Rotary platform angular position parameter calibration method

Abstract

The invention discloses a rotating platform angular position parameter calibration method, which comprises the following steps of: connecting a rotating platform to be calibrated with a coordinate measuring machine, and fixing a plurality of high-precision positioning standard balls on the periphery of the rotating platform to be calibrated; measuring the high-precision positioning standard ball through a coordinate measuring machine, and calculating and determining an initial coordinate system when the rotating platform is static; enabling a rotating shaft and a pitch shaft of the rotating platform to move at intervals according to a fixed angle, measuring the high-precision positioning standard ball after each movement through a coordinate measuring machine, and establishing a pose coordinate system after the movement of the rotating shaft and the pitch shaft; the angular position parameters of the rotating shaft and the pitch shaft are precisely calibrated through the posture change of the high-precision positioning standard ball. According to the invention, the coordinate measuring machine can be used to calibrate the angular position parameter in situ, and the calibration efficiency of the measured rotating shaft angular position parameter is improved.

Description

Technical Field

[0001] The invention belongs to the field of geometric quantity calibration, and in particular relates to a method for calibrating angular position parameters of a rotating platform. Background Art

[0002] The rotating platform is a common auxiliary test device for coordinate measuring machines. The angular position is an important working state of the rotating platform. The positioning error is a combination of the measurement error and the control error. Its positioning accuracy directly affects the accuracy of component testing. Therefore, the calibration of the angular position parameters of different rotating axes is an essential task.

[0003] At present, there are many methods for angular position calibration in engineering applications, such as the photoelectric autocollimator and multifaceted prism method, laser interference angle measurement method, laser tracker calibration method, etc. Among them, in the low-speed calibration specification, the prism and light tube are used to calibrate the angular position positioning parameters. The calibration steps are to install the prism at the rotation center of the measured axis, install the light tube on a good seismic isolation foundation, and make the light axis of the light tube perpendicular to the prism or plane mirror. The prism starts from the digital display 0 position of the measured axis angle measurement system, and records the initial reading of the light tube and the angle value of the angle measurement system. Then, the axis is rotated by the angle specified by the prism surface, and the readings of the light tube and the angle measurement system are recorded. The forward measurement is one circle and the reverse measurement is one circle. The angular position positioning error takes half of the maximum and minimum errors of each calibration point as the calibration result. In this angular position calibration process, the installation of the prism and light tube is relatively troublesome, and the inspection personnel have high requirements on operating skills and environmental seismic isolation. It also needs to be sent for inspection and operation, and the calibration of the angular position parameters cannot be completed in situ. Summary of the invention

[0004] The object of the present invention is to provide a method for calibrating the angular position parameters of a rotating platform, which can utilize a coordinate measuring machine to calibrate the angular position parameters in situ and improve the calibration efficiency of the angular position parameters of a measured rotating axis.

[0005] In order to achieve the above object, one aspect of the present invention provides a rotation platform posture calibration method, comprising:

[0006] Step S1, connecting the rotating platform to be calibrated to a coordinate measuring machine, and fixing a plurality of high-precision positioning standard balls around the rotating platform to be calibrated;

[0007] Step S2, measuring the high-precision positioning standard ball by a coordinate measuring machine, calculating and determining the initial coordinate system when the rotating platform is stationary

[0008] Step S3, using the posture change of the high-precision positioning standard ball before and after the rotation axis of the rotating platform moves, calibrating the angular position parameters of the rotation axis of the rotating platform, including:

[0009] The rotary axis of the rotating platform is moved at fixed angle intervals, and a high-precision positioning standard ball is measured by a coordinate measuring machine after each movement to obtain measurement data;

[0010] Performing Gaussian fitting on the measurement data of the high-precision positioning standard ball to calculate the coordinates of each sphere center point;

[0011] Determine the coordinate system of the rotating platform after the rotation axis moves according to the coordinates of each spherical center point

[0012] Based on the initial coordinate system and the coordinate system after the rotary axis moves Calculate and determine the first coordinate system transformation matrix;

[0013] According to the calculated first coordinate system transformation matrix, the high-precision positioning standard ball is positioned in the initial coordinate system The rotation parameters under the calculation are obtained after the rotary axis moves at a fixed angle interval in the initial coordinate system. The rotation parameters under the above conditions are used to calculate the rotation angle and calibrate the angular position parameters of the rotation axis of the rotating platform;

[0014] Step S4, using the posture change of the high-precision positioning standard ball before and after the pitch axis movement of the rotating platform, calibrates the pitch axis angular position parameters of the rotating platform, including:

[0015] The pitch axis of the rotating platform is moved at fixed angle intervals, and the coordinate measuring machine measures the high-precision positioning standard ball after each movement to obtain measurement data;

[0016] Fitting the measurement data of the high-precision positioning standard ball to calculate the coordinates of the ball center point;

[0017] Determine the coordinate system after the pitch axis of the rotating platform moves according to the coordinates of each spherical center point

[0018] Based on the initial coordinate system and the coordinate system after the pitch axis moves Calculate and determine the second coordinate system transformation matrix;

[0019] According to the calculated second coordinate system transformation matrix, the high-precision positioning standard ball is positioned in the initial coordinate system The rotation parameters under the calculation are obtained after the pitch axis moves at a fixed angle interval in the initial coordinate system The rotation parameters under the above conditions are used to calculate the rotation angle and calibrate the angular position parameters of the pitch axis of the rotating platform.

[0020] Preferably, step S2 comprises:

[0021] Returning the position and posture of the rotating platform to zero, measuring the high-precision positioning standard ball by a coordinate measuring machine, and obtaining measurement data of the high-precision positioning standard ball;

[0022] Performing Gaussian fitting on the measurement data of the high-precision positioning standard ball to calculate the coordinates of each sphere center point;

[0023] Determine the coordinate system of the rotating platform when it is stationary according to the coordinates of each spherical center point

[0024] Preferably, there are three high-precision positioning standard balls, and the coordinates of the three ball center points when stationary are A 11 , A 12 , A 13 , then the coordinate system of the rotating platform when it is stationary is The corresponding coordinate system matrix is ​​[A 12 -A 11 , V calm11 , V calm12 ],in,

[0025] V calm11 =(A 12 -A 11 )×(A 13 -A 11 ), V calm12 =(A 12 -A 11 )×V calm11 .

[0026] Preferably, in step S3, the coordinates of the three sphere center points after the rotary axis moves at fixed angle intervals are A 21 , A 22 , A 23 , then the coordinate system after the rotary axis moves The corresponding coordinate system matrix is ​​[A 22 -A 21 , V calm21 , V calm22 ], where V calm21 =(A 22 -A 21 )×(A 23 -A 21 ), V calm22 =(A 22 -A 21 )×V calm21 ;

[0027] The first coordinate system transformation matrix is:

[0028]

[0029] Wherein, λ1 is the first scale parameter, R1 is the first rotation parameter, and Δ1 is the first translation vector;

[0030] X1, Y1, Z1 are the initial coordinate systems Next point A 11 , A 12 , A 13 The X, Y, and Z coordinate values ​​of

[0031] X2, Y2, Z2 are the coordinate systems after the rotary axis moves Next point A 21 , A 22 , A 23 The X, Y, and Z coordinate values ​​of the

[0032] Preferably, in step S4, after the pitch axis moves at fixed angle intervals, the coordinates of the three sphere center points are A 31 , A 32 , A 33 , then the coordinate system after the pitch axis moves The corresponding coordinate system matrix is ​​[A 32 -A 31 , V calm31 , V calm32 ], where V calm31 =(A 32 -A 31 )×(A 33 -A 31 ), V calm32 =(A 32 -A 31 )×V calm31 ;

[0033] The second coordinate transformation matrix is:

[0034]

[0035] Wherein, λ2 is the second scale parameter, R2 is the second rotation parameter, and Δ2 is the second translation vector;

[0036] X1, Y1, Z1 are the initial coordinate systems Next point A 11 , A 12 , A 13 The X, Y, and Z coordinate values ​​of

[0037] X3, Y3, Z3 are the coordinate systems after the pitch axis moves Next point A 31 , A 32 , A 33 The X, Y, and Z coordinate values ​​of the

[0038] Preferably, the fixed angle interval is 30°.

[0039] Preferably, in step S1, the high-precision positioning standard ball is rigidly connected to the rotating platform via rigid pillars to ensure that the rotation axis and pitch axis of the high-precision positioning standard ball and the rotating platform are always in the same coordinate system.

[0040] According to the rotation platform angular position parameter calibration method of the above aspect of the present invention, the angular position parameters can be calibrated in situ using a coordinate measuring machine, thereby improving the calibration efficiency of the angular position parameters of the measured rotation axis. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the technical solution of the present invention, the following briefly introduces the drawings used in the description of the embodiments of the present invention. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative work:

[0042] Figure 1 is a flow chart of a method for calibrating the angular position parameters of a rotating platform according to an embodiment of the present invention;

[0043] Figure 2 It is a schematic diagram of the application of a method for calibrating the angular position parameters of a rotating platform according to an embodiment of the present invention. DETAILED DESCRIPTION

[0044] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0045] An embodiment of the present invention provides a method for calibrating the angular position parameters of a rotating platform, which calibrates the angular position parameters of the rotation axis and the pitch axis of the rotating platform. Figure 1 As shown, the method for calibrating the angular position parameters of a rotating platform according to an embodiment of the present invention includes steps S1-S4.

[0046] In step S1, the rotation axis and pitch axis of the rotating platform to be calibrated are connected to a coordinate measuring machine, and a plurality of high-precision positioning standard balls are fixed around the rotating platform to be calibrated. Figure 2 As shown, the high-precision positioning standard balls are multiple high-precision coordinate balls that are distributed around the rotating platform and are perpendicular to each other. The number of coordinate balls can be three, or four or more. Figure 2Four coordinate balls 4, 5, 6, and 7 are shown in the figure. The fixture 3 is fixed to the central axis of the rotating platform, and the central axis of the fixture 3 coincides with the central axis of the rotating platform, and is used to clamp parts. The high-precision positioning standard ball is rigidly connected to the rotating platform through a rigid support to ensure that the high-precision positioning standard ball and the rotation axis 1 and pitch axis 2 of the rotating platform are always in the same coordinate system. The method of the embodiment of the present invention measures the position and posture changes of the multiple high-precision positioning standard balls before and after the movement of the rotation axis 1 and pitch axis 2 of the rotating platform by a coordinate measuring machine, and calculates the position and posture changes of the rotation axis 1 and pitch axis 2 of the rotating platform, thereby calibrating the angular position parameters of the rotating platform. The coordinate measuring machine can calibrate the rotating platform before each test of the parts.

[0047] In step S2, the high-precision positioning standard ball is measured by a coordinate measuring machine to calculate and determine the initial coordinate system when the rotating platform is stationary.

[0048] In one embodiment, step S2 comprises the following steps:

[0049] S21: Returning the position of the rotating platform to zero, measuring the high-precision positioning standard ball by a coordinate measuring machine, and obtaining measurement data of the high-precision positioning standard ball;

[0050] S22: performing Gaussian fitting (least square fitting) on ​​the measurement data of the high-precision positioning standard ball to calculate the coordinates of each sphere center point;

[0051] S23: With three sphere center points A 11 , A 12 , A 13 , through two vector cross products, determine the coordinate system when the rotating platform is stationary The corresponding coordinate matrix in this coordinate system is [A 12 -A 11 , V calm11 , V calm12 ].

[0052] Specifically, the vector (A 12 -A 11 ) as the X-axis vector, through the vector (A 12 -A 11 ) and vector (A 13 -A 11 ) cross product to get the Y axis vector V calm11 , the Z-axis vector V is obtained by cross-producting the X-axis vector and the Y-axis vector calm12 ,Right now:

[0053] V calm11 =(A 12 -A11 )×(A 13 -A 11 ), V calm12 =(A 12 -A 11 )×V calm11 .

[0054] In step S3, the angular position parameters of the rotary axis of the rotating platform are calibrated by utilizing the position change of the high-precision positioning standard ball before and after the rotary axis of the rotating platform moves. The position change is determined by the coordinate system change of the high-precision positioning standard ball before and after the rotary axis of the rotating platform moves. The specific steps include:

[0055] Step S31: the rotary axis of the rotating platform moves at a fixed angle interval (30° interval), and the high-precision positioning standard ball is measured by a coordinate measuring machine after each movement to obtain measurement data;

[0056] Step S32: performing Gaussian fitting (least square fitting) on ​​the measurement data of the high-precision positioning standard ball to calculate the coordinates of each sphere center point;

[0057] Step S33: Using three sphere center points A 21 , A 22 , A 23 , through two vector cross products, determine the coordinate system of the rotating platform after the rotation axis moves The corresponding coordinate matrix in this coordinate system is [A 22 -A 21 , V calm21 , V calm22 ], where V calm21 =(A 22 -A 21 )×(A 23 -A 21 ), V calm22 =(A 22 -A 21 )×V calm21 ;

[0058] Step S34: Based on the coordinate system and the coordinate system Calculate and determine the first coordinate system transformation matrix as follows:

[0059]

[0060] Wherein, λ1 is the first scale parameter, R1 is the first rotation parameter, and Δ1 is the first translation vector;

[0061] X1, Y1, Z1 are Point A in the coordinate system 11 , A12 , A 13 The X, Y, and Z coordinate values ​​of

[0062] X2, Y2, Z2 are Point A in the coordinate system 21 , A 22 , A 23 The X, Y, and Z coordinate values ​​of the

[0063]

[0064] Among them, |A 21 A 22 |It is A 21 , A 22 Two o'clock Distance in coordinate system;

[0065] |A 11 A 12 |It is A 11 , A 12 Two o'clock Distance in coordinate system;

[0066] |A 22 A 23 |It is A 22 , A 23 Two o'clock Distance in coordinate system;

[0067] |A 12 A 13 |It is A 12 , A 13 Two o'clock Distance in coordinate system;

[0068] |A 23 A 21 |It is A 23 , A 21 Two o'clock Distance in coordinate system;

[0069] |A 13 A 11 |It is A 13 , A 11 Two o'clock Distance in coordinate system.

[0070]

[0071] Where I is the identity matrix,

[0072]

[0073] in, Indicates A 11 , A 12 Two o'clock The difference in the Z-axis coordinate value in the coordinate system;

[0074] Indicates A 21 , A 22 Two o'clock The difference in the Z-axis coordinate value in the coordinate system;

[0075] Indicates A 11 , A 12 Two o'clock The difference between the Y-axis coordinate values ​​in the coordinate system;

[0076] Indicates A 21 , A 22 Two o'clock The difference between the Y-axis coordinate values ​​in the coordinate system;

[0077] Indicates A 11 , A 12 Two o'clock The difference between the X-axis coordinate values ​​in the coordinate system;

[0078] Indicates A 21 , A 22 Two o'clock The difference in the X-axis coordinate values ​​in the coordinate system.

[0079] Substitute the coordinates of any point into the formula and calculate Δ1. The arbitrary point refers to A before the movement. 11 Point and corresponding movement after A 21 point, or A before movement 12 Point and corresponding movement after A 22 point, or A before movement 13 Point and corresponding movement after A 23 point.

[0080] S35: Based on the calculated coordinate system transformation matrix, the high-precision positioning standard ball is positioned at The quaternion parameters (rotation parameters) of the position in the coordinate system are calculated to obtain the rotation axis of the rotating platform after moving at 30° intervals. The new quaternion parameters of the position in the coordinate system are used to calculate the rotation angle and calibrate the angular position parameters of the rotation axis of the rotating platform. The calibration of the angular position positioning error generally takes 1 / 2 of the difference between the maximum and minimum errors of each calibration point as the calibration result.

[0081] Step S4, using the posture change of the high-precision positioning standard ball before and after the pitch axis movement of the rotating platform, calibrate the angular position parameters of the pitch axis of the rotating platform, which is determined by the change of the coordinate system of the high-precision positioning standard ball before and after the pitch axis movement of the rotating platform, and the specific steps include:

[0082] Step S41: the pitch axis of the rotating platform moves at 30° intervals, and the coordinate measuring machine measures the high-precision positioning standard ball after each rotation to obtain measurement data;

[0083] Step S42: performing Gaussian fitting (least square fitting) on ​​the measurement data of the high-precision positioning standard ball to calculate the coordinates of the ball center point;

[0084] Step S43: Using three sphere center points A 31 , A 32 , A 33 , determine the coordinate system of the rotating platform after the pitch axis moves by two vector cross products The corresponding coordinate matrix in this coordinate system is [A 32 -A 31 , V calm31 , V calm32 ], where V calm31 =(A 32 -A 31 )×(A 33 -A 31 ), V calm32 =(A 32 -A 31 )×V calm31 ;

[0085] Step S44: Based on the coordinate system and the coordinate system Calculate and determine the second coordinate transformation matrix as follows

[0086]

[0087] Wherein, λ2 is the second scale parameter, R2 is the second rotation parameter, and Δ2 is the second translation vector;

[0088] X1, Y1, Z1 are Point A in the coordinate system 11 , A 12 , A 13 The X, Y, and Z coordinate values ​​of

[0089] X3, Y3, Z3 are Point A in the coordinate system 31 , A 32 , A 33 The X, Y, and Z coordinate values ​​of the

[0090]

[0091] Among them, |A 31 A 32 |It is A 31 , A 32 Two o'clock Distance in coordinate system;

[0092] |A 11 A 12 |It is A 11 , A 12 Two o'clock Distance in coordinate system;

[0093] |A 32 A 33 |It is A 32 , A 33 Two o'clock Distance in coordinate system;

[0094] |A 12 A 13 |It is A 12 , A 13 Two o'clock Distance in coordinate system;

[0095] |A 33 A 31 |It is A 33 , A 31 Two o'clock Distance in coordinate system;

[0096] |A 13 A 11 |It is A 13 , A 11 Two o'clock Distance in coordinate system.

[0097]

[0098] Where I is the identity matrix,

[0099]

[0100] in, Indicates A 11 , A 12 Two o'clock The difference in the Z-axis coordinate value in the coordinate system;

[0101] Indicates A 31 , A 32Two o'clock The difference in the Z-axis coordinate values ​​in the coordinate system;

[0102] Indicates A 11 , A 12 Two o'clock The difference between the Y-axis coordinate values ​​in the coordinate system;

[0103] Indicates A 31 , A 32 Two o'clock The difference between the Y-axis coordinate values ​​in the coordinate system;

[0104] Indicates A 11 , A 12 Two o'clock The difference between the X-axis coordinate values ​​in the coordinate system;

[0105] Indicates A 31 , A 32 Two o'clock The difference in the X-axis coordinate values ​​in the coordinate system.

[0106] Substitute the coordinates of any point into the formula and calculate Δ2. The arbitrary point refers to A before the movement. 11 Point and corresponding movement after A 31 point, or A before movement 12 Point and corresponding movement after A 32 point, or A before movement 13 Point and corresponding movement after A 33 point.

[0107] Step S45: Based on the calculated second coordinate system transformation matrix, the high-precision positioning standard ball is positioned at The quaternion parameters of the position in the coordinate system are calculated to obtain the pitch axis of the rotating platform after moving at 30° intervals. The new quaternion parameters of the coordinate system are used to calculate the rotation angle and calibrate the angular position parameters of the pitch axis of the rotating platform.

[0108] The rotary platform angular position parameter calibration method of the above embodiment of the present invention has the following beneficial effects:

[0109] 1. The present invention uses the change in the position of a high-precision positioning standard ball fixed on a rotating platform through coordinate system conversion to calibrate the angular position parameters of the rotation axis and the pitch axis. The calibration idea is simple, and the coordinate machine operator can calibrate the accuracy of the rotating platform in real time, which is helpful to assist in improving the measurement accuracy.

[0110] 2. The present invention utilizes a coordinate measuring machine to calibrate the angular position parameters in situ, thereby reducing the use of polyhedrons or calibration gratings and improving the calibration efficiency of the angular position parameters of the measured rotating axis.

[0111] The rotating platform angular position parameter calibration method of the above embodiment of the present invention is suitable for calibrating the angular position parameters of the rotating axes in a five-axis compound coordinate measuring machine (three axes of the coordinate machine and two axes of the turntable). The five-axis compound coordinate measuring machine has simple operation for measuring the standard ball. Compared with the traditional angular position parameter calibration method, the calibration can be completed in situ, thereby improving the calibration accuracy and efficiency of the angular position parameters.

[0112] The above description is only by way of illustration of certain exemplary embodiments of the present invention. It is undoubted that those skilled in the art can modify the described embodiments in various ways without departing from the spirit and scope of the present invention. Therefore, the above drawings and descriptions are illustrative in nature and should not be construed as limiting the scope of protection of the claims of the present invention.

Claims

1. A method for calibrating a rotation platform posture, characterized in that: include: Step S1, connecting the rotating platform to be calibrated to a coordinate measuring machine, and fixing a plurality of high-precision positioning standard balls around the rotating platform to be calibrated; Step S2, measuring the high-precision positioning standard ball by a coordinate measuring machine, calculating and determining the initial coordinate system when the rotating platform is stationary Step S3, using the posture change of the high-precision positioning standard ball before and after the rotation axis of the rotating platform moves, calibrating the angular position parameters of the rotation axis of the rotating platform, including: The rotary axis of the rotating platform is moved at fixed angle intervals, and a high-precision positioning standard ball is measured by a coordinate measuring machine after each movement to obtain measurement data; Performing Gaussian fitting on the measurement data of the high-precision positioning standard ball to calculate the coordinates of each sphere center point; Determine the coordinate system of the rotating platform after the rotation axis moves according to the coordinates of each spherical center point Based on the initial coordinate system and the coordinate system after the rotary axis moves Calculate and determine the first coordinate system transformation matrix; According to the calculated first coordinate system transformation matrix, the high-precision positioning standard ball is positioned in the initial coordinate system The pose parameters under the above conditions are calculated to obtain the initial coordinate system after the rotary axis moves at a fixed angle interval. The posture parameters under the condition are used to calculate the rotation angle and calibrate the angular position parameters of the rotation axis of the rotating platform; Step S4, using the posture change of the high-precision positioning standard ball before and after the pitch axis movement of the rotating platform, calibrates the pitch axis angular position parameters of the rotating platform, including: The pitch axis of the rotating platform is moved at fixed angle intervals, and the coordinate measuring machine measures the high-precision positioning standard ball after each movement to obtain measurement data; Fitting the measurement data of the high-precision positioning standard ball to calculate the coordinates of the ball center point; Determine the coordinate system after the pitch axis of the rotating platform moves according to the coordinates of each spherical center point Based on the initial coordinate system and the coordinate system after the pitch axis moves Calculate and determine the second coordinate system transformation matrix; According to the calculated second coordinate system transformation matrix, the high-precision positioning standard ball is positioned in the initial coordinate system The pose parameters under the above equations are calculated to obtain the initial coordinate system after the pitch axis moves at a fixed angle interval. The posture parameters under the above conditions are used to calculate the rotation angle and calibrate the angular position parameters of the pitch axis of the rotating platform.

2. The method according to claim 1, characterized in that Step S2 includes: Returning the position and posture of the rotating platform to zero, measuring the high-precision positioning standard ball by a coordinate measuring machine, and obtaining measurement data of the high-precision positioning standard ball; Performing Gaussian fitting on the measurement data of the high-precision positioning standard ball to calculate the coordinates of each sphere center point; Determine the coordinate system of the rotating platform when it is stationary according to the coordinates of each spherical center point 3. The method according to claim 2, characterized in that There are three high-precision positioning standard balls. When stationary, the coordinates of the three ball center points are A 11 , A 12 , A 13 , then the coordinate system of the rotating platform when it is stationary is The corresponding coordinate system matrix is ​​[A 12 -A 11 , V calm11 , V calm12 ],in, In calm11 =(A 12 -A 11 )×(A 13 -A 11 ),In calm12 =(A 12 -A 11 )×V calm11 。 4. The method according to claim 3, characterized in that In step S3, the coordinates of the three sphere center points after the rotary axis moves at a fixed angle interval are A 21 , A 22 , A 23 , then the coordinate system after the rotary axis moves The corresponding coordinate system matrix is ​​[A 22 -A 21 , V calm21 , V calm22 ], where V calm21 =(A 22 -A 21 )×(A 23 -A 21 ), V calm22 =(A 22 -A 21 )×V calm21 ; The first coordinate system transformation matrix is: Wherein, λ1 is the first scale parameter, R1 is the first rotation parameter, and Δ1 is the first translation vector; X1, Y1, Z1 are the initial coordinate systems Next point A 11 , A 12 , A 13 The X, Y, and Z coordinate values ​​of X2, Y2, Z2 are the coordinate systems after the rotary axis moves Next point A 21 , A 22 , A 23 The X, Y, and Z coordinate values ​​of the 5. The method according to claim 3 or 4, characterized in that: In step S4, the coordinates of the three sphere center points after the pitch axis moves at fixed angle intervals are A 31 , A 32 , A 33 , then the coordinate system after the pitch axis moves The corresponding coordinate system matrix is ​​[A 32 -A 31 , V calm31 , V calm32 ], where V calm31 =(A 32 -A 31 )×(A 33 -A 31 ), V calm32 =(A 32 -A 31 )×V calm31 ; The second coordinate transformation matrix is: Wherein, λ2 is the second scale parameter, R2 is the second rotation parameter, and Δ2 is the second translation vector; X1, Y1, Z1 are the initial coordinate systems Next point A 11 , A 12 , A 13 The X, Y, and Z coordinate values ​​of X3, Y3, Z3 are the coordinate systems after the pitch axis moves Next point A 31 , A 32 , A 33 The X, Y, and Z coordinate values ​​of the 6. The method according to any one of claims 1 to 4, characterized in that The fixed angle interval is 30°.

7. The method according to any one of claims 1 to 4, characterized in that: In step S1, the high-precision positioning standard ball is rigidly connected to the rotating platform through rigid pillars to ensure that the rotation axis and pitch axis of the high-precision positioning standard ball and the rotating platform are always in the same coordinate system.

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