Closed cabin sleeving coaxiality adjusting method

Abstract

The invention discloses a closed cabin sleeving coaxiality adjusting method, and aims to solve the problem that in the prior art, a closed cabin sleeving coaxiality adjusting method is urgently needed to test and adjust the coaxiality of a sleeving mechanism before sleeving and reduce the direction error between sleeving shafts. Determining a conversion relation between a laser contour visual coordinate system and a robot base coordinate system; installing a calibration target ball on the cabin section pose adjusting platform, controlling the calibration target ball to perform single-axis motion, acquiring multiple groups of calibration ball motion data by using a laser contourgraph, performing circle center fitting on the calibration ball data, performing spatial position fitting on the fitted circle center, outputting a direction vector corresponding to the motion direction, and performing calibration on the calibration target ball; and finally, calculating a vector error included angle by using the output direction vector, and adjusting the motion platform to eliminate an error angle. According to the technical scheme, the coaxiality of the multi-degree-of-freedom motion platform can be adjusted, and the direction error between the sleeving shafts is reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of automated production, and specifically to a method for adjusting the coaxiality of closed cabin segment socket joints. Background Art

[0002] With the continuous development of the aerospace industry, the heat insulation technology on the surface of aircraft has become an important part affecting the flight performance of high-speed aircraft. Therefore, a new automated assembly field for the socket joints of aircraft cabin segments and protective layers has gradually emerged at home and abroad. The automated closed cabin segment socket joint system has the characteristics of rapid production and the ability to replace and combine process equipment at low cost according to requirements, which can significantly improve production efficiency.

[0003] Currently, the equipment for closed cabin segment socket joints is mainly completed manually. In recent years, with the rapid development of industrial automation technology, the application of mechanical automated socket joint methods in the manufacturing industry has attracted extensive attention. However, these methods still have significant deficiencies in the face of products with non-standard geometric closed shapes, high socket joint accuracy requirements, and small socket joint gaps. The main reason is that the coaxiality requirements of the products for the socket joint mechanism are relatively high during socket joint. When the geometric errors, especially the angular errors, between the socket joints exceed a certain range, it is possible for interference to occur between the inner and outer products, resulting in socket joint failure and even product damage.

[0004] Therefore, there is an urgent need for a method for adjusting the coaxiality of closed cabin segment socket joints to test and adjust the coaxiality of the socket joint mechanism before socket joint, and reduce the directional error between the socket joints. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for adjusting the coaxiality of closed cabin segment socket joints to solve the problem in the prior art that there is an urgent need for a method for adjusting the coaxiality of closed cabin segment socket joints to test and adjust the coaxiality of the socket joint mechanism before socket joint, and reduce the directional error between the socket joints.

[0006] The technical solution adopted by the present invention to solve the above technical problems is as follows: A method for adjusting the coaxiality of closed cabin segment socket joints, the method is implemented based on a closed cabin segment socket joint coaxiality adjustment system, and the closed cabin segment socket joint coaxiality adjustment system includes a collaborative robot 1, a cabin segment pose adjustment platform 2, a linear motion platform 3, a laser profiler 4, and a calibration target ball 5; The linear motion platform 3 is fixed on the ground, the cabin segment pose adjustment platform 2 is arranged on the linear motion platform 3, the calibration target ball 5 is arranged on the cabin segment pose adjustment platform 2, the collaborative robot 1 is fixed on the ground, and the laser profiler 4 is arranged on the collaborative robot 1; The method includes the following steps: Step 1: Perform hand-eye calibration on the collaborative robot 1 to obtain a hand-eye calibration matrix N; Step 2: Control the cabin attitude adjustment platform 2 to perform single-axis movement, and at the same time use the laser profiler 4 to collect multiple single-line data for the calibration target ball 5 to obtain multiple groups of data; Step 3: Based on the hand-eye calibration matrix N, and use the obtained multiple groups of data for circle center fitting, and then perform spatial position fitting on the fitted circle centers to obtain the direction vector of the straight line and the direction vector of the rolling axis; Step 4: Calculate the vector error angle using the direction vector of the straight line and the direction vector of the rolling axis, and operate the cabin attitude adjustment platform 2 to eliminate the vector error angle.

[0007] Furthermore, the specific steps of the said Step 1 are as follows: Step 1-1: Set the calibration target ball 5 on the cabin attitude adjustment platform 2, and use the laser profiler 4 to collect single-line data for the calibration target ball 5 to obtain the outer contour curve of any cross-section of the sphere, that is, collect data, and record the attitude of the robot in the robot coordinate system at this time; Step 1-2: Obtain the motion transformation matrix A of the robot end effector according to the corresponding attitude of the robot in the robot coordinate system; Step 1-3: Obtain the position indicator of the actual center of the calibration target ball 5 relative to the laser profiler 4 and the radius R of the calibration target ball 5, and use the position indicator of the actual center of the calibration target ball 5 relative to the laser profiler 4 and the radius R of the calibration target ball 5 to perform circle center fitting on the calibration target ball 5, and use the calibration target ball 5 as the calibration basis, combined with the motion transformation matrix A of the robot end effector, to solve the equation , where B is the motion transformation matrix of the camera, and N is the hand-eye transformation matrix. For each motion, there is , linearize the equation to obtain , where is the identity matrix. Finally, substitute the collected data and perform singular value decomposition and reconstruction to obtain the hand-eye calibration matrix N.

[0008] Furthermore, the specific steps of the said Step 2 are as follows: Step 2-1: Define the movement direction of the cabin attitude adjustment platform 2 along the linear movement platform 3 as the X direction, the upward movement direction of the cabin attitude adjustment platform 2 perpendicular to the ground as the Z direction, the Y direction forms a right-handed system with the X and Z directions, the cabin rolling axis direction is parallel to the X direction, the yaw axis direction is parallel to the Z direction, and the pitch axis direction is parallel to the Y direction; Step 22: Control the pose adjustment platform 2 of the cabin to move only along any single axis direction. At the same time, use the laser profiler 4 to collect single - strip data from the calibration target ball 5 to obtain the outer contour curve of any cross - section of the sphere, that is, collect data, and simultaneously record the pose of the robot in the base coordinate system, the radius R of the calibration target ball 5, and the target ball center position indicator; Step 23: Repeat Step 22 to collect multiple groups of data and save them.

[0009] Further, the specific steps of Step 3 are as follows: Perform sphere center fitting on the collected data, and use the hand - eye calibration matrix N for coordinate transformation to obtain the set of corresponding sphere center coordinates in the robot base coordinate system , and perform sphere center fitting on the sphere center in each single - axis direction according to the sphere center coordinates. Among them, for the X, Y, and Z directions, linear fitting is used, and for the roll axis, yaw axis, and pitch axis directions, circular fitting is used; The specific linear fitting is as follows: Step 311: Obtain the mean coordinate in the set , where , , is the th sphere center coordinate in the set i ; Step 312: Take the mean coordinate as the center of the centered point set, and combine it with to obtain the centered vector , ; Step 313: Calculate the covariance matrix according to the centered vector , and perform eigenvalue decomposition on the covariance matrix to make , where V is the eigenvector matrix and Λ is the diagonal matrix; Step 314: Based on the result of eigenvalue decomposition, select the eigenvector corresponding to the largest eigenvalue as the direction vector of the line; The specific circular fitting is as follows: Step 321: Obtain the mean coordinate in the set , where , , is the th sphere center coordinate in the set i ; Step 322: Take the mean coordinate as the center of the centered point set, and combine it with , a centralized vector is obtained , ; Step 323: Calculate the covariance matrix based on the centralized vector , and perform eigenvalue decomposition on the covariance matrix so that , where V is the eigenvector matrix and Λ is the diagonal matrix; Step 324: Based on the result of eigenvalue decomposition, select the eigenvector corresponding to the minimum eigenvalue as the normal vector of the fitting plane; Step 325: Determine the fitting plane according to the normal vector of the fitting plane, and project the set onto the fitting plane. The circle formed by the center coordinates on the projection plane is , where is the center coordinate, is the center coordinate of the projected sphere, is the radius of the circle; Step 326: Define an error function to minimize the sum of the squared errors of all projection points; Step 327: Linearize the error function and rewrite the equation of the circle as , let the difference so that . Substitute the projection points to obtain , solve to obtain the center coordinate on the projection plane, and convert the center coordinate back to the initial coordinate system to obtain the center .

[0010] Furthermore, the mean coordinate is expressed as: .

[0011] Furthermore, the covariance matrix is expressed as: .

[0012] Furthermore, the sum of the squared errors is expressed as: where is the error function.

[0013] Furthermore, the error function is expressed as: where is the projected coordinate.

[0014] Further, the center of the circle is expressed as: wherein and are the first two eigenvectors of the covariance matrix.

[0015] Further, the specific steps of Step 4 are as follows: According to the center of the circle and the radius of the circle , project and onto the XOY, YOZ, and XOZ planes respectively, and use the vector angle formula to calculate the angle between the projection vectors and in the projection planes. Finally, rotate the pose adjustment platform 2 of the operation cabin section by the corresponding angle to achieve coaxiality adjustment.

[0016] The beneficial effects of the present invention are as follows: In this application, the robot is first calibrated for hand-eye coordination to determine the conversion relationship between the laser profile vision coordinate system and the robot base coordinate system; then, a calibration target ball is installed on the pose adjustment platform of the cabin section, and its single-axis movement is controlled. At the same time, a laser profiler is used to collect multiple groups of calibration ball movement data, and the center of the calibration ball data is fitted. The center of the fitted circle is spatially fitted to output the direction vector in the corresponding movement direction. Finally, the vector error angle is calculated using the output direction vector, and the movement platform is adjusted to eliminate the error angle. The technical solution of this application can perform coaxiality adjustment of a multi-degree-of-freedom movement platform and reduce the direction error between the socket shafts. The technical solution of this application is simple, highly accurate, and reliable. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 is the overall framework diagram of this application; Figure 2 is the overall process of this application Figure 1 ; Figure 3 is the overall process of this application Figure 2 . DETAILED DESCRIPTION OF THE EMBODIMENTS

[0018] It should be specifically noted that, without conflict, the various embodiments disclosed in this application can be combined with each other.

[0019] Embodiment 1: A method for adjusting the coaxiality of closed cabin segments. The method is implemented based on a closed cabin segment coaxiality adjustment system, which includes a collaborative robot 1, a cabin position and attitude adjustment platform 2, a linear motion platform 3, a laser profiler 4, and a calibration target ball 5; The linear motion platform 3 is fixed on the ground. The cabin position and attitude adjustment platform 2 is arranged on the linear motion platform 3. The calibration target ball 5 is arranged on the cabin position and attitude adjustment platform 2. The collaborative robot 1 is fixed on the ground. The laser profiler 4 is arranged on the collaborative robot 1; The method includes the following steps: Step 1: Perform hand-eye calibration on the collaborative robot 1 to obtain a hand-eye calibration matrix N; Step 2: Control the cabin position and attitude adjustment platform 2 to perform single-axis motion, and at the same time use the laser profiler 4 to collect multiple single-line data of the calibration target ball 5 to obtain multiple groups of data; Step 3: Based on the hand-eye calibration matrix N, and use the obtained multiple groups of data for center fitting, and then perform spatial position fitting on the fitted centers to obtain the direction vector of the line and the direction vector of the rolling axis; Step 4: Calculate the vector error angle using the direction vector of the line and the direction vector of the rolling axis, and operate the cabin position and attitude adjustment platform 2 to eliminate the vector error angle.

[0020] The linear motion platform is fixed on the ground. The cabin position and attitude adjustment platform is installed on the linear motion platform. The calibration target ball is installed on the cabin position and attitude adjustment platform.

[0021] The collaborative robot is fixed on the ground. The laser profiler is installed on the collaborative robot.

[0022] As Figure 2 shown, the method of this application includes the following steps: The first step is to perform hand-eye calibration on the collaborative robot to determine the conversion relationship between the laser profile vision coordinate system and the robot base coordinate system; Install the calibration target ball on the cabin position and attitude adjustment platform, and use the laser profiler to collect single-line data of the calibration target ball to obtain the outer contour curve of any cross-section of the sphere. The collected data is expressed as a three-dimensional point cloud file, where the three-dimensional point cloud coordinates represent the spatial position of the points on the target ball relative to the laser profiler vision coordinate system, and at the same time record the corresponding attitude of the robot in the robot coordinate system at this time . Define the radius R of the target ball and define the position indicator of the actual center of the target ball relative to the laser profiler. If the center of the ball is in front of the laser profiler, it is recorded as +1. If the center of the ball is behind the laser profiler, it is recorded as -1. Record multiple sets of data. After the data recording is completed, first perform a center fitting on the target ball using R and the center position indicator. Since the position of the target ball does not move during the data acquisition process, the center position does not change either and can be used as a calibration basis. Solve the equation , where A is the motion transformation matrix of the robot end effector. B is the motion transformation matrix of the camera. N is the hand-eye transformation matrix, that is, the transformation from the robot end to the camera. For each motion, there is , linearize the equation to obtain , substitute the collected data and perform singular value decomposition and solution, and then reconstruct to obtain the hand-eye calibration matrix N.

[0023] The cabin pose adjustment platform can realize the 6-degree-of-freedom position and attitude adjustment function. The horizontal motion range is not less than 100 mm, the vertical motion range is not less than 100 mm, the pitch motion range is not less than 5°, the yaw motion range is not less than 30°, and the roll motion range is not less than 360°. The calculation method of B: For two different robot poses i and j , the positions of the calibration ball in the camera are respectively and , then: , and , where is the 4×4 pose matrix of the calibration ball in the camera coordinate system (since the ball has no rotation, the rotation part is the identity matrix, and the translation part is the center coordinate of the ball), that is , where x, y, z are the coordinates of the center of the ball in the camera coordinate system.

[0024] A is the relative pose change between two different moments i and j of the robot end, and the calculation formula is , where T is generated from the recorded robot attitude R, and N can be solved through the above formula.

[0025] Step 2: Control the cabin pose adjustment platform to perform uniaxial motion, and at the same time use the laser profiler to collect multiple sets of calibration ball data.

[0026] Such as Figure 3As shown in the figure, define the forward movement direction of the linear motion platform of the cabin position and attitude adjustment platform as the X direction, the upward movement perpendicular to the ground of the cabin position and attitude adjustment platform as the Z direction, the Y direction forms a right-handed system with the X and Z directions, the rolling axis direction of the cabin is parallel to the X direction, the yaw axis direction is parallel to the Z direction, the pitch axis direction is parallel to the Y direction, and the rotation center is O. Control the cabin position and attitude adjustment platform to move only along a single axis direction. At the same time, use a laser profiler to collect single-line data on the calibration target ball, and obtain the outer contour curve of any cross-section of the sphere. The representation method is the same as in the first step. At the same time, save and record the corresponding attitude of the robot in the base coordinate system. , the radius R of the target ball, the target ball center position indicator, collect multiple groups of data and save them. This process is repeated six times to ensure that the six-degree-of-freedom platform completes single-axis movement in each direction and saves multiple groups of data.

[0027] Step 3: Fit the center of the calibration ball data, fit the centers of the completed fits in space, and output the direction vector of the corresponding movement direction.

[0028] After the recording is completed, perform sphere center fitting on the data, and use the hand-eye calibration matrix N obtained in the first step for coordinate transformation to obtain a series of sphere center coordinates C in the robot base coordinate system, and perform fitting on the sphere centers in each single-axis direction respectively.

[0029] For the X, Y, and Z directions, the fitting method is linear fitting. Define the set of sphere center coordinates in the single-axis direction as , where . Calculate the mean coordinate of the point set as: where is the center of the point set, centralize the point set to obtain , where . Calculate the covariance matrix C such that , perform eigenvalue decomposition on C such that , where V is the eigenvector matrix, each column is an eigenvector, Λ is a diagonal matrix, and the elements on the diagonal are eigenvalues. Select the eigenvector corresponding to the largest eigenvalue as the direction vector of the line, where .

[0030] For the roll, yaw, and pitch directions, the fitting method is circle fitting. First, define the set of sphere center coordinates in the single-axis direction as , where . Calculate the mean value of the coordinate values of the sphere center point set , where is the center of the point set, centralize the point set to obtain , where . Calculate the covariance matrix C such that , perform eigenvalue decomposition on C such that , where V is the eigenvector matrix, each column is an eigenvector, Λ is a diagonal matrix, and the elements on the diagonal are eigenvalues. Select the eigenvector corresponding to the smallest eigenvalue as the normal vector of the fitting plane, where .

[0031] Secondly, project the point set onto the fitted plane. The plane equation is expressed as , then The projected point of the point is . Define a circle formed by the center point set on the projected plane. The equation is , where (a, b) is the center coordinate, r is the radius of the circle. For each projected point Define an error function. Define the error function , and the goal is to minimize the sum of the squared errors of all points .

[0032] Subsequently, linearize the error function. Rewrite the circle equation as , let , such that , substitute the projected point to get , the matrix form is , solve to obtain a, b, c, and get the center coordinate and radius on the projected plane. Convert the center coordinate back to the initial coordinate system (i.e., the robot base coordinate system), that is , where and are the first two eigenvectors of the covariance matrix C; Finally, the direction vector of the roll axis can be obtained , the center and the radius.

[0033] Fourthly, calculate the vector error angle using the output direction vector and adjust the pose of the cabin section adjustment platform 3 to eliminate the error angle.

[0034] and are both three-dimensional space vectors. According to the direction characteristics of the corresponding axes, project them onto the XOY, YOZ, and XOZ planes respectively. Use the vector angle formula to calculate the angle between the projected vectors and in the projected plane, and operate the cabin section adjustment platform to rotate the corresponding angle to achieve coaxiality adjustment.

[0035] It should be noted that the specific implementation manners are merely explanations and illustrations of the technical solutions of the present invention, and the scope of the rights protection cannot be limited thereby. Those that are only partial changes made according to the claims and the specification of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A method for adjusting the coaxiality of the socket connection of a closed cabin section, characterized in that The method is implemented based on a coaxiality adjustment system for enclosed cabin sections sleeving, and the coaxiality adjustment system for enclosed cabin sections sleeving includes a collaborative robot (1), a cabin pose adjustment platform (2), a linear motion platform (3), a laser profiler (4), and a calibration target ball (5); The linear motion platform (3) is fixed on the ground, the cabin pose adjustment platform (2) is arranged on the linear motion platform (3), the calibration target ball (5) is arranged on the cabin pose adjustment platform (2), the collaborative robot (1) is fixed on the ground, and the laser profiler (4) is arranged on the collaborative robot (1); The method includes the following steps: Step 1: Perform hand-eye calibration on the collaborative robot (1) to obtain a hand-eye calibration matrix N; Step 2: Control the cabin pose adjustment platform (2) to perform single-axis motion, and at the same time use the laser profiler (4) to collect multiple single-line data of the calibration target ball (5) to obtain multiple groups of data; Step 3: Based on the hand-eye calibration matrix N, and use the obtained multiple groups of data for circle center fitting, and then perform spatial position fitting on the fitted circle center to obtain the direction vector of the straight line and the direction vector of the roll axis; Step 4: Calculate the vector error angle using the direction vector of the straight line and the direction vector of the roll axis, and operate the cabin pose adjustment platform (2) to eliminate the vector error angle.

2. A method for adjusting the coaxiality of the socket connection of a closed cabin section according to claim 1, characterized in that The specific steps of Step 1 are as follows: Step 1-1: Set the calibration target ball (5) on the cabin pose adjustment platform (2), and use the laser profiler (4) to collect single-line data of the calibration target ball (5) to obtain the outer contour curve of any cross-section of the sphere, that is, collect data, and record the pose of the robot in the robot coordinate system at this time; Step 1-2: Obtain the motion transformation matrix A of the robot end effector according to the corresponding pose of the robot in the robot coordinate system; Step 1-3: Obtain the position indicator of the actual center of the calibration target ball (5) relative to the laser profiler (4) and the radius R of the calibration target ball (5), and use the position indicator of the actual center of the calibration target ball (5) relative to the laser profiler (4) and the radius R of the calibration target ball (5) to perform sphere center fitting on the calibration target ball (5). Taking the calibration target ball (5) as the calibration basis and combining with the motion transformation matrix A of the robot end effector, solve the equation , where B is the motion transformation matrix of the camera and N is the hand-eye transformation matrix. For each motion, there is . Linearize the equation to obtain , where is the identity matrix. Finally, substitute the collected data and perform singular value decomposition and reconstruction to obtain the hand-eye calibration matrix N.

3. A method for adjusting the coaxiality of the socket connection of a closed cabin section according to claim 2, characterized in that The specific steps of Step 2 are as follows: Step 2-1: Define the motion direction of the cabin pose adjustment platform (2) along the linear motion platform (3) as the X direction, the upward motion direction of the cabin pose adjustment platform (2) perpendicular to the ground as the Z direction, the Y direction forms a right-hand system with the X and Z directions, the roll axis direction of the cabin is parallel to the X direction, the yaw axis direction is parallel to the Z direction, and the pitch axis direction is parallel to the Y direction; Step 2-2: Control the cabin pose adjustment platform (2) to move only along any single-axis direction, and at the same time use the laser profiler (4) to collect single-line data of the calibration target ball (5) to obtain the outer contour curve of any cross-section of the sphere, that is, collect data, and save and record the pose of the robot in the base coordinate system, the radius R of the calibration target ball (5), and the target ball center position indicator; Step 2-3: Repeat Step 2-2 to collect multiple groups of data and save them.

4. A method for adjusting the coaxiality of the socket connection of a closed cabin section according to claim 3, characterized in that The specific steps of Step 3 are as follows: Perform spherical center fitting on the acquired data, and use the hand-eye calibration matrix N for coordinate transformation to obtain the set of spherical center coordinates corresponding to the robot base coordinate system. Then, fit the spherical centers in each single-axis direction according to the spherical center coordinates. Among them, for the X, Y, and Z directions, linear fitting is adopted, and for the roll axis, yaw axis, and pitch axis directions, circular fitting is adopted. The linear fitting is specifically as follows: Step III: Obtain the set of the mean coordinates , where , , is the center coordinate of the th ball in the set i . Step 312: Take the mean coordinates as the center of the centered point set, and combine with to obtain the centered vector , ; Step Sanyi-San: According to the centralized vector calculate the covariance matrix , and perform eigenvalue decomposition on the covariance matrix such that , where V is the eigenvector matrix and Λ is the diagonal matrix; Step 3-14: Based on the result after eigenvalue decomposition, select the eigenvector corresponding to the largest eigenvalue as the direction vector of the line; The circle fitting is specifically as follows: Step three two one: Obtain the set of the mean coordinates , where , , is the set the i th center-of-sphere coordinate; Step Three Two Two: Take the mean coordinates as the center of the centralized point set, and combine with to obtain the centralized vector , ; Step 323: According to the centralized vector calculate the covariance matrix , and perform eigenvalue decomposition on the covariance matrix such that , where V is the eigenvector matrix and Λ is the diagonal matrix; Step 324: Based on the result after eigenvalue decomposition, select the eigenvector corresponding to the smallest eigenvalue as the normal vector of the fitting plane; Step 325: Determine the fitted plane according to the normal vector of the fitted plane, and project the set onto the fitted plane. The circle formed by the center coordinates on the projection plane is , where is the center coordinate, is the center coordinate of the sphere after projection, and is the radius of the circle; Step 3-26: Define an error function to minimize the sum of the squares of the errors of all projection points; Step 3-27: Linearize the error function and rewrite the equation of the circle as , let the difference , such that , substituting the projection point gives , solving to obtain the center coordinates on the projection plane, and converting the center coordinates back to the initial coordinate system to get the center .

5. A method for adjusting the coaxiality of the socket connection of a closed cabin section according to claim 4, characterized in that The mean coordinates are expressed as: 。 6. A method for adjusting the coaxiality of the socket connection of a closed cabin section according to claim 5, characterized in that The covariance matrix is expressed as: 。 7. A method for adjusting the coaxiality of the socket joint of a closed cabin section according to claim 6, characterized in that The sum of the squares of the errors is expressed as: wherein, is an error function.

8. A method for adjusting the coaxiality of the socket connection of a closed cabin section according to claim 7, characterized in that The error function is expressed as: Among them, is the projected coordinate.

9. A method for adjusting the coaxiality of a closed cabin section socket connection according to claim 8, characterized in that The center of the circle is expressed as: Among them, and are the first two eigenvectors of the covariance matrix.

10. A method for adjusting the coaxiality of the socket joint of a closed cabin section according to claim 9, characterized in that The specific steps of Step 4 are as follows: According to the center of the circle and the radius of the circle , project and onto the XOY, YOZ, and XOZ planes respectively, and use the vector angle formula to calculate the angle between the projection vectors and in the projection planes. Finally, rotate the pose adjustment platform (2) of the operation cabin section by the corresponding angle to achieve coaxiality adjustment.

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