ³ ) ′ are respectively expressed by the following formulas (49 ) To (52).

When the relations expressed by the equations (49) to (52) are deduced, the rotation angle calculation value θ _{1 (} m ⁿ⁻¹ ) ′ is expressed as the following equation (53).

まず、式（５４）右辺のθ_１（ｍ^ｎ−２）’を左辺に移動すると、式（５５）が得られる。

ここで、ｎを２、基本単位量ｕを１とすると、

が得られる。ここで、式（４４）に示される関係からθ_１（ｍ^１）にｍｏｄ（θ_１，４）を、またθ_１（ｍ^０）’は、式（４７）に示されるように、θ_１（ｍ^０）にほぼ等しいので、式（４３）に示されるｍｏｄ（θ_１，１）を式（５６）にそれぞれ代入すると、

が成立する。ただし、ｍは４である。 Rotation angle calculated value ^{_{θ 1 (m n-1)}} ' is in consideration of approximately equal to the rotation angle detection value ^{_{θ 1 (m n-1)}} , the above equation (47), the relationship (53), the following equation (54) is obtained. By selecting a coefficient R _n−2 that satisfies the relationship of Expression (54), the coefficient R _n−2 is determined as follows.

First, when θ ₁ (m ⁿ⁻² ) ′ on the right side of Expression (54) is moved to the left side, Expression (55) is obtained.

Here, when n is 2 and the basic unit quantity u is 1,

Is obtained. Here, from the relationship shown in the equation (44), mod (θ ₁ , 4) is changed to θ ₁ (m ¹ ), and θ ₁ (m ⁰ ) ′ is changed to θ ₁ as shown in the equation (47). Since it is almost equal to (m ⁰ ), substituting mod (θ ₁ , 1) shown in equation (43) into equation (56), respectively,

Is established. However, m is 4.

Mod (θ ₁ , 4) in equation (57) is a sawtooth wave of period 4 in which the height rises from 0 to 4, and mod (θ ₁ , 1) rises from 0 to 1 in height. Therefore, the coefficient R _{0 in the} equation (57) forms a three-step staircase waveform having a height of 1 and a period of 4, as shown in the lower part of FIG.

が成立する。 In the formula (52), when u is 1 and n is 3, and the same processing as described above is performed,

Is established.

In the equation (58), mod (θ ₁ , 16) is a sawtooth wave having a height of 16 and a period of 16 and mod (θ ₁ , 4) is a sawtooth wave having a height of 4 and a period of 4. The coefficient R ₁ represented by the equation (58) forms a three-step staircase waveform having a height of 1 having a period of 16 as shown in the middle stage of FIG.

が成立する。 Further, in the equation (54), when u is 1 and n is 3, and the same processing as described above is performed,

Is established.

In the equation (59), mod (θ ₁ , 64) is a sawtooth wave having a height of 64 and a period of 64, and mod (θ ₁ , 16) is a sawtooth wave having a height of 16 and a period of 16. coefficient R ₂ of formula (59), as shown in the upper part of FIG. 10, to form a stepped waveform of the three-stage height 1 is a period 64.

Since the integer part of the rotation angle calculation value θ ₁ (m ³ ) ′ calculated by the equation (28) is the sum of the coefficients R _{0 to} R ₂ multiplied by ₁ , 4 and 16, respectively, the waveform thereof is as shown in FIG. As shown in That is, the calculated rotation angle value θ ₁ (m ³ ) ′ is obtained by adding the angle detection value p ₁ of the first rotation axis to this integer part.

ｕが１、ｎが２〜４の場合、係数Ｒ_０〜Ｒ_２は次式で示される。

Here, when the coefficient R _n−2 is derived from the equation (54), it is transformed into the following equation (60).

When u is 1 and n is 2 to 4, the coefficients R _{0 to} R ₂ are expressed by the following equations.

ここで、ＩＮＴ（ｘ）は、数値ｘを小数点以下で切り捨てる演算を意味する。また、単位量をｍとする剰余演算を行っているのは、係数Ｒ_ｎ−２が０〜ｍ−１の有効な範囲の計算結果を得るためである。以上のように、式（６５）により係数Ｒ_０〜Ｒ_ｎ−２を計算するための一般式が得られた。 Since the coefficients R _{0 to} R _n−2 are integers, for example, as shown in the following formula (64), 0.5 is added to the right side of the formula (60), and the decimal part is rounded down to obtain the coefficient R _n. An integer of _-2 is calculated. Then, by substituting S (m ^n-1 ) × m ^n-1 (formula (42)) for θ ₁ (m ^n-1 ) in formula (64), formula (65) is obtained.

Here, INT (x) means an operation of truncating the numerical value x below the decimal point. The reason why the remainder calculation with the unit amount as m is performed is to obtain a calculation result in an effective range where the coefficient R _n−2 is 0 to m−1. As described above, the general formula for calculating the coefficients R _{0 to} R _n−2 is obtained from the formula (65).

Next, the multi-rotation rotation angle calculated value θ ₁ (m ⁿ⁻¹ ) ′ of the first rotation axis is specifically obtained using the equation (65) for calculating the coefficients R _{0 to} R _n−2 . Here, in order to simplify the description of the calculation procedure, the rotation angle of the first rotation shaft is assumed with the number of rotation shafts nmax being 4, the speed ratio being 3/4 (m = 4), and the basic unit amount u being 1. The calculated value θ ₁ (m ³ ) ′ is obtained. First, when calculating the calculated rotation angle θ ₁ (m ³ ) ′ of the first rotation axis, the theory of each rotation axis when the rotation angle θ ₁ of the first rotation axis is 53.5 (rev). Angle detection values p ₁ , p ₂ , p ₃ , and p ₄ are obtained.

The rotation angles θ ₂ , θ ₃ , and θ ₄ of the _second , _third , and fourth rotation shafts with respect to the rotation angle θ ₁ of the first rotation shaft are expressed by the following equation from Equation (1).

Also, (when the rotation shaft rotates once, the angle detector outputs a detection signal of one period.) Of the angle detector shaft angle multiplier 1 when using the angle detection value p _n of each rotating shaft, p _n = Mod (θ _n , 1), the theoretical angle detection values p ₁ , p ₂ , p ₃ , and p ₄ of the respective rotation axes are numerical values obtained by the following equations.

However, since the output signal from the actual angle detector includes an error, an error of 0.05 (rev) is added to the theoretical angle detection values p ₁ , p ₂ , p ₃ , and p ₄ , for example. Assuming that the following angle detection values are detected, the rotation angle calculation value θ ₁ (m ³ ) ′ is calculated.
p ₁ = 0.500 + 0.05 = 0.550
p ₂ = 0.875 + 0.05 = 0.925
p ₃ = 0.094 + 0.05 = 0.144
p ₄ = 0.430 + 0.05 = 0.480

したがって、回転角計算値θ_１（ｍ^３）’を求めるために、式（３７）、式（６５）、式（２７）、式（３６）、をｎ＝２，３，４に対して適用し、係数Ｒ_０，Ｒ_１，Ｒ_２を順次計算する。 Assuming that the number of rotation axes nmax is 4, m = 4, and the basic unit amount u is 1, the rotation angle calculated value θ ₁ (m ³ ) ′ is expressed by the following equation (66) as is apparent from equation (27). It is expressed as

Therefore, in order to obtain the rotation angle calculation value θ ₁ (m ³ ) ′, the expressions (37), (65), (27), and (36) are applied to n = 2, 3, and 4. The coefficients R ₀ , R ₁ and R ₂ are calculated sequentially.

The procedure for calculating the coefficients R ₀ , R ₁ , R ₂ is as follows. As shown in the flowchart of FIG. 12, first, the number of rotation axes nmax (4 in the following example) is set, and 2 is set to the counter value n (step 121). When the counter value n is 2, the periodic signal value S (m ¹ ) is calculated from the detected angle values p ₁ and p _{2 according} to the equation (39) (step 122). Next, a coefficient R ₀ corresponding to the periodic signal S (m ¹ ) is obtained by the equation (65) (step 123). The coefficient R ₀ is stored in the memory for use in calculating the next rotation angle calculation value. When the coefficient R ₀ is obtained, the rotation angle calculated value θ ₁ (m ¹ ) ′ when the counter value n is 2 is calculated from the coefficient R ₀ by the expression (50) and stored in the memory (step 124). . Next, when the counter value n is incremented by 1 and becomes larger than nmax, the calculation for calculating the rotation angle calculation ends, otherwise, the process proceeds to step 126 (step 125). The calculated rotation angle calculated value θ ₁ (m ¹ ) ′ includes a detection error in terms other than the angle detection value p _{1 in} this equation (50) (in this case, the term R ₀ × m ⁰ ). Therefore, the angle correction value p ₂ ′ corresponding to the calculated rotation angle calculated value θ ₁ (m ¹ ) ′ is obtained by the equation (36) and stored in the memory (step 126). This angle correction value p ₂ ′ is used when calculating the next rotation angle calculation value θ ₁ (m ² ) ′. The above steps are repeatedly executed for the number of rotation axes n of 3 and 4, and the coefficients R ₁ and R ₂ are sequentially obtained. Finally, the calculated rotation angle value θ ₁ (m ³ ) ′ is calculated (step 124), and this flow ends (step 125). The above outlines the steps for calculating the rotation angle calculation value when the number of rotation axes is 4, but the same processing is repeated for the case where the number of rotation axes exceeds 4, and the coefficients R _{0 to} R _n are calculated. _-2 are sequentially obtained, and finally a rotation angle calculation value θ ₁ (m ^n-1 ) ′ is calculated. Hereinafter, each step described above will be described in more detail.

ここで、ｋ_１，ｋ_２は、１である。 First, the rotation axis number nmax is set to 4 and the counter value n is set to 2 (step 121). At this time, if the periodic signal S (m ¹ ) is substituted by p ₁ = 0.550 and p ₂ = 0.925 in the following equation (67), the value of the periodic signal S (m ¹ ) is 0 by the following calculation. .475 (step 122).

Here, k ₁ and k ₂ are 1.

この係数Ｒ_０は、最終的に求める回転角検出値を算出するときに使用するためにメモリに格納される。 Next, the coefficient R ₀ is obtained by substituting S (m ¹ ) = 0.475, m = 4, θ ₁ (m ⁰ ) ′ = p ₁ = 0.550 into the following equation (68) by the following calculation: The coefficient _R0 is 1 (step 123).

This coefficient R ₀ is stored in the memory for use when calculating the rotation angle detection value finally obtained.

When R ₀ is obtained, the rotation angle calculated value θ ₁ (m ¹ ) ′ is obtained from the equation (50) as the following equation (69) (step 124).

この角度補正値ｐ_２’は、カウンタ値ｎが３の場合の係数Ｒ_１を求める際に使用される。 When the counter value n is incremented by 1 and the counter value n has not reached 4, the process proceeds to the next step (step 125). In step 126, an angle correction value p ₂ ′ of the second rotation axis corresponding to the calculated rotation angle value θ ₁ (m ¹ ) ′ is obtained by equation (36) (step 126).

The angle correction value p ₂ ′ is used when obtaining the coefficient R ₁ when the counter value n is 3.

ここで、ｋ_１＝１，ｋ_２＝２，ｋ_３＝１である。 Next, the processing flow returns from step 126 to step 122, and the same processing as described above is repeated. That is, when the counter value n is 3, the periodic function S (m ² ) is obtained from the equation (37) as follows (step 122).

Here, k ₁ = 1, k ₂ = 2 and k ₃ = 1.

The coefficient R ₁ is calculated by substituting S (m ² ) = 0.370, m = 4, and θ ₁ (m ¹ ) ′ = 1.55 into the equation (65). As in the following calculation, the coefficient R ₁ is 1 (step 123).

When R ₁ is obtained, the rotation angle calculated value θ ₁ (m ² ) ′ is obtained from the equation (51) as the following equation (step 124).

The angle correction value p ₃ ′ of the third rotation axis corresponding to this rotation angle calculated value θ ₁ (m ² ) ′ is obtained from the equation (36) as follows and stored in the memory (step 126). This angle correction value p ₃ ′ is used when obtaining the coefficient R ₂ when the counter value n is 4.

ここで、ｋ_１＝１，ｋ_２＝３，ｋ_３＝３，ｋ_４＝１である。 Next, when the number of rotation axes n is 4, the periodic function S (m ³ ) is obtained from the equation (37) as follows (step 122).

Here, k ₁ = 1, k ₂ = 3, k ₃ = 3, k ₄ = 1.

The coefficient R ₂ is calculated by substituting S (m ³ ) = 0.91, m = 4, and θ ₁ (m ² ) ′ = 5.55 into the equation (65). Coefficient _{R 2} by the following calculation is three (step 123).

When R ₂ is obtained, the calculated rotation angle θ ₁ (m ³ ) ′ is obtained from the equation (52) as follows (step 124).

Since the counter value n is 4, the process for obtaining the rotation angle calculation value ends (step 125). From the above calculation, the rotation angle calculated value θ ₁ (m ³ ) ′ of the first rotating shaft was calculated as 53.55. As described in paragraph 0088 above, since the calculation is based on the assumption that the rotation angle of the first rotation axis is 53.5 (rev), the calculated rotation angle θ ₁ (m ³ ) as the calculation result. The error of 'is only 0.05 given to the angle detection value of the first rotation axis, and the detection errors of the angle detectors after the second rotation axis are not accumulated.

Next, another calculation method for obtaining the coefficients R _{0 to} R _n−2 in Expression (27) will be described. The method corrected angle correction value of each rotating axis calculated from the rotation axis of the angle detection value p _n and equation (27) multiple rotations obtained by the rotation angle calculated value ^{_{θ 1 (m n-1)}} ' p _n 'calculated (formula (36), the angle detection value p _n and angle correction value p _n' on the assumption that a is approximately equal to the angle correction value p _{n 'is} closest to the detected angle value p _n This is a method for determining the coefficients R _{0 to} R _n-2 .

なお、上式（７４）における剰余計算中の右の括弧内は、式（２７）の回転角計算値θ_１（ｍ^ｎ−１）に相当する。 The rotation angle calculated value θ ₁ (m ⁿ⁻¹ ) ′ of the first rotation axis is expressed by the equation (27), and the angle detection value p ₁ of the first rotation axis and the multi-rotation rotation speed of the first rotation axis. As described above, it can be expressed mathematically by the sum of. If the equation (27) is substituted into the calculated rotation angle value θ ₁ (m ⁿ⁻¹ ) ′ in the equation (36), the angle correction value p _n ′ can be expressed by the following equation (74). The angle correction value _{p n} 'approximates a detected angle value _{p n.}

The right parenthesis in the remainder calculation in the above equation (74) corresponds to the calculated rotation angle θ ₁ (m ⁿ⁻¹ ) in equation (27).

と表され、この角度補正計算式の計算結果が角度検出値ｐ_２に最も近くになるように０≦Ｒ_０＜ｍである整数の係数Ｒ_０を適切に選択すればよい。このように決定した係数Ｒ_０を式（７４）に代入することにより、角度補正値ｐ_２’が求められる。このようにして、ｎを２からｎｍａｘまで繰り返して、係数Ｒ_０〜Ｒ_{ｎｍａｘ−２}を決定し、式（２７）に代入することにより、最終的に第１回転軸の多回転回転角計算値θ_１（ｍ^{ｎｍａｘ−１}）’を求めることができる。 In the above equation (74), the angle detection value _pn is an angle within one rotation detected by an angle detector attached to each rotation shaft, and the coefficients R _{0 to} R _n−2 are 0 and m−. Since it is an integer from 0 to m-1, including 1, the angle correction value _pn 'is determined by appropriately selecting the coefficients _R0 to Rn _-2 so as to approximate the detected angle value _pn most closely. be able to. For example, the angle correction value p ₂ ′ of the second rotation axis can be determined from the detected angle value p _{2 as} follows. That is, from the equation (74), the angle correction value calculation formula is

The integer coefficient R ₀ satisfying 0 ≦ R ₀ <m may be appropriately selected so that the calculation result of the angle correction calculation formula is closest to the detected angle value p ₂ . The angle correction value p ₂ ′ is obtained by substituting the coefficient R ₀ determined in this way into the equation (74). In this way, by repeating n from 2 to nmax, the coefficients R _{0 to} R _nmax−2 are determined and substituted into the equation (27), thereby finally calculating the multi-rotation rotation angle of the first rotation axis. θ ₁ (m ^nmax−1 ) ′ can be obtained.

Next, an equation for calculating the coefficients R _{0 to} R _nmax−2 is obtained from the equation (74). When the deformation represented by the equation (53) is substituted into the equation (74), the angle correction value p _n ′ is represented by an angle correction value calculation formula of the following equation (75).

Further expanding the expression (75), the angle correction value p _n ′ is expressed as the following expression (76).

Further transforming the equation (76), the angle correction value p _n ′ is expressed as the following equation (77).

In addition, even if a numerical value obtained by multiplying a divisor by an integer is added or subtracted in the remainder operation, the result of the remainder operation is not affected, and the numerical value is removed from the remainder operation. That is, when b is an integer, the relationship y = mod (a + b × c, c) = mod (a, c) is established. Therefore, in the equation (77), since R _n−2 and m ^m−2 are both natural numbers, the term of −1 × R _n−2 × m ^m−2 × u is deleted. As a result, the equation (77) is transformed into the following equation (78).

Since the detected angle value _pn is substantially equal to the corrected angle value _pn ′, the detected angle value _pn is expressed by the following equation (79).

As in the above equation (79), since the relationship between the detected angle value p _n and the coefficient R _n-2 is derived, as defined by the remainder operation, as can be determined coefficient R _n-2 as follows Become. In general, the remainder calculation for obtaining the remainder y when a ± b is divided by c is expressed as y = mod (a ± b, c), and therefore the mathematical formula a ± b = n × c + y is established. Here, n is an integer and y is 0 ≦ y <c. When a is moved to the right side, the above formula becomes ± b = n × c + ya. The remainder calculation for calculating the remainder when both sides of this formula are divided by c can be expressed as mod (± b, c) = mod (n × c + y−a, c). As explained in paragraph 0112, the n × c term in parentheses can be deleted, so the above equation can be rearranged as mod (± b, c) = mod (ya, c). it can. Here, when b is 0 ≦ b <c, b = mod (± (ya), c) is established. Using this relationship, an equation for obtaining the coefficient R _n−2 from Equation (79) is derived as shown below.

The coefficient R _{n−2 in} equation (79) is 0 ≦ R _n−2 <m, as described in paragraph 0065, so that 0 ≦ (1 / m) × R _n−2 × u <u Is established. Therefore, in Formula (79), p _n ′ is y, (− (m ± 1) / m) ⁿ⁻¹ × θ ₁ (m ⁿ⁻² ) ′ is a, (1 / m) × R _n−2 Assuming that x u is b and u is c, as described above, mod (± b, c) = mod (y−a, c) is such that when b is 0 ≦ b <c, b = mod ( It can be calculated as ± (y−a), c). That is, (1 / m) × R _n−2 × u in the remainder calculation of Expression (79) is obtained by the following Expression (80).

係数Ｒ_ｎ−２は、式（８１）によって求められるが、係数Ｒ_ｎ−２は整数であるので、上式（８１）の演算結果を四捨五入する。その整数化は、次式（８２）に示されるように、演算結果に０．５を加え、剰余演算によって桁上がり処理を行なうことにより達成できる。なお、ＩＮＴ（Ｘ）は、Ｘの小数点以下を切り捨てる演算子である。

In the remainder calculation, mod (a, c) × b = mod (a × b, c × b) is established, so that the right side of the above equation (80) can be further transformed as the following equation (81). it can.

The coefficient R _n−2 is obtained by the equation (81). Since the coefficient R _n−2 is an integer, the calculation result of the above equation (81) is rounded off. The integerization can be achieved by adding 0.5 to the operation result and performing a carry process by a remainder operation, as shown in the following equation (82). Note that INT (X) is an operator that truncates the decimal part of X.

Actually, mod (mod (a, c) + b, c) = mod (a + b, c) is established, so that the equation (82) is transformed into the following equation (83), and the remainder operation is performed once. Can be reduced.

Now, since the calculation formula for calculating the coefficient R _n−2 is obtained by the above formula (83), from the formula (83) using the detected values (paragraph 0091) of the respective rotary shafts as in the first embodiment. R ₀ , R ₁ , and R ₂ are obtained and substituted into Equation (27) to calculate the calculated rotation angle θ ₁ (m ³ ) ′ of the first rotation axis. In the following calculation example, the basic unit number u = 1000, the detection values p ₁ = 550, p ₂ = 925, p ₃ = 144, and p ₄ = 480 of each rotation axis.

The procedure for calculating the coefficients R ₀ , R ₁ , R ₂ is as follows. As shown in the flowchart of FIG. 13, first, the number of rotation axes nmax (4 in the following example) is set, and the counter value n is set to 2 (step 131). When the counter value n is 2, the rotation angle calculation value θ ₁ (m ⁰ ) ′ (= p ₁ ) and the angle detection value p ₂ are substituted into the equation (83), the coefficient R ₀ is calculated, and the coefficient R ₀ Is stored in the memory for use in calculating the next calculated rotation angle (step 132). When the coefficient R ₀ is obtained, the detected angle value p ₁ and the coefficient R ₀ are substituted into the equation (27), and the rotation angle calculated value θ _{1 (} m ¹ ₎ ′ is calculated and stored in the memory (step 133). . Next, the counter value n is incremented by 1, and the process returns to step 132 (step 134). The above calculation process is repeatedly executed for the counter values n = 3 and 4, and the coefficients R ₁ and R ₂ are obtained. Finally, the rotation angle calculated value θ ₁ (m ³ ) ′ is calculated (step 133). When the counter value n is larger than nmax, the calculation for calculating the rotation angle calculation ends (step 134). The above outlines each step when the number of rotation axes is 4, but the same processing is repeated for the case where the number of rotation axes exceeds 4, and the coefficients R _{0 to} R _n−2 are sequentially obtained, and finally Thus, the rotation angle calculation value θ ₁ (m ⁿ⁻¹ ) ′ of the first rotation axis is calculated. Hereinafter, each step described above will be described in more detail.

さらに、回転軸間の歯車は減速すると想定し、ｐ_２＝９２５、θ_１（ｍ^０）’＝５５０（＝ｐ_１）、ｍ＝４、ｕ＝１０００を上式（８４）に代入すると、次式（８５）となる。

算出された係数Ｒ_０は、後続の処理のためにメモリに格納される。 First, the number of rotation axes nmax is set to 4, and the counter value n is set to 2 (step 131). Substituting n = 2 into the equation (83), the coefficient _R0 is obtained by the following equation (84) (step 132).

Furthermore, assuming that the gear between the rotating shafts decelerates, substituting p ₂ = 925, θ ₁ (m ⁰ ) ′ = 550 (= p ₁ ), m = 4, u = 1000 into the above equation (84), The following equation (85) is obtained.

The calculated coefficient R ₀ is stored in the memory for subsequent processing.

と表されるので、式（８６）にｐ_１＝５５０，Ｒ_０＝１，ｍ＝４、ｕ＝１０００を代入すると、回転角計算値θ_１（ｍ^１）’は、次式のように計算される、メモリに格納される（ステップ１３３）。

Next, the rotation angle calculated value θ ₁ (m ¹ ) ′ is calculated from the equation (50).

Therefore, when p ₁ = 550, R ₀ = 1, m = 4, and u = 1000 are substituted into the equation (86), the rotation angle calculated value θ ₁ (m ¹ ) ′ is expressed by the following equation: Calculated and stored in memory (step 133).

さらに、上式にｐ_３＝１４４、θ_１（ｍ^１）’＝１５５０、ｍ＝４、ｕ＝１０００を代入すると、係数Ｒ_１は次式（８８）によって求められる（ステップ１３２）。

係数Ｒ_１は１となり、その値は後続の処理のためにメモリに格納される（ステップ１３２）。 Next, the counter value n is incremented by 1 (n = 3), and the process returns to step 132 (step 134). Substituting n = 3 into the equation (83), the coefficient R ₁ is obtained by the following equation (87) (step 132).

Further, when p ₃ = 144, θ ₁ (m ¹ ) ′ = 1550, m = 4, and u = 1000 are substituted into the above equation, the coefficient R ₁ is obtained by the following equation (88) (step 132).

The coefficient R ₁ becomes 1, and the value is stored in the memory for subsequent processing (step 132).

と表されるので、式（８９）にθ_１（ｍ^１）’＝１５５０，Ｒ_１＝１，ｍ＝４、ｕ＝１０００を代入すると、回転角計算値θ_１（ｍ^２）’は、次式のように計算される（ステップ１３３）。

Further, the calculated rotation angle value θ ₁ (m ² ) ′ is calculated from the equation (51).

Therefore, substituting θ ₁ (m ¹ ) ′ = 1550, R ₁ = 1, m = 4, and u = 1000 into Equation (89), the rotation angle calculated value θ ₁ (m ² ) ′ is It is calculated as follows (step 133).

さらに、上式にｐ_４＝４８０、θ_１（ｍ^２）’＝５５５０、ｍ＝４、ｕ＝１０００を代入すると、係数Ｒ_２は次式（９１）によって求められる（ステップ１３２）。

係数Ｒ_２は３となり、その値は後続の処理のためにメモリに格納される（ステップ１３２） Next, the counter value n is incremented by 1 (n = 4), and the process returns to step 132 (step 134). Substituting n = 4 in formula (83), the coefficient _{R 2} is determined by the following equation (90).

Furthermore, when p ₄ = 480, θ ₁ (m ² ) ′ = 5550, m = 4, and u = 1000 are substituted into the above equation, the coefficient R ₂ is obtained by the following equation (91) (step 132).

Coefficient R ₂ is 3, and the value is stored in memory for subsequent processing (step 132)

と表されるので、式（９２）にθ_１（ｍ^２）’＝５５５０，Ｒ_２＝３，ｍ＝４、ｕ＝１０００を代入すると、回転角計算値θ_１（ｍ^３）’は、次式のように計算される（ステップ１３３）。

この結果、実施例２における方法によって計算された第１回転軸の回転角計算値θ_１（ｍ^３）’は、５３５５０（基本単位量ｕ＝１０００）となる。この回転角計算値は、実施例１において求めた第１回転軸の回転角計算値θ_１（ｍ^３）’＝５３．５５（基本単位量ｕ＝１）と同等である。 Further, θ ₁ (m ³ ) ′ is calculated from the equation (52).

Therefore, if θ ₁ (m ² ) ′ = 5550, R ₂ = 3, m = 4, and u = 1000 are substituted into Equation (92), the calculated rotation angle θ ₁ (m ³ ) ′ is It is calculated as follows (step 133).

As a result, the rotation angle calculated value θ ₁ (m ³ ) ′ of the first rotating shaft calculated by the method in Embodiment 2 is 53550 (basic unit amount u = 1000). This rotation angle calculation value is equivalent to the rotation angle calculation value θ ₁ (m ³ ) ′ = 53.55 (basic unit amount u = 1) obtained in the first embodiment.

  FIG. 14 is a block diagram showing the configuration of the transmission mechanism 140 of the rotation angle detection device according to the third embodiment of the present invention. This transmission mechanism 140 is a transmission mechanism in which the transmission mechanism 10 shown in FIG. 1 is provided in parallel, and is formed by a first-line gear mechanism 141 and a second-line gear mechanism 142. The gear 144a attached to the motor rotation shaft 144 of the motor 143 is meshed with the gear 145a attached to the first rotation shaft 145, and the gear ratio between the motor rotation shaft 144 and the first rotation shaft 145 is 1: N. In the embodiment shown in FIG. 1, the first rotating shaft 145 is a gear mechanism that is common to the first and second series gear mechanisms 141 and 142, but is not necessarily common.

The first series gear mechanism 141 transmits the rotation of the motor from the first rotating shaft 145 to the second and third rotating shafts 146 and 147. The gear 145b of the first rotating shaft 145 meshes with the gear 146a of the second rotating shaft 146, and the gear 146c of the second rotating shaft 146 meshes with the gear 147a of the third rotating shaft 147. The rotation angles of the first to third rotation shafts are detected by angle detectors S1 to S3, respectively. The gear ratio of the meshed gears of the first series gear mechanism 141 is set to (m ₁ ± 1) / m ₁ .

As shown, the second series gear mechanism 142 has gears 148a, 148b, 149a attached to the fourth and fifth rotary shafts 148, 149, and the motor 143 rotates from the gear 145c of the first rotary shaft 145 to the gears. It is transmitted to the gear 149a via 148a and 148b. The rotation angles of the first and second rotation shafts are detected by angle detectors S3 and S4, respectively. The gear ratio of the meshed gears of the second gear mechanism 142 is set to (m ₂ ± 1) / m ₂ .

The rotation of the motor 143 is decelerated to 1 / N via the gear 144a and the gear 145a and transmitted to the first rotating shaft 145. The rotation of the first rotating shaft 145 is transmitted from the gear 145b to the first series gear mechanism 141 and from the gear 145c to the second series gear mechanism 142. The periodic signals obtained based on the angle detection values detected by the angle detectors S1 to S3 of the first series gear mechanism 141 and the angle detectors S1, S4, and S5 of the second series gear mechanism 142 are: This is the same as the periodic signal calculation method described in the embodiment. As described in Patent Documents 2 and 3, when the periods obtained in each series are relatively prime, the number of rotations of the least common multiple of these periods can be detected. Therefore, for example, if the periodic signals of the first and second series have C ₁ and C ₂ periods, respectively, the rotation signal of the least common multiple can be detected by generating the periodic signal of the least common multiple of C ₁ and C _2. It becomes.

In the transmission mechanism 140 of FIG. 14, when m ₁ is 15, m ₂ is 16, and N is 10, the multi-rotation rotational speed that can be detected by the transmission mechanism 140 is as follows. That is, since the first series gear mechanism 141 and the second series gear mechanism 142 are formed by three stages of rotating shafts, as described in paragraph 0038, m ₁ ² = 225 periods, m A periodic signal of ₂ ² = 256 periods can be created. Since their periods are relatively prime, their least common multiple is 225 periods × 256 periods = 57,600 periods. Further, since the first rotation shaft 145 is decelerated to 1/10 with respect to the motor rotation shaft 144, the multi-rotation detection range that can be detected by the motor rotation shaft is 106,000 times 576,000 rotations.

  As described above, in the third embodiment, the transmission mechanism of the first embodiment is provided in parallel, and the rotation speed detection range or the period of the periodic signal obtained from each transmission mechanism provided in parallel is relatively prime. Thus, the multi-rotation detection range of the rotation angle detection device can be easily expanded. Moreover, although the said 3rd Example provides two parallel transmission mechanisms, it can implement | achieve the rotation angle detection apparatus which has a wider multi-rotation rotation angle detection range by providing a parallel transmission mechanism further.

  In the above embodiment, an optical encoder is used as the angle detector for the first rotation shaft, and an MR rotation angle sensor using an MR element is used as the angle detector for the second to fourth rotation shafts. In order to implement the present invention, the present invention is not limited to the type of angle detector. Further, although a gear is used as the transmission means, the means for changing the rotation angle is not limited to the gear, and includes a transmission such as a belt, a chain, and a traction drive. Further, (m ± 1) / m mentioned above means a gear ratio, and in the embodiment, the gear is used as the transmission means, so m and m ± 1 correspond to the number of gear teeth. However, the number of gear teeth is not necessarily limited.

In the present embodiment, the basic unit amount for detecting the rotation angle is u = 1 (REV).
Alternatively, although an example of u = 1000 (Pulse / REV) has been shown, u = 360 (°) or any other unit amount may be used as long as the basic unit amounts of the respective rotation axes are aligned.

  Furthermore, in the present embodiment, an example in which a detector with a shaft angle multiplier of 1X is used is shown. However, a detector with a shaft angle multiplier of nX (when the rotating shaft makes one revolution, an n-cycle signal is output) is used. Even in this case, it is possible to calculate the multi-rotation rotation angle in the same manner. In that case, the detection range of the multi-rotation rotation angle is 1 / n. Even if detectors with different shaft angle multipliers are used, a multi-rotation rotation angle can be calculated even if detectors with different shaft angle multipliers are used if calculation processing for matching the basic unit amounts is performed.

11-15, 23-26, 73-75 Rotating shaft 11a, 12a, 12b, 13a, 13b, 14a, 14b, 23a, 24a, 24b, 25a, 25b, 26a, 26b, 73a, 74a, 74b, 75a Gear 21 , 71 Motor 22 Optical absolute encoder 28, 82 Signal processing circuits 29a, 29b, 29c Magnets 30a, 30b, 30c MR rotation angle sensors S1 to Sn angle detectors

Claims (20)

A transmission mechanism for transmitting rotation from a first rotation axis to an nmax rotation axis, wherein the numerical values nmax and m are integers of 3 or more with respect to the rotation angle θ ₁ of the first rotation shaft, and the numerical value n is If 1 ≦ n ≦ nmax, the rotation angle θ _n of the n-th rotation axis is

Satisfies the relationship, the transmission mechanism, and a multi-rotation absolute rotational angle detecting device having an angle detector for detecting an angle detected value p ₁ ~p _nmax within one revolution of the first nmax rotating shaft from said first rotary shaft In the method of calculating the multi-rotation absolute rotation angle of the first rotation axis,
(1) detecting the angle detection value p _n in one rotation of the first n rotation axis by the angle detector,
(2) determining a coefficient _{R n-2} from the rotation angle calculated value ^{_{θ 1 (m n-2)}} ' and the detected angle value _{p n,}
(3) Using the determined coefficient R _n−2 as a rotation angle calculation formula,

Substituting for the rotation angle calculation value θ ₁ (m ⁿ⁻¹ ) ′,
The step of calculating the rotation angle consisting of is repeated from the numerical value n from 2 to nmax, thereby sequentially determining values from the coefficient R ₀ to the coefficient R _nmax-2, and calculating the multi-rotation absolute rotation angle of the first rotation axis. ^{Determining a} value θ ₁ (m ^nmax−1 ) ′;
Here, the coefficients R _{0 to} R _nmax-2 are integers from 0 to m−1 including 0 and m−1, u is the basic unit amount, and the calculated rotation angle θ ₁ (m ⁰ ) ′ is the first rotation axis. The detected angle value p ₁ of
A method of calculating a multi-rotation absolute rotation angle characterized by: Determining the coefficient R _n-2 includes:
The periodic signal S (m ⁿ⁻¹ ) obtained from the detected value of the n axis is

K ₁ , k ₂ ,..., K _n is an expansion expression k ₁ × x ⁰ + k ₂ × x ¹ + k ₃ × x ² ... K _n x of (x + 1) ^{n−1. n−1} is a coefficient of the n−1 order term of x at n−1, mod (x, a) is a remainder operation for obtaining a remainder when x is divided by a, and J is a gear ratio between adjacent rotating shafts. Is a sign adjustment term in which J = 1 when J is − (m−1) / m and J = −1 when the gear ratio is − (m + 1) / m;
Multiplying the periodic signal S (m ^n-1 ) of the ^n- th rotation axis by m ^n-1 to obtain a rotation angle detection value θ ₁ (m ^n-1 );
Coefficient R _n−2 where the calculation result of the rotation angle calculation formula for obtaining the rotation angle calculation value θ ₁ (m ⁿ⁻¹ ) ′ of the ^n- th rotation axis approximates the rotation angle detection value θ ₁ (m ⁿ⁻¹ ). And the stage of determining
The calculated rotation angle θ ₁ (m ⁿ⁻¹ ) ′ of the ^n- th rotation axis is obtained by substituting the determined coefficient R _n−2 into the rotation angle calculation formula,
The angle correction value p _n ′ is obtained by calculating the calculated rotation angle θ ₁ (m ⁿ⁻¹ ) ′.

Calculated by substituting
The method of calculating a multi-rotation absolute rotation angle according to claim 1. Determining the coefficient R _n-2 includes:

Including the step of determining an integer that most closely approximates the result of
3. The method of calculating a multi-rotation absolute rotation angle calculation value according to claim 1 or 2. Determining the coefficient R _n-2 includes:

INT (x) is an operation for rounding down the decimal point of the numerical value x.
3. The method of calculating a multi-rotation absolute rotation angle according to claim 2.   A step of calculating a multi-rotation absolute rotation angle based on an angle detection value detected by an angle detector of the transmission mechanism and the plurality of transmission mechanisms, further comprising a plurality of transmission mechanisms provided in parallel with the transmission mechanism; The method of claim 1 further comprising:   The method further includes a plurality of transmission mechanisms provided in parallel with the transmission mechanism, and further comprising calculating the periodic signal based on an angle detection value detected by an angle detector of the transmission mechanism and the plurality of transmission mechanisms. The method according to claim 2.   The method according to claim 6, wherein periods of the periodic signals obtained from the transmission mechanism and the plurality of transmission mechanisms are disjoint.   The method according to claim 5, wherein the first rotation shaft of the transmission mechanism and the plurality of transmission mechanisms is the same rotation shaft. A transmission mechanism for transmitting rotation from a first rotation axis to an nmax rotation axis, wherein the numerical values nmax and m are integers of 3 or more with respect to the rotation angle θ ₁ of the first rotation shaft, and the numerical value n is If 1 ≦ n ≦ nmax, the rotation angle θ _n of the n-th rotation axis is

Satisfying the relationship:
An angle detector for detecting angle detection values p _{1 to} p _nmax within one rotation of the nmax rotation shaft from the first rotation shaft;
An arithmetic device that calculates a multi-rotation absolute rotation angle calculation value θ ₁ (m ^nmax−1 ) ′ of the first rotation axis based on the detected angle values p _{1 to} p _nmax ;
The arithmetic unit is:
A coefficient R _n-2 is determined from the calculated rotation angle value θ ₁ (m ⁿ⁻² ) ′ and the detected angle value pn of the _n- th rotation axis, and the calculated rotation angle value based on the determined coefficient R _n−2. θ ₁ (m ⁿ⁻¹ ) ′ is a rotation angle calculation formula,

By repeating the numerical value n from 2 to nmax, the values from the coefficient R ₀ to the coefficient R _nmax−2 are sequentially determined, and the multi-rotation absolute rotation angle calculated value θ ₁ (m ^{nmax− 1} ) ′, where the coefficients R _{0 to} R _nmax−2 are integers from 0 to m−1 including 0 and m−1, u is the basic unit amount, and the calculated rotation angle θ ₁ (m ⁰ ) 'Is the detected angle value p ₁ of the first rotation axis.
A device for calculating a multi-rotation absolute rotation angle. The arithmetic unit is:
The periodic signal S (m ⁿ⁻¹ ) obtained from the detected value of the n axis is

And means for calculating a periodic signal S ^{(m n-1)} determined _{by, k 1, k 2, ···} k n is, (x + ¹⁾ expansions of _{^{n-1 k 1 × x 0}} + k 2 × x ¹ + k ₃ × x ² ... K _n x ⁿ⁻¹ is the coefficient of the (n−1) th-order term of x, and mod (x, a) is a remainder operation for calculating the remainder when x is divided by a. , J is a sign that J = 1 when the gear ratio between adjacent rotating shafts is − (m−1) / m, and J = −1 when the gear ratio is − (m + 1) / m. Means for calculating a periodic signal, which is an adjustment term;
Means for multiplying the periodic signal S (m ^n-1 ) of the ^n- th rotation axis by m ^n-1 to obtain a rotation angle detection value θ _{1 (} m ^n-1 ₎ ;
Coefficient R _{n− that} the calculation result of the rotation angle calculation formula for calculating the rotation angle calculation value θ ₁ (m ⁿ⁻¹ ) ′ of the ^n- th rotation axis approximates the rotation angle detection value θ ₁ (m ⁿ⁻¹ ) ′. Means for determining ₂ ;
Means for substituting the determined coefficient R _n−2 into the rotation angle calculation formula to obtain a rotation angle calculation value θ ₁ (m ⁿ⁻¹ ) ′ of the ^n- th rotation axis;
The calculated rotation angle calculated value θ ₁ (m ⁿ⁻¹ ) ′ is

Substituting into, means for obtaining the angle correction value p _n ′,
The apparatus for calculating a multi-rotation absolute rotation angle according to claim 9, comprising: The means for determining the coefficient R _n-2 is:

Including the step of determining an integer that most closely approximates the result of
The apparatus for calculating a multi-rotation absolute rotation angle according to claim 9 or 10, characterized by comprising: The means for determining the coefficient R _n-2 is:

The coefficient R _n−2 is determined by calculating
11. The apparatus for calculating a multi-rotation absolute rotation angle according to claim 10, wherein INT (x) is an operation for rounding down the decimal point of the numerical value x.   A plurality of transmission mechanisms provided in parallel with the transmission mechanism; and calculating a multi-rotation absolute rotation angle based on an angle detection value detected by an angle detector of the transmission mechanism and the plurality of transmission mechanisms. The apparatus for calculating a multi-rotation absolute rotation angle according to claim 9.   And further comprising a plurality of transmission mechanisms provided in parallel with the transmission mechanism, wherein the periodic signal is calculated based on an angle detection value detected by an angle detector of the transmission mechanism and the plurality of transmission mechanisms. The apparatus for calculating a multi-rotation absolute rotation angle according to claim 10.   15. The apparatus for calculating a multi-rotation absolute rotation angle according to claim 14, wherein the periods of the periodic signals obtained from the transmission mechanism and the plurality of transmission mechanisms are relatively prime.   16. The apparatus for calculating a multi-rotation absolute rotation angle according to claim 13, wherein the first rotation shafts of the transmission mechanism and the plurality of transmission mechanisms are the same rotation shaft. A transmission mechanism for transmitting rotation from a first rotation axis to an nmax rotation axis, wherein the numerical values nmax and m are integers of 3 or more with respect to the rotation angle θ ₁ of the first rotation shaft, and the numerical value n is If 1 ≦ n ≦ nmax, the rotation angle θ _n of the n-th rotation axis is

Satisfies the relationship, the transmission mechanism, and a multi-rotation absolute rotational angle detecting device having an angle detector for detecting an angle detected value p ₁ ~p _nmax within one revolution of the first nmax rotating shaft from said first rotary shaft The method of calculating the multi-rotation absolute rotation angle calculated value θ ₁ (m ^nmax−1 ) ′ of the first rotation axis is as follows:
And detecting the detected angle value _p 1 _{~p nmax} within one revolution of the first nmax rotary shaft from the first rotation axis by the angle detector,
A step of determining values from a coefficient R ₀ to a coefficient R _nmax−2 , determining a coefficient R _n−2 from a rotation angle correction value p _n ′ of the n-th rotation axis, and determining the determined coefficient R _{n− 2} is determined so that the angle correction value _pn ′ obtained by the following equation for calculating the angle correction value is closest to the detected angle value pn of the _n- th rotation axis,

Sequentially determining values from the coefficient _R0 to the coefficient _Rnmax-2 by repeating the numerical value n from 2 to nmax in the angle correction value calculation formula;
The determined coefficients _{R0 to Rnmax-2} are calculated as a rotation angle calculation formula,

To calculate a multi-rotation absolute rotation angle calculated value θ ₁ (m ^nmax−1 ) ′ of the first rotation axis, and coefficients R _{0 to} R _nmax−2 are from 0 including 0 and m−1. an integer of m−1, u is a basic unit quantity, and an angle correction value p ₁ ′ is an angle detection value p ₁ of the first rotation axis;
A method of calculating a multi-rotation absolute rotation angle characterized by comprising: Determining the coefficient R _n-2 includes:

Including the step of determining an integer that most closely approximates the result of
The method of calculating a multi-rotation absolute rotation angle according to claim 17.   A step of calculating a multi-rotation absolute rotation angle based on an angle detection value detected by an angle detector of the transmission mechanism and the plurality of transmission mechanisms, further comprising a plurality of transmission mechanisms provided in parallel with the transmission mechanism; The method of claim 17, further comprising: 20. The method according to claim 17, wherein the first rotation shaft of the transmission mechanism and the plurality of transmission mechanisms are the same rotation shaft.

Images