Kinematic Calibration Of Redundantly Actuated Parallel Kinematic Machines

Redundantly actuated parallel kinematic machines(RA-PKMs)have received more and more attention from researchers in recent years,because it has a good performance of singularity,stiffness and load capacity.Since the redundant limb make the hinge clearance more controllable,RA-PKMs can theoretically achieve higher motion accuracy.However,the current kinematic calibration methods used to improve the motion accuracy of non-redundant parallel mechanisms cannot be applied to RA-PKMs directly.In this paper,the kinematic calibration method of parallel mechanism with redundant actuated limbs is studied.The main contents cover the following aspects(1)Based on the vector chain method and the external calibration method,the kinematics calibration for the non-redundant parallel mechanism is introduced first.And the feasibility and difficulty of applying this method to RA-PKMs are analyzed.(2)The 3-DOF RA-PKM 2UPR-2RPU is selected as the research example,the motion state of the mechanism is analyzed when the driving values of each limb cannot meet the geometric constraints.Several non-redundantl sub-mechanisms are constructed by treating different limbs as passive limb without changing the degree of freedom.The forward kinematics model of RA-PKM is the intersection of the adjustable spaces of all sub-mechanisms.(3)The error sources are determined,and the error models of the non-redundant sub-mechanisms are obtained based on geometric method and numerical method.After preprocessing the the error mapping Jacobian matrix of each sub-mechanism,and the error model of the 2UPR-2RPU is obtained by the weighted average method.(4)The external calibration method of 2UPR-2RPU mechanism based on laser tracker is simulated.The deviation between the nominal position and the actual position of the end point of the mechanism is taken as the optimization target to identify the kinematic error.The parameters of the control model are compensated finally.(5)The calibration experiment was carried out to verify the error modeling and parameter identification method,and the absolute positioning accuracy of the mechanism was significantly improved after kinematic calibrationThis paper enriches the theoretical research on kinematic calibration of mechanism,realizes the application of calibration method in new fields,and promotes the application and development of redundantly actuated parallel kinematic machine.