JPH05277974A - Calibration method for positioning mechanism having rotary shaft - Google Patents

Abstract

PURPOSE:To perform simple detection of a vertical direction as seen from a base coordinate system and to perform automatic calibration by attaching a sensor, which detects the vertical direction, to the tip of a positioning mechanism having a rotary shaft and displacing the positioning mechanism in plurality of different postures. CONSTITUTION:A robot 1 being about to execute calibration is controlled by a robot controller 4. A force sensing sensor 2 is attached to the tip of the robot 1 and an object 3 having a known weight is attached thereto. Further, a controller 5 for the force sensing sensor 2 is connected to the robot controller 4. In this case, a positioning mechanism to which the force sensing sensor 2 is attached is displaced in a plurality of different postures and each rotary shaft position and a vertical direction are determined in each posture. An angle parameter related to conversion of the posture of the positioning mechanism and a vertical direction as seen from a mechanism base coordinate system are determined. This constitution performs automatic calibration of the positioning mechanism.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention is used to obtain a reference position (0 degree) of each rotary shaft of a positioning mechanism having a rotary shaft such as an industrial robot or a 6-axis NC machine tool having a rotary shaft. Regarding calibration method.

[0002]

2. Description of the Related Art Conventional calibration performed to obtain a reference position (0 degree) of each rotating shaft is such that a convex jig is attached to the tip of a positioning mechanism and the position of the base of the positioning mechanism is changed. A concave jig having a dial gauge is attached to a known position, and the positioning mechanism is driven so as to press the convex jig on the concave jig until the dial gauge shows a predetermined value. The moving position of each rotary shaft of the positioning mechanism is detected by a position detector attached to each shaft, and the detected value of each rotary shaft and each rotary shaft when the convex jig is positioned on the concave jig A method of obtaining a deviation of a theoretical position (reference position) as an offset amount is adopted.

[0003]

In the conventional calibration method described above, the positioning mechanism is manually driven,
It is necessary to position the attachment jig at the tip of the positioning mechanism at a specific position, which requires skill. Also, the inclination of the base coordinate system of the positioning mechanism from the horizontal plane, that is,
It is not possible to know the deviation between the actual vertical direction and the vertical direction in the base coordinate system.

Therefore, an object of the present invention is to easily know the vertical direction viewed from the base coordinate system and to relate to an offset amount which is a deviation between a reference position and an actual position, that is, a posture conversion of a positioning mechanism. It is to provide a calibration method capable of obtaining a parameter value.

[0005]

According to the present invention, a sensor capable of knowing the vertical direction is attached to the tip of a positioning mechanism having a rotating shaft, and the positioning mechanism is moved to several different postures. From the rotational axis position and the vertical direction, the angle parameter regarding the posture conversion of the positioning mechanism and the vertical direction viewed from the mechanism base coordinate system are obtained.

[0006]

First, the principle of operation of the present invention will be described. The element that connects the rotation axes is called a link, and the position / orientation of the positioning mechanism is represented by fixing the coordinate system to this link. The DH notation has been conventionally known as one method for describing the relationship between link coordinate systems. When this DH notation is used for explanation, link parameters and link coordinate systems are as shown in FIGS. 1 and 2. That is, the rotation angle of the rotation axis i is θi, the link driven by the rotation axis i is Li,
The link length between the rotation axis i and the rotation axis i + 1 is ai, and the inclination angle is αi. The rotation matrix of 3 rows and 3 columns showing the posture of the link coordinate system Σi viewed from the link coordinate system Σ (i-1) at this time is ^i-1
R _i , and the rotation matrix ^i-1 R _i is expressed by the following equation 1.

[0007]

[Equation 1] However, in Equation 1, Ci = cos (θi + φi) Si = sin (θi + φi) Cαi = cosαi Sαi = sinαi, where φi is the offset value of the rotation angle θi generated when the link and the actuator are attached to the rotation axis i. is there.

Therefore, in a positioning mechanism having n rotation axes, the base coordinate system is ΣB, the coordinate system of the sensor attached to the tip of the mechanism is ΣS, and the conversion from the base coordinate system ΣB to the sensor coordinate system is ΣS. Considering the base coordinate system, ΣB is considered to be the link 0, and the sensor coordinate system ΣS does not lose generality even if the sensor is mounted so as to take the same posture as the coordinate system Σn of the mechanism tip. The rotation matrix ^B _RS that represents the posture of the sensor coordinate system Σ _{S when the} system is viewed from Σ ^B is represented by the following two equations from one equation. ^B _RS = ⁰ R ₁ ··· ^n-1 R _n (2) On the contrary, the base coordinate system ΣB seen from the sensor coordinate system Σ S
The rotation matrix ^S R _B representing the attitude is expressed by the following three equations. _{^{S R B = (0 R 1}} · ...... n-1 R n) -1 = n-1 R n -1 ...... 0 R 1 -1 = n R n-1 ...... 1 R 0 ... (3) However , ^I R _i-1 = ^i-1 R _i ^-1 , and ^i-1 R _i is a rotation matrix, the rotation matrix ⁱ R _i-1 can be expressed by the following four equations from Equation ₁ .

[0009]

[Equation 4] Further, the fifth expression holds for j <i.

^I R _j = ⁱ R _i-1 ··· ^{j + 1} R _j (5) Then, when the gravity direction vector viewed from the base coordinate system is a vector ^B g of 3 rows and 3 columns, ^B g = G ^B e ... (6) However, G is a scalar quantity representing the gravitational acceleration, ^B e is a unit vector representing the direction of gravity as viewed from the base coordinate system .SIGMA.B.

If the gravity direction unit vector (in the sensor coordinate system Σs) acquired by the sensor attached to the tip of the positioning mechanism and capable of knowing the gravity direction is ^S e,
The following 7 expressions are established. ^S e = ^S R _B ^B e (7) In the above formula 7, ^S R _B is the rotation angle θi of the angular rotation axis i, the offset value φi of the rotation angle i, as is clear from the above formulas 3 and 4. It is a function of the axis inclination angle αi (i = 1, 2, ... N), and θ = [θ1, ...... θn] ^T φ = [φ1, ......... φn] ^T α = [α1, ... .alpha.n] expressed as ^T, since the equation 7 is a function of the non-linear, ^S R _B explicitly this (θ, φ, α) when expressed with the 7
The equations are the following eight equations. ^S e = ^S R _B ( θ , φ , α ) ^B e (8) Since the vector θ is a vector that collects the rotation angles θi of the respective rotation axes, the positioning mechanism was moved to an appropriate L positions. When θ j (where j = 1,
2, 3, ... L), the gravity direction unit vector ^S e _j acquired from the sensor when the posture is θ _j is represented by the following 9 equations. _{^{S e j = S R B (}} θ j, φ, α) B e ... (9) above 9 equations is phi, alpha, although ^B e holds when the true value. Normal,
Depending on the machining accuracy of the parts, mounting error, and installation error, φ ,
alpha, the value of ^B e set value is not a true value. Therefore, the design value φ o, α o, ^B eo and the error between the true value delta phi, delta
alpha, when the delta ^B e, the φ = φ o + Δ φ α = α o + Δ α B e = B eo + Δ B e. Therefore, the true value of the parameter phi, alpha, ^B e
Is obtained by focusing only on the conversion of the posture of the positioning mechanism. At this time, (phi, alpha) Since the ^B e are not independent, the gravity direction unit vector ^B e viewed from the base coordinate system as there is no error ^(B e = ^B eo), parameter phi, estimates the alpha.

The unit of gravitational direction viewed from the base coordinate system
vector^BWhen it is necessary to obtain e, the base coordinates
A rotation matrix that represents the attitude of the coordinate system of the first link viewed from the system
⁰R₁Is represented by initial estimated values φ1,0 and α1,0⁰R₁(Θ1
 , Φ1, o, α1, o) and estimated parameters φ1, α1
 Represented by⁰R₁Using (θ1, φ1, α1),⁰R₁(Θ1, φ1, o, α1, o)^Be =⁰R₁(Θ1, φ1, α1)^BSince it is eo, the following formula 10 is obtained.
Gravity direction unit vector viewed from the coordinate system^Bask for e
You can

[0013] _{^{B e = 0 R 1 -1 (}} θ1, φ1, o, α1, o) 0 R 1 (θ1, φ1, α1) B eo ... (10) Now, the design value φ o the initial value of the parameter, α when the o, gravity direction unit vector ^S ej viewed from the sensor when the orientation theta j can be calculated from the unit vector ^B e, o is from 9 ^{equation, S ej, o = S R} B (θ j, φ o , Α o) ^B e (11) At this time, the following 12 expressions, which are linearly approximated using Δ φ and Δ α , hold between ^S ej and ^S ej, o.

[0014]

[Equation 12] In the above formula 12, “×” indicates the outer product of two vectors, and the partial differential on the right side is a matrix of 3 rows and n columns,
^{When i} R _k is expressed as ⁱ R _k = [ ⁱ x k ^T ( θ ), ⁱ y k ^T ( θ ), ⁱ z k ^T ( θ )] ^T (13), the vectors φ and θ are respectively Since the rotation angles are around the Z axis and the X axis, the following equations 14 and 15 are established.

[0015]

[Equation 14]

[0016]

[Equation 15] The above equation (12) is delta phi when the rotation angle of theta j, but represents a linear three equations for Δ α, Δ φ, the unknowns of 2n combined delta alpha (n is the number of the rotation axis) Since we have an integer L that satisfies 3L ≧ 2n, we have L data, that is,
^{12 for S} e _j and θ j (where j = 1, 2, ... L)
Formulas are created, these are made simultaneous, and it is set as Au = b ... (16). Where A is a matrix of 3L rows and 2n columns shown in the following 17 equation, u is a vector shown in 18 equation of 2n rows and 1 column, and b is 3
It is a vector shown in Expression 19 in L row and 1 column.

[0017]

[Equation 17]

[0018]

[Equation 18]

[0019]

[Formula 19] When solving the above 16 equation, it solves as follows according to the magnitude of L and n. (1) When 3L = 2n By solving the simultaneous equations of Equation 6 by the well-known Gaussian elimination method or the like, u , that is, the error Δ of the offset value
φ, the error of the inclination angle Δ α is uniquely determined.

(2) When 3L> 2n: u is obtained by the method of least squares. Specifically, from Equation 12, A ^T Au = A ^T b , and A ^T A = A ′, A ^T b = b ′, then A ′ u = b ′ (20) In the above 20 equation, A ′ Is a matrix of 2L rows and 2n columns, and b '
Is a matrix of 2n rows and 1 column, 2L equations are derived from the 20 equations, and by solving the 20 equations by the Gaussian elimination method or the like, the offset value error Δ φ and the tilt angle error Δ α
Is required.

The above way error delta phi offset value of the parameter, but the error delta alpha of inclination is obtained, since the equation (12) is an approximate expression was determined offset value delta phi, delta alpha
The initial value φ o, added to the α o (φ o + Δ φ ), (α o +
The delta alpha) new initial value phi o, an offset value repeatedly as α o Δ φ, seeking delta alpha, the offset value delta phi, at the time the delta alpha becomes sufficiently small value (φ o + Δ φ), (α o +
Let Δ α ) be the true values of the parameters φ and α .

[0022]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS FIG. 3 is a schematic view of an embodiment in which the calibration system of the present invention is applied to a robot as a positioning mechanism. Reference numeral 1 is a robot to be calibrated, and the robot 1 is a robot controller. Four
Controlled by. Robot controller 4 is processor 4
The processor 41 includes a memory 42 for storing control programs and data, a D / A converter 43, an A / D converter 45, and an input / output circuit 47 in the processor 41. Connected at 48. Also, D / A
An amplifier 44 that drives various actuators (servo motors, etc.) of the robot 1 is connected to the converter 43.
The converter 45 can receive signals from various sensors (position detectors that detect the rotation angle of each axis) provided in the robot 1 via an amplifier 46. The configuration of such a robot is the same as that of a conventional robot.

In order to execute the calibration of the present invention, a force sensor 2 is attached to the tip of the robot, and the force sensor 1 has a known weight M (when the gravitational acceleration is Go). The object 3 can be attached. The controller 5 of the force sensor 2 is connected to the input / output circuit 47.

The translational forces in the X-axis, Y-axis, and Z-axis directions generated at the origin of the force sensor coordinate system (X, Y, Z) that can be detected by the force sensor 2 are ^S fx, ^S fy, and ^S fz, The torque around the X, Y and Z axes generated at the origin of the force sensor coordinate system is ^S τ
x, ^S .tau.y, and ^{S τz, S f = [S} fx, S fy, S fz] T S τ = [S τx, S τy, S τz] When ^{T, S f = M · (} G / Go) ^S e (21) ^S τ = M (G / Go) ^S p × ^S e (22) The following relational expression holds. It should be noted that ^S p is the position of the center of gravity expressed in the sensor coordinate system of the object 3 of weight M, and is expressed in a matrix of 3 rows and 1 column.

The force sensor is a 6-axis sensor and the translational force is
^{If S} f and torque ^S τ can be detected, the vertical unit vector ^S e in the sensor coordinate system can be obtained by solving the above equations 21 and 22. However, even if the six values of the translational force ^S f and the torque ^S τ cannot be detected, the vertical unit vector ^S e
Can be asked. Therefore, the minimum data detected by the force sensor 2 will be examined.

(A) When the gravitational acceleration G is not known When the gravitational acceleration G is known or cannot be regarded as G = Go, when the position of the center of gravity ^S P is unknown, the translational force ^S f, that is, [ ^S fx , ^S fy, 3 of ^S fz]
It suffices if the component can be detected.

When the center of gravity position ^S P is known [ ^S fx, ^S fy, ^S τz], [ ^S fy, ^S fz, ^S τ
x], [ ^S fz, ^S fx, ^S τy] other than the arbitrary combination of three components can be detected.

(B) When the gravitational acceleration G is known Since it is possible to utilize that the vertical unit vector ^S e is a unit vector, it is sufficient if at least two components can be detected. It is only necessary to be able to detect any two translational force components when the center of gravity position ^S P is unknown. When the gravity center position ^S P is known, it is sufficient if any two components of translational force and torque can be detected.

In the case of (b) above, two components of the vertical unit vector ^S e can be obtained by solving the above equations 21 and 22. For example, when ^S ex and ^S ey are obtained, ^S ez Can be obtained as follows. ^S ez = ± [1- ( ^S ex ² + ^S ey ² )] ^1/2 (23) Further, even if the vertical direction unit vector ^S e is obtained as described above, the output of the force sensor 2 has an error. Therefore, this vector ^S e is not a unit vector. So next 2
Vertical unit vector ^S is calculated by normalizing after calculating 4 equations.
Try to find e.

^S e = (1 / | ^S e |) ^S e = ^S e / ( ^S ex ^{2 + S} ey ^{2 + S} ez ² ) ^1/2 (24) In addition, the force sensor 2 is the above formula 21. , when it is possible to obtain more than necessary detection data in terms of solving the 22 expression may be determined to ^S e in a least square method.

4 to 6 are flowcharts of the calibration process executed by the processor 41 of the robot controller 4 in this embodiment. First, the force sensor 2 is attached to the tip of the wrist of the robot 1, and the object 3 such as a tool having a known weight M is attached to the force sensor 2.
Is attached so that the translational force ^S f and the torque ^S τ can be detected by the force sensor control 5. Then, the initial value of the offset value of each axis rotation angle is the design value φ o, the initial value of the inclination of each axis is the design value α o, and 3L ≧ 2n according to the number n of the rotation axes of the robot, and the number of L To set. And
When the calibration command is input to the robot controller, the processor 41 firstly makes an index j for the posture.
Is set to “1” (step S1), and the robot 1 is moved to the posture of the rotation angle θ j (step S2). In addition,
The posture of θ j (j = 1, 2 ... L) may be set in advance, or the robot controller may be displayed on the display unit of the robot controller so that the robot can be moved manually, and then the data can be captured. You may make it input a command.
In this case, the posture θ j is stored.

Next, the detection data from the force sensor 2 (^S
fj,^Sdata such as τj) to the force sensor controller
Detected through (step S3), the detected data^Sf
j, ^STo perform the above formulas 21 and 22 from τj
Therefore, the vertical direction in the sensor coordinate system for posture j
Unit vector^Sej is calculated and stored (step S4).
Next, the index j is incremented by "1" (step S
5) Determine whether the index exceeds the set value L (S
Step S6), if not exceeded, return to Step S2
Perform the processing from step S2 onward until the index j exceeds the set value L.
Run. Thus L different robot poses
Vertical unit vector^Sej (where j = 1, 2, ...
L), then the calibration calculation process (step
S7) is started.

The parameters φ and α are set to initial values φ o and α o (step S100), and the index i for the rotation axis and the index j for the posture are set to "1" (step S100).
101), the rotation angle of the angular rotation axis of the posture determined in step S2, and the parameters φ 1 and α 2 , the coordinate system Σ of the link Li in the posture j (at this point, the posture at j = 1).
The rotation matrix ⁱ R _i-1 representing a coordinate system .SIGMA.i-1 in the posture of the link Li-1 as viewed from the i obtained by performing the calculation of Equation 4 (step S102). Next, the index i for the rotation axis is incremented by "1" (step S103) until the index i exceeds the number n of rotation axes (step S104).
The processing from step S102 is repeated to rotate the rotation matrix ⁱ R
_{When i-1} (where i = 1, 2 ... n) is obtained, the index i is set to n
-2 (step S105) and step S10
From the rotation matrix obtained in step 2, ⁿ R _{i + 1} · ^{i + 1} R _i is calculated to obtain the rotation matrix ⁿ R _i (step S106), and the index i is decremented by “1” (step S107). Until the index i becomes smaller than “0”, step S106.
~ The process of S108 is repeated. As a result, when the index i becomes smaller than 0, the rotation matrix ⁿ R ₀ is obtained,
^S R _B representing a base coordinate system as viewed from the sensor coordinate system so that is required. That is, the processing of steps S105 to S108 is the calculation of three expressions.

[0034] the obtained rotation matrix ^S R _B from the equation (11) the gravity direction unit vector ^S ej of calculating the go viewed from the sensor in orientation theta j of obtaining the o (step S109). Then, ^S ej obtained in step S4 and this unit vector
Outer product of ^S ej, o (j = 1 at this point) ^S ej × ^S ej,
o is calculated and set in the matrix b of Expression 19 (step S1)
10). Next, the index i is set to "0" (step S1
11), 13 Equation than ⁿ Zi (θ j), ⁿ obtains the xi (theta j) is set to 17 Expressions matrix A (step S11
2). After that, the index i is incremented by "1" (step S113), it is determined whether the index exceeds n-1 (step S114), and the processes of steps S112 to S114 are repeated until the index i is exceeded. Index i is n-1
When the value exceeds the value of, the value of the jth row and the 1st column of the matrix A of Expression 17 is determined. When the index i exceeds the value of n-1, the index j for the posture is incremented by "1" (step S115), and it is judged whether or not the index j exceeds the set value L (step S116). , Index i
Is set to "1" (step S117), the process returns to step S102, and the processes of steps S102 to S116 are repeated.

Thus, when the value of the index j exceeds the value of the set value L, the value of each element of the matrix A and the matrix b is determined, and the matrix A
And the matrix b is determined. Next, it is determined whether or not 3L = 2n, and if they are equal, 1 is obtained from the obtained matrix A and matrix b.
The calculation of Equation 6 is executed by the Gaussian elimination method or the like to obtain the matrix u 1 , that is, Δ φ and Δ α (step S123). When 3L> 2n, the transposed matrix A ^T of the matrix A is calculated and A
The calculation of ^T A is performed to obtain the matrix A ′ = A ^T A (step S119), and then the calculation b ′ = A ^T b is performed to obtain the matrix b ′ (step S120). Matrix A obtained in this way
Equation 20 is calculated from ′ and b ′ to obtain the matrix u by the Gaussian elimination method or the like (step S121).

Step S121 or step S123
Obtained in the matrix u, i.e. Δ φ, Δ α initial value phi o
, Α o to obtain new initial values φ o and α o (step S122), and the index i is set to “1” (step S122).
125), step S121 or step S123
In the obtained delta phi, error Δφi offset value in the rotation axis i in delta alpha, the inclination of the axis Δαi is determined whether a smaller paddle predetermined value epsilon (step S126), the smaller, the index i to "1" Increment (step S12
7) until the index i exceeds 2n (step S12)
8), and the processing of steps S126 to S128 is repeated.
Then, if Δφi and Δαi are equal to or greater than the predetermined value ε, the process returns to step S101, and the processes of step S101 and subsequent steps described above are performed again. Thus, when the error Δφi of the offset value and the inclination Δαi of the axis with respect to all the rotation axes become smaller than the predetermined value ε, the initial value φ o obtained in step S122,
α o is set as the error φ of the offset value and the inclination α of the axis (step S129), and the calibration process ends.

Further, the vertical direction ^B seen from the base coordinate system.
If it is necessary to obtain e, the link L1 of the error φ 1 of the offset value obtained in step S129 and the inclination α of the axis
From the values φ1, α1 and the respective rotations θ1 of the link L1, and the initial setting values φ1, o, α1, o for the link L1.
May be obtained in the vertical direction ^B e viewed from the base coordinate system by performing the operation of Equation.

In the above embodiment, the force sensor is used as the sensor capable of knowing the vertical direction, but another sensor capable of knowing the vertical direction may be used. For example,
In a two-degree-of-freedom tilt angle sensor such as a bubble deformation tilt angle sensor using a four-division photodiode array or a two-axis measurement parical gyro, the horizontal plane is perpendicular to the sensor horizontal plane (for example, the XY plane) and the vector r = [X, y, 0]
It is possible to detect that β is tilted in the ^T direction. This allows
As shown in FIG. 7, each axis component of the vertical unit vector ^S e in the sensor coordinate system in the sensor coordinate system is as follows: X-axis component = sin β · cos θ = sin β · x / (x ²
+ Y ² ) ^1/2 Y-axis component = sin β · sin θ = sin β · y / (x ²
+ Y ² ) ^1/2 Z-axis component = −cos β, so that the gradient β and the vector r in the direction of this gradient =
When [x, y, 0] ^T is detected by the two-degree-of-freedom tilt angle sensor, the value of each axis component is calculated from the detected value by the sensor controller or the robot controller to determine the vertical direction in the sensor coordinate system. The unit vector ^S e can be known.

In some cases, it may be desirable to obtain only a part of the above parameters without obtaining them. For example, not determined that there is no change inclination angle α of the axis, the case of obtaining only the error delta phi offset value of the rotation angle, the matrix A described above ^{n x0 (θ 1) ~ n} xn-1 (θ L ) Is eliminated, the number of elements is reduced and the amount of calculation is small. Also the matrix
u becomes u = Δ φ. Then, when the 3L = n uniquely determined, may be found the u ie delta phi than the minimum square method when the 3L> n.

[0040]

According to the present invention, since the positioning mechanism can be automatically calibrated by using a sensor capable of knowing the vertical direction, it can be easily performed without requiring any skill.

[Brief description of drawings]

FIG. 1 is an explanatory diagram of a link parameter and a link coordinate system using a DH method.

FIG. 2 is an explanatory diagram of a link parameter and a link coordinate system using the same DH method.

FIG. 3 is a block diagram of an embodiment when the method of the present invention is applied to calibration of a robot.

FIG. 4 is a part of a flowchart of a calibration process in the embodiment.

FIG. 5 is a continuation of the flowchart of the calibration process in the embodiment.

FIG. 6 is a continuation of the flowchart of the calibration process in the embodiment.

FIG. 7 is an explanatory diagram of how to obtain a vertical direction unit vector in a sensor coordinate system by a two-degree-of-freedom tilt angle sensor.

[Explanation of symbols]

 1 Robot 2 Force sensor 3 Object 4 Robot controller 5 Force sensor controller

Claims (6)

[Claims] 1. A sensor capable of knowing the vertical direction is attached to the tip of a positioning mechanism having a rotation axis, the positioning mechanism is moved to several different postures, and the rotation axis position and the vertical direction obtained in each posture A calibration method for a positioning mechanism having a rotation axis, which is characterized in that an angle parameter for posture conversion of a positioning mechanism and a vertical direction viewed from a mechanism-based coordinate system are obtained. 2. The calibration method for a positioning mechanism having a rotating shaft according to claim 1, wherein a vertical direction viewed from a mechanism base coordinate system is obtained from the obtained angle parameter relating to the posture conversion of the positioning mechanism. 3. The positioning mechanism is moved to two or more different postures in which the degree of freedom of the positioning mechanism is 2/3 or more, and the offset value of each rotary shaft of the positioning mechanism, the tilt of the rotary shaft, and the mechanism base coordinate system are used. A calibration method for a positioning mechanism having a rotating shaft according to claim 1 or 2, wherein a vertical direction is obtained. 4. The sensor according to claim 1, wherein the sensor is composed of a force sensor capable of detecting a force in each axial direction of an orthogonal three-dimensional coordinate system and a load having a known weight. Calibration method of positioning mechanism with rotation axis. 5. The force sensor according to claim 1, wherein the sensor is composed of a force sensor capable of detecting a force in each axial direction of an orthogonal three-dimensional coordinate system and a torque around each axis, and a load having a known weight and center of gravity. A calibration method of a positioning mechanism having a rotating shaft according to claim 2 or 3. 6. The calibration system for a positioning mechanism having a rotating shaft according to claim 1, wherein the sensor is a two-degree-of-freedom tilt angle sensor.