44 results about "Contour error" patented technology

The present invention relates to a contour accuracy compensation method and system for a precision hot-press forming mold. The method comprises: delineating grids on a three-dimensional model of a hot-press forming mold to obtain mold surface grid data; performing curvature analysis to obtain a high-curvature region and a low-curvature region; performing high-density sampling on the high-curvature region, and performing low-density sampling on the low-curvature region, so as to obtain a sampling point set; using a coordinate measuring machine to perform three-dimensional coordinate measurement on the sampling point set to obtain surface contour data; performing comparative analysis on the surface contour data and a theoretical model to obtain a contour error distribution; on the basis of the contour error distribution, using an inverse distance weighted interpolation algorithm to perform interpolation operation on an entire mold surface to obtain a mold surface compensation amount distribution; and on the basis of the mold surface compensation amount distribution, correcting the three-dimensional model of the hot-press forming mold to generate a compensated mold processing model. The implementation of the present invention realizes intelligent and automated contour accuracy compensation.

The invention provides a digital twinning five-axis machine tool contour error prediction method and system and electronic equipment, and belongs to the technical field of numerical control machine tool precision control and digital twinning. According to the method, servo axis data are collected in real time at a numerical control system end, electromechanical parameters are identified on line, comprehensive disturbance is estimated, and an autoregressive exogenous (ARX) model is updated accordingly; an interpolation instruction is generated in a digital twin body end mirror image numerical control system process, an updated model is utilized to predict a shaft position with deviation, a tool path is obtained through kinematics positive solution, and finally contour errors are calculated through geometric alignment. According to the digital twinning five-axis machine tool contour error prediction method and system and the electronic equipment, dynamic and high-precision prediction of the five-axis machine tool machining track contour error is achieved through the online identification and digital twinning technology, the limitation of a traditional static compensation method is overcome, and the precision of the digital twinning five-axis machine tool contour error prediction is improved. And a key basis is provided for prospective process optimization and precision control, and the machining precision and efficiency are effectively improved.

The application discloses a multi-axis linkage contour error control method based on time delay synchronization, position data of initial reference trajectories and actual trajectories is acquired in the axis coordinate system, the synchronization delay time is calculated according to the position data of the reference trajectories and the actual trajectories, the coupling error is calculated based on the synchronization delay time, the initial trajectory is compensated according to the coupling error, the ideal reference trajectory is obtained to make the delay time synchronization, the new reference trajectory is run, the operation of steps S1-S3 is repeated until the accuracy requirement is met. The application does not need to perform the contour error estimation, avoids the accuracy decline caused by the estimation error, does not need to perform the coordinate transformation of the axis coordinate system and the workpiece coordinate system, and directly performs the compensation in the machine tool coordinate system, so that the application has wide applicability.

The invention provides a numerical control turning adaptive compensation control method based on a contour error prediction model, and belongs to the technical field of numerical control turning compensation control. In order to solve the technical problem that contour errors occur in the numerical control turning machining process, actual contour coordinate values of at least three positions of a workpiece to be detected are collected in an automatic or manual detection mode; on the basis of the collected coordinate values, one of a least square method, an NX curve fitting method and trigonometric function calculation is adopted, arc fitting processing is conducted on the collected data, an arc contour with the minimum error is solved, and the actual contour value of the workpiece is obtained; according to the calculated actual contour value of the workpiece, running a preset program, automatically adjusting a cutter compensation value, and controlling compensation operation; the method is applied to adaptive compensation control of numerical control turning.

The invention relates to the technical field of numerical control machining error compensation, and discloses a ball-end milling cutter contour error compensation method and device, a medium and equipment, and the method comprises the steps: obtaining contour error values between actual cutter contours and theoretical cutter contours of a ball-end milling cutter in a plurality of spatial orientations; an original cutter location file generated based on the theoretical cutter contour is obtained, and the original cutter location file comprises cutter location points and cutting contact points; based on the contour error value, a tool contour error compensation model with the normal direction of the cutting contact point as the compensation direction is established; and correcting the cutter location point coordinates of the cutter location points by using the cutter contour error compensation model to generate a compensated cutter location data file. According to the method, point-by-point compensation is carried out in the normal direction of the cutting contact point based on the multi-azimuth actual measurement contour error, and high-precision and space self-adaptive 3D cutter radius compensation is achieved.

The invention discloses a closed-loop control method of a lathe numerical control system fused with cam wear compensation, and relates to the field of industrial control systems.The method comprises the steps that under the no-load running state of a lathe, multi-source time sequence data are collected; calculating a no-load contour error based on the multi-source time sequence data, inputting the no-load contour error and the temperature signal into the geometric feature extraction model, and outputting a comprehensive contour distortion coefficient; the comprehensive contour distortion coefficient and the current machining process parameters are jointly input into a control parameter compensation model, and the contour height correction amount used for correcting the electronic cam is generated; inputting the contour height correction into a lathe digital twinning performance boundary model for feasibility verification and safety amplitude limiting, and generating a safety compensation instruction; and executing a safety compensation instruction, and optimizing the geometric feature extraction model and the control parameter compensation model according to a processing result. The problems that in the prior art, due to abrasion of an electronic cam pair, instruction execution is distorted, precision is degraded, and accurate recognition of abrasion errors is disturbed are solved.

The invention belongs to the field of five-axis numerical control milling, and discloses a five-axis side milling test piece contour error prediction method considering a tool pose. Comprising the following four steps: establishing a spatial position transformation relation calculation model, calculating the length of a focusing tool and acquiring a track point set, fitting an intelligent algorithm optimized track, calculating a cutting contact track and solving a contour error, and substituting a tool path code of a five-axis side milling machining inspection test piece into a spatial error model considering the tool length. The method comprises the following steps: calculating cutter center point pose data corresponding to the contour of a cutting test piece, carrying out trajectory fitting on the pose data by introducing a spline curve fitting method, improving the precision of the fitting trajectory in combination with a particle swarm optimization algorithm, and finally shifting the cutter along the radius through a homogeneous coordinate transformation method to obtain an actual cutting contact trajectory of the test piece. And high-precision rapid prediction of the contour error of the five-axis machining test piece is realized.

The application discloses a numerical control machine tool control method and system for complex curved surface machining, and relates to the field of numerical control machine tool control. The method comprises the following steps: extracting an original G code instruction stream, reconstructing ideal position instruction sequences and ideal speed instruction sequences of each motion shaft according to a machine tool kinematic chain model; estimating instruction phase lag amounts of each motion shaft through an inter-shaft phase lag predictor; combining geometric curvatures and tangent directions of a machining path, calculating estimated profile error vectors through a profile error coupling mapping model; combining profile accuracy requirement constraints of a surface to be machined and a shaft contribution weight matrix, and constructing a compensation optimization model; and fusing inter-shaft phase compensation instructions and the original G code instruction stream in a numerical control machining program according to a solution of the compensation optimization model, generating a synchronized instruction stream, and driving each shaft of the machine tool to move. The method solves the problems of poor synchronization of multi-shaft cooperative movement, low estimation accuracy, and low adaptability of instructions to mechanical structure characteristics of the machine tool.

This invention provides a device and method for improving the contour accuracy of a direct-drive XY motion platform servo system, relating to the field of CNC motion control technology. The device includes a rectifier filter circuit, an IPM inverter circuit, a detection circuit, a DSP processor, an IPM isolation protection drive circuit, a host computer, and a direct-drive XY motion platform. The method first calculates the contour error using a reference-adjusted contour error estimation method, which serves as the input to an adaptive nonlinear sliding mode contour controller. Then, the adaptive nonlinear sliding mode contour controller is used to control the contour error, and a nonlinear sliding surface is designed to improve the system's dynamic response speed and contour tracking accuracy. To further reduce the error between the reference model and the actual object, an uncertainty compensator is designed to compensate for uncertainties such as parameter changes, external disturbances, and friction, thereby improving the system's robustness.

The invention discloses a rotor contour error separation method based on seven-error coupling, and relates to a rotor contour error separation method. The problems that in the prior art, error separation is insufficient, and multiple errors cannot be separated at a time are solved. According to the method, firstly, a seven-error model is established, and then error separation is performed based on deep reinforcement learning. According to the method, high-precision and high-efficiency separation of the rotor contour error can be realized. The invention belongs to the technical field of ultra-precision geometric measurement, and is particularly suitable for geometric precision detection and error traceability of a high-precision rotating machinery rotor.

This invention discloses a method and system for dynamic task allocation in edge-cloud collaborative computing for the entire CNC machining process. The system includes a process analysis module for real-time identification of process boundaries and technological features; a machining task perception module for automatically generating a list of various computing tasks required for the current process based on process features (including tool wear monitoring, spindle vibration monitoring, thermal error compensation, machining parameter optimization, workpiece quality prediction, contour error compensation, etc.); a process-driven dynamic decision engine for independently deciding whether to allocate each computing task to the edge or the cloud; and a CNC instruction collaboration module for converting the decision results into compensation instructions and writing them into the CNC system. This invention combines process flow features with various computing task types throughout the CNC machining process, achieving refined dynamic allocation at the process and task levels. It also ensures task continuity through the migration of intermediate computing results during process switching, making it suitable for various intelligent application scenarios throughout the entire CNC machining process.

The invention provides a multi-axis numerical control machine tool precision error distribution method and device and belongs to the technical field of medium precision manufacturing and machine tool design. The method comprises the steps that a machine tool comprehensive error transmission model is established; the machine tool comprehensive error transfer model maps the geometric error of each motion axis of the machine tool into a space contour error of a tool nose point relative to a workpiece based on a multi-body system theory and a homogeneous coordinate transformation principle; performing global sensitivity analysis on the comprehensive error transfer model by adopting a Sobol global sensitivity analysis method, and calculating a total global sensitivity coefficient of each geometric error term to the contour error; by taking the total global sensitivity coefficient as a weight, constructing an optimization objective function, setting a constraint condition, and establishing an error allocation optimization model; solving the error allocation optimization model by adopting a heuristic optimization algorithm to obtain a tolerance allocation value of each geometric error term; according to the method, collaborative optimization of precision and cost is achieved, and scientificity and economical efficiency of machine tool design are remarkably improved.

This invention discloses a method and product for contour error compensation in five-axis machining of impeller disk-type parts, relating to the field of precision CNC machining technology. The invention first acquires point cloud data of a preliminary machining sample based on theoretical toolpaths. After preprocessing including denoising and coordinate registration, the actual machining surface is reconstructed. The actual machining surface is then accurately calculated by registering and comparing the data with the theoretical surface. Next, based on the contour deviation value, the toolpath is compensated for using the kinematic characteristics of the five-axis CNC machine tool, and the tool attitude is adjusted. Combined with balancing, adaptive correction of the toolpath is achieved, thus enabling effective control of contour errors in subsequent machining.

This application relates to the field of CNC machine tool servo control technology, and particularly to a method, apparatus, device, medium, and program product for generating machine tool servo parameters. The method includes: acquiring parameter data of the machine tool servo system to be optimized; calculating the actual distortion error value between the input trajectory data and the actual output trajectory data of the machine tool servo system to be optimized based on the parameter data; determining the speed loop proportional gain value and / or speed loop integral gain value of the machine tool servo system to be optimized based on the actual distortion error value, and controlling the machine tool servo system to be optimized to operate according to the speed loop proportional gain value and / or speed loop integral gain value. This solves the problems in related technologies, such as long trial cycles and high costs leading to low equipment utilization; reliance on experience leading to local optima; lack of trajectory spectrum adaptation analysis, requiring readjustment of new trajectories and difficulty in data reuse; and the lack of a quantitative relationship between parameters and contour errors, making it difficult to guide optimization and cross-device adaptation.

The application discloses a super-precision turning profile error prediction method and system of a series attention mechanism, and the method comprises the following steps: acquiring a multi-physical field feature; organizing the feature into a one-dimensional time sequence and inputting the one-dimensional time sequence into a first deep learning prediction model to output a three-direction dynamic cutting force prediction value in a future preset time period; sampling the feature into a multi-channel two-dimensional spatial feature map according to a mapping relationship with a machining surface position, adding the predicted three-direction dynamic cutting force prediction value as an additional feature channel to the two-dimensional spatial feature map, inputting the fused two-dimensional feature map into a second deep learning prediction model, and outputting a two-dimensional machining surface profile error distribution map. The application has the advantages that a long-distance time sequence dependence relationship of a cutting force signal can be effectively captured, a global context correlation is established on a two-dimensional plane, super-precision turning profile error high-precision prediction is realized, and the model generalization capability and physical interpretability are improved.

The invention provides an actuating mechanism speed planning method based on a contour error and duration control, and the method comprises the steps: representing the moving speed of an actuating mechanism, the position of the actuating mechanism, and the curvature of a corresponding reference position point on a set moving track through a contour error mechanism model; and the corresponding relation of the contour error between the position of the execution mechanism and the corresponding reference position point is obtained. And based on the multi-objective optimization function, optimizing a movement sequence when the execution mechanism moves to each reference position point by using an optimization algorithm to obtain an optimal movement sequence. The optimal moving sequence is used for enabling the weighted sum of the total machining time and the total contour error to be minimum when the executing mechanism moves with the set moving track as the reference. The movement control of the execution mechanism is completed according to the optimal movement sequence, and when the curvature of the track is large, the movement speed can be reduced to reduce errors; and when the track is smooth, the moving speed is increased, so that the machining time is shortened. Therefore, the machining precision and the machining efficiency are both considered.

The cable contour laser positioning method and system based on Newton iteration and integral sliding mode are characterized in that cable contour data are collected in real time by a laser displacement sensor, high-precision contour error calculation is realized through dynamic contour error estimation based on Newton update algorithm, contour error is integrated into an integral sliding mode controller through a feedback modification strategy, high-precision tracking and positioning of the cable outer contour are realized, and in combination with an adaptive disturbance estimation technology, system uncertainty disturbance is compensated, and the robustness of the system is improved. The profile control technology is integrated into the cable processing system, the profile positioning precision and adaptive capacity in the stripping and cutting processing of high-voltage cables are improved, the quality of cable joint manufacturing is ensured, intelligent, accurate and stable tracking of the cable outer contour is realized, the automation level and reliability of the cable stripping operation are improved, the operation safety of the power system is maintained, and the method has important engineering application value in the field of high-voltage cable joint manufacturing.

The invention relates to the technical field of numerical control machine tool error analysis and precision control, in particular to an ultra-precision machine tool contour error estimation method and a contour error compensation system. The method comprises the following steps: collecting internal data of a machine tool, preprocessing and constructing a data set; the tracking error of each axis of the machine tool is predicted based on a CNN-BisLSTM-MHA deep learning model; calculating the actual position of each axis based on the predicted tracking error; and by adopting a Hermite spline-Taylor series composite algorithm, calculating a contour error based on the calculated actual position of each axis and the reference position corresponding to each axis. According to the invention, contour errors with higher precision can be obtained.

This invention discloses an online contour error compensation method and system for a machining-inspection synchronized machine tool, belonging to the field of CNC related technology. It constructs a generalized tool space kinematic model including the spindle, tool, and scanning probe, establishing the transformation relationship between the probe coordinate system and the tool coordinate system; plans the cooperative trajectory of the tool machining path and the probe scanning path, avoiding the probe in non-inspection areas and constraining its posture and feed rate in the inspection area; during machining, it collects workpiece contour point cloud data in real time, maps it to tool tip coordinates using the transformation relationship, reconstructs the actual contour surface, and calculates its contour error compared to the desired surface; it decouples the error into servo axis components, generates axis compensation commands, and corrects the servo drive signals to achieve real-time closed-loop compensation. This invention solves the problem of difficulty in synchronizing online inspection and error compensation in complex surface machining, realizing real-time contour accuracy control under integrated machining-inspection.

The invention relates to the technical field of numerical control engraving equipment servo control, and discloses an engraving machine servo parameter self-tuning method, device and equipment and a medium, and the method comprises the steps: determining a contour error which is matched with a standard test track and is used for representing the machining precision; determining a vibration index which is matched with the standard test track and is used for representing the machining stability; and based on a fitness function constructed by the contour error and the vibration index, determining a target servo parameter combination adapted to the current processing working condition, so that a servo controller of the carving machine carries out carving processing according to the target servo parameter combination, the full-process autonomous decision-making from state perception, performance evaluation to parameter self-optimization is realized, so that the technical problem of how to carry out self-adjustment according to specific working conditions in the actual machining process of the engraving machine is solved.

The embodiment of the present disclosure provides a feed speed smooth planning method, which comprises the following steps: acquiring a curve machining track, sampling the curve machining track to obtain a corresponding discrete point track; calculating a maximum normal acceleration and a profile error set by a numerical control system to obtain a transition speed extreme value of each discrete point as an initial transition speed of each discrete point, performing bidirectional scanning on each discrete point, and correcting the initial transition speed of each discrete point according to the kinematics tangent constraint of the numerical control system to obtain a target transition speed of each discrete point; for any point on the curve machining track, the target transition speed constraint of adjacent discrete points is used for interpolation smoothing to obtain a planning speed. The embodiment of the present disclosure plans the speed based on the included angle geometric characteristics of the discrete points to solve the complexity problem of curvature calculation, and performs speed smoothing through the interpolation method to solve the feed speed fluctuation problem, so that the machining surface quality and the machining efficiency can be improved, and the adaptability to the numerical control system is high.

The application provides a speed preview method, device and medium for a motion control system, and relates to the field of high-end manufacturing technology; the method constructs a G2 continuous curve between two adjacent initial cutter track segments corresponding to an interception distance meeting a preset smoothing condition through a quintic Bezier curve, and truncates the two adjacent initial cutter track segments; the initial cutter track segment and the G2 continuous curve are taken as a target cutter track segment, a preset sliding window with a window length greater than a step length is used to obtain a plurality of target cutter track segment combinations with overlapping areas; an initial planning speed of a speed planning point in each target cutter track segment combination is obtained through a bidirectional scanning method; and a target planning speed of the speed planning point is determined based on the initial planning speed of the speed planning point; global speed continuous planning under limited cache resources is achieved, frequent start and stop in the machining process is effectively avoided, and instantaneous acceleration exceeding a standard or a contour error caused by a change in path length is avoided.

A three-axis machine tool track contour error calculation method considering geometric and motion characteristics comprises the following steps: firstly, establishing a geometric error equivalent mapping model of a three-axis machine tool, and uniformly describing a positioning error, a straightness error, an angle error and an inter-axis perpendicularity error of each motion axis; the geometric error is mapped to a tool nose space position error through homogeneous coordinate transformation; secondly, a three-ring servo linkage control equivalent model containing a position loop, a speed loop and a current loop is established, a dynamic response relation between interpolation instruction displacement and actual axis displacement is obtained through transfer function derivation, and a three-axis machine tool servo linkage control equivalent model is established; integrating the geometric error mapping result with the three-axis linkage control dynamic position deviation to realize the prediction of the actual track of the tool nose of the tool; and finally, based on the interpolation instruction position point and the predicted actual position point, a contour error is calculated by adopting an interpolation line segment perpendicular foot method. The method has the advantages of unified modeling, high calculation efficiency and high engineering applicability.

The application discloses a profile error calculation method for a numerical control machining device, and relates to the technical field of numerical control machining.The method takes a time point corresponding to an expected position point as an initial value of a Newton iteration method, determines a potential time interval in which a time point corresponding to a minimum value of a profile error evaluation function is located by using a gradient descent method, and then dynamically switches the Newton iteration method and a dichotomy method to accurately solve a target time point in the potential time interval, so that the method quickly and reliably converges to a local optimal point closest to the expected position point.The method has the speed of the Newton iteration method and the stability of the dichotomy method, improves the reliability and robustness of a profile error calculation result, and provides an efficient and stable calculation basis for subsequent profile precision control and real-time compensation.

A method for smoothing two linear trajectories based on a parameter database and an optimization algorithm belongs to the technical field of numerical control machining, and comprises the following steps: firstly, establishing an optimal parameter database offline: based on multiple groups of two linear segment trajectories with different included angles and length ratios, determining a group of optimal trajectory smoothing parameters for each group of included angles and length ratios through the optimization algorithm; enabling the maximum contour error of the generated B spline curve to be minimum, and establishing a parameter database of correlation included angles and optimal trajectory smoothing parameters; secondly, online track parameter matching: calculating an included angle and a length ratio of two straight line segment tracks to be smoothed, querying a corresponding optimal track smoothing parameter from the parameter database in the first step according to a calculation result, and automatically generating a smooth cubic B-spline curve as a transition track by utilizing the queried optimal track smoothing parameter; according to the method, full-automatic and optimal determination of smoothing parameters is realized, and the efficiency and quality of trajectory planning are remarkably improved while the machining precision is strictly guaranteed.

The invention discloses a method for solving a contour error in grinding cam simulation, which relates to the field of numerical control grinding machine simulation, and comprises the following steps of: establishing a contour model of a processed raw material and a grinding cutter, and simulating a grinding process by moving the center of the cutter around the raw material along a motion path; the method comprises the following steps: carrying out logic NOT operation on a cutter contour and a raw material contour in a motion process to obtain a simulated cam contour, carrying out circumferential step pitch homogenization approximation on a target cam and the simulated cam to obtain an approximate cam contour with equal step pitches, carrying out radial difference on points on each step pitch to obtain a radial contour error, according to the method, the normal of the point on each step pitch is solved, the difference between the normal and the intersection point of the two contours is obtained, a normal contour error is obtained, the normal contour error is superposed with the normal size of the driven piece to obtain a stroke error of the driven piece, and the cam contour error with a good effect is obtained at a low sampling rate through the contour error solving method.

The invention discloses a gear measurement center motion control method and system, and relates to the technical field of gear measurement center motion control, and the method comprises the steps: building a kinematic model of a gear measurement center, and carrying out the coordinate transformation between a machine tool coordinate system and a workpiece coordinate system; establishing an electromechanical coupling control model; constructing a contour error calculation model, and decoupling a contour error and a trajectory tracking error; designing a single-axis position loop P control and speed feedforward combined composite controller; and designing a cross-coupling coordination controller based on the contour error model, generating real-time compensation amounts for the X axis and the theta axis by using the contour error and the trajectory tracking error through PID control, and feeding back the real-time compensation amounts to a single-axis controller to realize closed-loop compensation of multi-axis coordination motion. The system comprises a motion control unit, a coordination control unit, an error calculation unit and a servo driving unit. According to the method, the problem of contour errors caused by multi-axis dynamic response differences and nonlinear coupling is effectively solved, and the contour tracking precision is improved.

This invention belongs to the field of grinding and error compensation technology, specifically a method, processing method, and system for generating dual-axis contour error compensation for cam grinding machines. The process involves obtaining the theoretical lift table of the cam and the corresponding actual lift measurement data; determining the base circle radius from the base circle segment; obtaining the theoretical and actual extreme diameters; obtaining the theoretical contour points in polar coordinates based on the theoretical extreme diameter; obtaining the actual contour points after trial cutting based on the phase deviation of the C-axis and the actual extreme diameter; obtaining the error vector based on the actual and theoretical contour points after trial cutting; obtaining the X-axis contour error based on the error vector and the unit normal vector of the theoretical contour; constructing an objective function with the goal of aligning the actual lift after trial cutting with the theoretical lift in angle; calculating the phase deviation; redistributing the compensation for the X-axis and C-axis according to the distribution rate; and allocating the remaining contour error to phase compensation to obtain the phase compensation for the C-axis.

The application discloses a parallel robot dynamic contour error pre-compensation method and device, wherein the method comprises the following steps: acquiring the dynamic parameters of a parallel machining robot, and determining the rigid body dynamics model of the parallel machining robot; based on the preset rigid body dynamics model, the theoretical driving force of each driving shaft of the parallel machining robot is calculated and input to the torque feedforward channel of a servo driving system to perform dynamics feedforward control; by using a pre-constructed tracking error estimation model of the driving shaft of the parallel machining robot, the dynamic contour error of tool movement is estimated, and the motion trajectory is corrected in the task space according to the dynamic contour error, so as to perform high dynamic precision control on the parallel machining robot. Thus, the problem that the dynamic precision and machining quality of the robot are difficult to guarantee due to the mismatch between the controller performance and the nonlinear dynamics characteristics and nonlinear friction force characteristics of the controlled object, i.e., the parallel machining robot, in the prior art is solved.

This invention discloses a method for predicting the pose error of a machine tool slide and the force on the slider, specifically for a double-guide-rail, four-slider linear motion system. First, a unified geometric and mechanical model of the system is established. The guide rail is abstracted as a continuous, smooth curve in space, and the interface between the guide rail and the slider is assumed to be continuous, uniform, and linearly elastic, with constant stiffness coefficients per unit length in both directions. The slide and guide rail are considered rigid bodies. Then, based on the model, the system is decoupled between the horizontal and vertical planes, using the position and attitude errors of the slide as generalized coordinates. Based on deformation compatibility conditions and the principle of minimum potential energy, a balance equation is established between the slide pose error caused by the guide rail contour error and the force on the slider. Solving this equation yields the slide pose error, which is then substituted into the slider force expression to obtain the force and torque distribution of each slider. This method enables the prediction of the multi-degree-of-freedom pose error of the slide and the force state of each slider throughout its entire stroke.