Error self-calibration method based on feature component for parallel coordinate measuring machine

Abstract

Disclosed in the present invention is an error self-calibration method based on a feature component for a parallel coordinate measuring machine. The method comprises: constructing a geometric error model of a parallel mechanism; measuring a feature component by means of a coordinate measuring machine, and then mounting the feature component within the workspace of a parallel coordinate measuring machine; performing data collection on the basis of a sphere‑center‑distance constraint and a sphere‑radius constraint, and correspondingly constructing an error equation based on the sphere‑center‑distance constraint and an error equation based on the sphere‑radius constraint; combining the error equations to obtain an error calibration model based on various feature constraints, using an LM method to identify, correct and substitute kinematic error parameters of the error calibration model, and repeating this process iteratively until kinematic error parameters no longer change, so as to obtain corresponding geometric error parameters of the parallel coordinate measuring machine; and on the basis of the geometric error parameters, compensating for an end pose error in the coordinate measuring machine caused by a geometric error. The present invention greatly improves the motion precision of a parallel coordinate measuring machine.

Description

An error self-calibration method for a parallel coordinate measuring machine based on feature components. Technical Field

[0001] This invention belongs to the field of error calibration, and particularly relates to an error self-calibration method for a parallel coordinate measuring machine based on feature components. Background Technology

[0002] Parallel robots, due to their high precision and rigidity, have been widely used in precision manufacturing, aerospace, and other fields. However, due to errors in machining and assembly, deviations will inevitably exist between the geometric parameters of the parallel coordinate measuring machine (PCM) and its design values. Performing motion calculations on the PCM based on these deviations will inevitably lead to pose errors in the end effector. Therefore, it is necessary to calibrate the geometric parameters and joint zero points of the PCM to improve the positioning accuracy of the end effector and lay the foundation for stable robot control.

[0003] Calibration methods are mainly divided into two types: external calibration and internal calibration. Internal calibration identifies error parameters by installing sensors on the active and driven joints in a number exceeding the robot's degrees of freedom, and measuring redundant motion information in real time. Internal calibration has advantages such as not requiring additional measuring instruments, strong environmental adaptability, fast detection speed, and ease of automated calibration and online error compensation. However, internal calibration requires measuring error information at all joints, and the installation of sensors increases the design complexity of parallel mechanisms and raises manufacturing costs.

[0004] Current methods for calibrating the geometric parameters of parallel robots using external calibration determine parameters by directly measuring the position and orientation of the robot's end effector using coordinates. However, this often requires high-precision measurement equipment, resulting in high costs. For example, Chinese patent application publication number CN114894086A discloses an error calibration method based on a laser tracker, which is costly and complex to measure. Chinese patent application publication number CN113183137A discloses a parameter calibration device based on displacement sensors. The device includes three mutually orthogonal planes, on which one, two, and three displacement sensors are fixed respectively. The probe axes of the displacement sensors are perpendicular to the corresponding planes. The device is fixed to a fixed platform of a six-degree-of-freedom parallel mechanism by a bracket, and the change in end-effector position is obtained by the extension and retraction of the displacement sensors. Its disadvantages are the need for a large number of sensors and the inability to calibrate the entire workspace of the parallel robot. Summary of the Invention

[0005] To address the problems of high calibration cost, long processing time, and poor environmental adaptability in existing methods, this invention provides an error self-calibration method for parallel coordinate measuring machines based on feature components, comprising:

[0006] Construct a parallel mechanism and build a geometric error model of the parallel mechanism to determine the error parameters;

[0007] The feature component is measured using a coordinate measuring machine to obtain the radius value of each standard sphere and the center-to-center distance between every two standard spheres. After the measurement is completed, the feature component is installed in the workspace of the parallel coordinate measuring machine. Data is collected based on the center-to-center distance constraint and the sphere diameter constraint, and error equations based on the center-to-center distance constraint and the sphere radius constraint are constructed accordingly.

[0008] The error equations based on the center distance constraint and the error equations based on the radius constraint are combined to obtain an error calibration model based on multiple feature constraints. The LM method is used to identify, correct and substitute the kinematic error parameters of the error calibration model. This process is repeated until the kinematic error parameters no longer change, at which point the iteration stops, and the corresponding geometric error parameters of the parallel coordinate measuring machine are obtained.

[0009] The end-effector attitude error caused by geometric errors in the coordinate measuring machine is compensated based on the geometric error parameters.

[0010] Preferably, the parallel mechanism includes a static platform, a branch chain, and a moving platform;

[0011] The parallel mechanism is driven by a moving pair input consisting of a servo motor, a ball screw, and a guide rail;

[0012] The branch includes a sliding joint and a Hooke's hinge;

[0013] The end of the moving platform is equipped with a trigger probe, which is used to output a contact trigger signal between the coordinate measuring machine and the measured part. When the parallel mechanism controller receives the motion command, it decomposes the target motion into the displacement of four translation axes. The ball screw is driven to rotate by the servo motor of the corresponding axis, so as to realize the movement of the slider on the translation axis. Through the coordinated movement of the four-axis slider, the end moving platform realizes the translational movement of the X, Y and Z axes and the rotational movement around the Z axis.

[0014] Preferably, the process of constructing the geometric error model of the parallel mechanism includes establishing kinematic equations;

[0015] The process of establishing the kinematic equations includes:

[0016] Establish the base coordinate system O-xyz of the parallel mechanism at the center of the static platform, and establish the moving coordinate system O′-xyz of the parallel mechanism at the center of the moving platform;

[0017] The inverse kinematics of the parallel mechanism is solved in the inverse kinematics model of the parallel mechanism, where the input variable is the pose of the moving coordinate system relative to the base coordinate system, and the output is the displacement of the four prismatic joints.

[0018] Analyzing the branches, let the vector from the center O of the base coordinate system to point A on the base be... The unit vector of the direction of motion of the sliding joint is The distance from point P on the movable secondary slider to point A on the base is That is, the driving variable of the parallel mechanism; the vector from point P on the sliding joint to point D at the center of the Hooke hinge 1 is The lengths of the rods from Hooke's hinge 1 to Hooke's hinge 2 are: Direction vector is The vector from the center O′ of the moving coordinate system to the center B of the Hooke's hinge 2 is The vector from the center O of the base coordinate system to the center O′ of the moving coordinate system is Let R be the rotation matrix from the base coordinate system to the moving coordinate system. Then, using the closed-loop vector method, the vector equation is: a i +p i e i +d i +L i u i =q+Rb i (1)

[0019] Based on the link length L i The invariant constraints are obtained as follows:

[0020] Where E i =q+Rb i -a i -d i ;

[0021] The kinematic forward solution of the parallel structure is solved iteratively using Newton's method. The iteration ends when the L2 norm of the difference between the results of the two consecutive iterations is less than the specified iteration precision.

[0022] Preferably, the process of constructing the geometric error model of the parallel mechanism includes establishing an error mapping model;

[0023] The process of establishing the error mapping model includes:

[0024] Considering the error sources of workpiece machining errors and assembly errors, the branches are analyzed, a kinematic error mapping model is established, and linearly dependent vectors are removed to obtain: [u x ,u y ,u x p,-u y p,-u T R,-1]·Δε=[u x ,u y ,u z ,u x (-b x sθ-by cθ)+u y (- b x cθ-b y sθ)]·ΔY(3)

[0025] Where ΔY=[Δx,Δy,Δz,Δθ] z ]=[ΔP,Δθ z ];

[0026] ΔY represents the difference between the actual end-effector pose and the theoretical pose, ΔP represents the end-effector position error, and Δθ represents the position error of the end-effector. z The z-axis attitude error at the end point is represented by Δε, where Δε represents the geometric error parameter. This represents the direction vector of the link;

[0027] The error model of the branch is further expressed as: A i ·ΔY=B i ·Δε i i = 1, 2, 3, 4 (4)

[0028] By combining the error models of the branches, we can obtain the geometric error model of the parallel mechanism: ΔY = J q -1 J ε ·Δε=J p ·Δε (5)

[0029] J q = [A1,A2,A3,A4], J ε =diag(B1,B2,B3,B4);

[0030] The influence of the geometric error of the mechanism on the end-effector pose error is calculated based on the geometric error model.

[0031] Preferably, the workpiece machining error includes: the positional error of the three Hooke hinges of the moving platform. Linkage length Position of the Hooke hinge adjacent to the slider Error of column position relative to the center of static platform

[0032] The assembly error includes: the axial direction of the sliding joint. and its position on the static platform The initial position positioning error affects the initial position Δp of the ball screw slider.

[0033] Preferably, the data acquisition process based on the sphere center distance constraint and the sphere diameter constraint includes:

[0034] The control coordinate measuring machine (CMM) is used to contact the standard ball in the feature component at the end of the control coordinate measuring machine. At each position, the control coordinate measuring machine uses a contact probe to uniformly measure the surface of the standard ball on the feature component multiple times. The measurement readings and position readings of the four translation axes are read and recorded for each measurement. The error at different workspace positions is also obtained. The position of the feature component in the workspace of the parallel coordinate measuring machine is changed multiple times to collect multiple sets of data.

[0035] Preferably, the process of constructing the error equation based on the sphere center distance constraint includes:

[0036] The recorded translation axis data and measurement readings are divided into several groups according to the position of the feature components during measurement. The difference between the fitted sphere center distance and the theoretical sphere center distance measured using a coordinate measuring machine is used to obtain the sphere center distance error. An error equation based on the sphere center distance constraint is constructed, and the expression is:

[0037] Among them, J s,i =[J p,i1 J p,i2 J p,i3 J p,i4 ] T J s,i This indicates the influence of the error parameter on the pose error of the four sampling points of each set of standard spheres.

[0038] Preferably, the process of constructing the error equation based on the sphere radius constraint includes:

[0039] The measured data of each sphere are grouped, and the difference between the fitted sphere radius and the theoretical sphere radius measured by the coordinate measuring machine is calculated to construct an error equation based on the sphere radius constraint.

[0040] Preferably, the formula expression of the error calibration model based on multiple feature constraints is as follows:

[0041] The error model for the i-th group of spherical sampling points is as follows:

[0042] n is the number of groups of standard spheres for sampling. This indicates the probe radius error.

[0043] Compared with the prior art, the present invention has the following advantages and technical effects:

[0044] Compared with traditional external calibration methods for parallel robots, the method of this invention has the advantages of low cost and good portability, and does not require additional sensors and is easy to operate. By using multiple feature constraints, the number of constraint equations is increased, thereby reducing the number of calibration positions required and shortening the calibration cycle. At the same time, it improves the robustness and noise resistance of the algorithm, effectively solves the problem of kinematic error parameter identification of parallel coordinate measuring machines, and significantly improves the motion accuracy of parallel coordinate measuring machines. Attached Figure Description

[0045] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

[0046] Figure 1 is a schematic diagram of the method flow according to an embodiment of the present invention. Detailed Implementation

[0047] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0048] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0049] As shown in Figure 1, this embodiment provides an error self-calibration method for a parallel coordinate measuring machine based on feature components, including:

[0050] Construct a parallel mechanism and build its geometric error model to determine the error parameters;

[0051] The feature component is measured by a coordinate measuring machine to obtain the radius value of each standard sphere and the center-to-center distance between every two standard spheres. After the measurement is completed, the feature component is installed in the workspace of the parallel coordinate measuring machine. Data is collected based on the center-to-center distance constraint and the sphere diameter constraint, and error equations based on the center-to-center distance constraint and the sphere radius constraint are constructed accordingly.

[0052] The error equations based on the center distance constraint and the error equations based on the radius constraint are combined to obtain an error calibration model based on multiple feature constraints. The LM method is used to identify, correct and substitute the kinematic error parameters of the error calibration model. This process is repeated until the kinematic error parameters no longer change, and the iteration stops to obtain the corresponding geometric error parameters of the parallel coordinate measuring machine.

[0053] The end-effector attitude error caused by geometric errors in the coordinate measuring machine is compensated based on the geometric error parameters.

[0054] Furthermore, the first step is to establish a 4PUU parallel mechanism;

[0055] The 4PUU parallel mechanism consists of a stationary platform, four branches, and a moving platform. Each branch comprises a prismatic joint (P-joint) and two Hooke joints (U-joints). The mechanism is driven by four prismatic joints consisting of servo motors, ball screws, and guide rails. A trigger-type probe is mounted at the end of the moving platform to output a contact trigger signal between the coordinate measuring machine and the workpiece. When the parallel mechanism controller receives a motion command, it decomposes the target motion into displacements along four translation axes. The corresponding servo motors drive the ball screws to rotate, thus moving the sliders on the translation axes. Through the coordinated movement of the four-axis sliders, the moving platform at the end can achieve translational motion along the X, Y, and Z axes and rotational motion around the Z-axis.

[0056] Furthermore, the second step is to establish a geometric error model of the 4PUU parallel mechanism and determine the error parameters;

[0057] Further optimize the scheme and establish kinematic equations;

[0058] The kinematic model of the 4PUU parallel mechanism is established by setting the base coordinate system O-xyz at the center of the static platform and the moving coordinate system O′-xyz at the center of the moving platform.

[0059] First, solve the inverse kinematics of the parallel mechanism: In the inverse kinematics model of the parallel mechanism, the input variable is the pose of the moving coordinate system relative to the base coordinate system, and the output is the displacement of the four prismatic joints.

[0060] Analyzing one of the branches, let the vector from the center O of the base coordinate system to point A on the base be... The unit vector of the direction of motion of the sliding joint is The distance from point P on the movable secondary slider to point A on the base is That is, the driving variable of the parallel mechanism; the vector from point P on the sliding joint to point D at the center of the Hooke hinge 1 is The lengths of the rods from Hooke's hinge 1 to Hooke's hinge 2 are: Direction vector is The vector from the center O′ of the moving coordinate system to the center B of the Hooke's hinge 2 is The vector from the center O of the base coordinate system to the center O' of the moving coordinate system is Let R be the rotation matrix from the base coordinate system to the moving coordinate system.

[0061] Then, using the closed-loop vector method, the vector equation is: a i +p ie i +d i +L i u i =q+Rb i (1)

[0062] Based on the link length L i The invariant constraints are obtained as follows:

[0063] Where E i =q+Rb i -a i -d i ;

[0064] Since Equation 1 cannot yield an explicit analytical expression for the pose q of the moving platform, Newton's method is used to iteratively solve for the forward kinematics of the 4PUU structure. Because the display unit of the parallel coordinate measuring machine is μm, setting the iteration accuracy to 1e-7 is sufficient. The iteration ends when the L2 norm of the difference between two consecutive iterations is less than the iteration accuracy.

[0065] Further optimize the scheme and establish an error mapping model;

[0066] Workpiece machining errors include: positional errors of the three Hooke hinges on the moving platform. Linkage length Position of the Hooke hinge adjacent to the slider Error of column position relative to the center of static platform

[0067] Assembly errors include: the axial direction of the sliding joint. and its position on the static platform The initial position positioning error affects the initial position Δp of the ball screw slider.

[0068] Considering the above error sources, we analyze one of the branches, establish a kinematic error mapping model, and remove linearly dependent vectors to obtain: [u x ,u y ,u x p,-u y p,-u T R,-1]·Δε=[u x ,u y ,u z ,u x (-b x sθ-b y cθ)+u y (- b x cθ-b y sθ)]·ΔY (3)

[0069] Where ΔY=[Δx,Δy,Δz,Δθ] z ]=[ΔP,Δθ z ];

[0070] ΔY represents the difference between the actual end-effector pose and the theoretical pose, ΔP represents the end-effector position error, and Δθ represents the position error of the end-effector. z Δε represents the z-axis attitude error at the end point, and Δε represents the geometric error parameter. This represents the direction vector of the link.

[0071] The error model of the branch is further expressed as: A i ·ΔY=B i ·Δε i i = 1, 2, 3, 4 (4)

[0072] Combining the error models of the four branches yields the error model of the parallel mechanism: ΔY = J q -1 J ε ·Δε=J p ·Δε (5)

[0073] J q = [A1,A2,A3,A4], J ε =diag(B1,B2,B3,B4);

[0074] Formula 5 can be used to calculate the relationship between the geometric error of the parallel mechanism and the end-effector pose error.

[0075] Furthermore, the third step is measurement and installation;

[0076] The standard spherical plate consists of four standard spheres. The centers of two spheres are 200 mm apart. The standard spheres are solid steel spheres with a diameter of 38.1 mm and a spherical roundness of 1 μm. The plate's posture can be adjusted via ball joints. A high-precision coordinate measuring machine (CMM) is used to measure the feature component, obtaining the radius value of each standard sphere and the center-to-center distance between every two standard spheres. After measurement, the feature component is installed in the workspace of the parallel coordinate measuring machine.

[0077] Furthermore, the fourth step is data collection;

[0078] The data acquisition process based on sphere center distance and sphere diameter constraints is as follows: A handheld controller is used to control the end effector of the coordinate measuring machine (CMM) to contact the standard sphere in the feature component. At each position, the CMM end effector uses a contact probe to uniformly measure the surface of the standard sphere on the feature component multiple times. The measurement readings and the position readings of the four translation axes for each measurement are read and recorded. To reduce measurement errors and obtain the errors at different workspace positions, the position of the feature component in the workspace of the parallel CMM is changed multiple times, and multiple sets of data are acquired.

[0079] Since the sampling points all satisfy the spherical constraint, if four points are uniformly sampled on the sphere, the following equation will be satisfied: (P c -P i ) T (P c -P i )=(R i +r) 2 ,i=1,2,3,4 (6)

[0080] Where R i Let be the radius of the sphere, and r be the radius of the probe. After radius error calibration, these are known quantities. Differentiating the above equation yields:

[0081] That is, the mapping relationship between the sampling point error and the sphere center error and sphere radius error.

[0082] Further, the fifth step is parameter identification;

[0083] The recorded translation axis data and measurement readings are divided into several groups according to the position of the feature components in the measurement. The difference between the fitted sphere center distance and the theoretical sphere center distance measured using CMM is obtained to obtain the sphere center distance error, and an error equation based on the sphere center distance constraint is constructed.

[0084] Among them, the sphere center distance constraint equation is:

[0085] Sphere center distance error mapping equation:

[0086] Substituting into Equations 5 and 8, the error equation based on the sphere center distance constraint can be obtained as follows:

[0087] J s,i =[J p,i1 J p,i2 J p,i3 J p,i4 ] T J s,i This indicates the influence of the error parameter on the pose error of the four sampling points of each set of standard spheres.

[0088] The measured data of each sphere are grouped, and the difference between the fitted sphere radius and the theoretical sphere radius measured by CMM is calculated to construct an error equation based on the sphere radius constraint.

[0089] By combining the error equations obtained from the two constraints, an error calibration model based on multiple feature constraints can be obtained.

[0090] Error model for the i-th group of spherical sampling points:

[0091] Where n is the number of groups of standard spheres for sampling. This indicates the probe radius error.

[0092] The LM method is used to identify the kinematic error parameters. The kinematic error model is corrected using the model parameters calculated at each step, and then the corrected parameters are substituted back into the kinematic error model. This process is repeated until the error parameters no longer change, at which point the iteration stops, and the corresponding geometric error parameters of the parallel coordinate measuring machine are obtained.

[0093] Further, the sixth step is error compensation;

[0094] By substituting the geometric error parameters identified in step five into the kinematic model containing these error parameters, and directly modifying the kinematic error parameters in the controller, a precise mapping relationship between the drive shaft position and the end effector attitude can be obtained. In actual control, only the kinematic model containing the error parameters needs to be used to compensate for the end effector attitude error caused by geometric errors in the coordinate measuring machine.

[0095] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. An error self-calibration method for a parallel coordinate measuring machine based on feature components, characterized in that, include: Construct a parallel mechanism and build a geometric error model of the parallel mechanism to determine the error parameters; The feature components are measured using a coordinate measuring machine to obtain the radius value of each standard sphere and the distance between the centers of every two standard spheres; After the measurement is completed, the feature component is installed in the workspace of the parallel coordinate measuring machine. Data is collected based on the sphere center distance constraint and the sphere diameter constraint, and error equations based on the sphere center distance constraint and the sphere radius constraint are constructed accordingly. The error equations based on the center distance constraint and the error equations based on the radius constraint are combined to obtain an error calibration model based on multiple feature constraints. The LM method is used to identify, correct and substitute the kinematic error parameters of the error calibration model. This process is repeated until the kinematic error parameters no longer change, at which point the iteration stops, and the corresponding geometric error parameters of the parallel coordinate measuring machine are obtained. The end-effector attitude error caused by geometric errors in the coordinate measuring machine is compensated based on the geometric error parameters.

2. The error self-calibration method for a parallel coordinate measuring machine based on feature components according to claim 1, characterized in that, The parallel mechanism includes a static platform, a branch chain, and a moving platform; The parallel mechanism is driven by a moving pair input consisting of a servo motor, a ball screw, and a guide rail; The branch includes a sliding joint and a Hooke's hinge; The end of the moving platform is equipped with a trigger probe, which is used to output a contact trigger signal between the coordinate measuring machine and the measured part. When the parallel mechanism controller receives the motion command, it decomposes the target motion into the displacement of four translation axes. The ball screw is driven to rotate by the servo motor of the corresponding axis, so as to realize the movement of the slider on the translation axis. Through the coordinated movement of the four-axis slider, the end moving platform realizes the translational movement of the X, Y and Z axes and the rotational movement around the Z axis.

3. The error self-calibration method for a parallel coordinate measuring machine based on feature components according to claim 1, characterized in that, The process of constructing the geometric error model of the parallel mechanism includes establishing kinematic equations; The process of establishing the kinematic equations includes: Establish the base coordinate system O-xyz of the parallel mechanism at the center of the static platform, and establish the moving coordinate system O′-xyz of the parallel mechanism at the center of the moving platform; The inverse kinematics of the parallel mechanism is solved in the inverse kinematics model of the parallel mechanism, where the input variable is the pose of the moving coordinate system relative to the base coordinate system, and the output is the displacement of the four prismatic joints; Analyzing the branches, let the vector from the center O of the base coordinate system to point A on the base be... The unit vector of the direction of motion of the sliding joint is The distance from point P on the movable secondary slider to point A on the base is That is, the driving variable of the parallel mechanism; the vector from point P on the sliding joint to point D at the center of the Hooke hinge 1 is The lengths of the rods from Hooke's hinge 1 to Hooke's hinge 2 are: Direction vector is The vector from the center O′ of the moving coordinate system to the center B of the Hooke's hinge 2 is The vector from the center O of the base coordinate system to the center O′ of the moving coordinate system is Let R be the rotation matrix from the base coordinate system to the moving coordinate system. Then, using the closed-loop vector method, the vector equation is: a i +p i e i +d i +L i u i =q+Rb i (1) Based on the link length L i The invariant constraints are used to obtain: Where E i =q+Rb i -a i -d i ; The kinematic forward solution of the parallel structure is solved iteratively using Newton's method. The iteration ends when the L2 norm of the difference between the results of the two consecutive iterations is less than the specified iteration precision.

4. The error self-calibration method for a parallel coordinate measuring machine based on feature components according to claim 1, characterized in that, The process of constructing the geometric error model of the parallel mechanism includes establishing an error mapping model; The process of establishing the error mapping model includes: Considering the error sources of workpiece machining errors and assembly errors, the branches are analyzed, a kinematic error mapping model is established, and linearly dependent vectors are removed to obtain: [in x ,in y ,in x p,-u y p,-u T R,-1]·Δε=[u x ,in y ,in z ,in x (-b x sθ-b y cθ)+u y (- b x cθ-b y sθ)]·ΔY (3) where ΔY = [Δx, Δy, Δz, Δθ z = [ΔP, Δθ z ; ΔY represents the difference between the actual end-effector pose and the theoretical pose, ΔP represents the end-effector position error, and Δθ represents the position error of the end-effector. z The z-axis attitude error at the end point is represented by Δε, where Δε represents the geometric error parameter. This represents the direction vector of the link; The error model of the branch is further expressed as: A i ·ΔY=B i ·No i ,i=1,2,3,4 (4) By combining the error models of the branches, the geometric error model of the parallel mechanism can be obtained: ΔY=J q -1 J ε ·No=J p ·No (5) J q = [A1,A2,A3,A4], J ε =diag(B1,B2,B3,B4); The influence of the geometric error of the mechanism on the end-effector pose error is calculated based on the geometric error model.

5. The error self-calibration method for a parallel coordinate measuring machine based on feature components according to claim 4, characterized in that, The workpiece machining error includes: the positional error of the three Hooke hinges on the moving platform. Linkage length Position of the Hooke hinge adjacent to the slider Error of column position relative to the center of static platform The assembly error includes: the axial direction of the sliding joint. and its position on the static platform The initial position positioning error affects the initial position Δp of the ball screw slider.

6. The error self-calibration method for a parallel coordinate measuring machine based on feature components according to claim 1, characterized in that, The data acquisition process based on sphere center distance constraints and sphere diameter constraints includes: The control coordinate measuring machine (CMM) is used to contact the standard ball in the feature component at the end of the control coordinate measuring machine. At each position, the control coordinate measuring machine uses a contact probe to uniformly measure the surface of the standard ball on the feature component multiple times. The measurement readings and position readings of the four translation axes are read and recorded for each measurement. The error at different workspace positions is also obtained. The position of the feature component in the workspace of the parallel coordinate measuring machine is changed multiple times to collect multiple sets of data.

7. The error self-calibration method for a parallel coordinate measuring machine based on feature components according to claim 1, characterized in that, The process of constructing the error equation based on the sphere center distance constraint includes: The recorded translation axis data and measurement readings are divided into several groups according to the position of the characteristic components during measurement. The difference between the fitted sphere center distance and the theoretical sphere center distance measured using a coordinate measuring machine is used to obtain the sphere center distance error. An error equation based on the sphere center distance constraint is constructed, and the expression is: Among them, J s,i =[J p,i1 J p,i2 J p,i3 J p,i4 ] T J s,i This indicates the influence of the error parameter on the pose error of the four sampling points of each set of standard spheres.

8. The error self-calibration method for a parallel coordinate measuring machine based on feature components according to claim 1, characterized in that, The process of constructing the error equation based on the sphere radius constraint includes: The measured data of each sphere are grouped, and the difference between the fitted sphere radius and the theoretical sphere radius measured by the coordinate measuring machine is calculated to construct an error equation based on the sphere radius constraint.

9. The error self-calibration method for a parallel coordinate measuring machine based on feature components according to claim 1, characterized in that, The formula expression for the error calibration model based on multiple feature constraints is as follows: The error model for the i-th group of spherical sampling points is as follows: n is the number of groups of standard spheres for sampling. This indicates the probe radius error.

Images