Sensitivity Analysis Of A Kinematically Redundant Planar Parallel Manipulator

The parallel manipulator has the advantages of high precision,high rigidity,strong bearing capacity,and has a wide range of application prospects.The development of parallel machine tools puts forward higher requirements for the accuracy of parallel manipulators.The kinematically redundant parallel manipulator introduces kinematically redundant units based on the traditional parallel manipulator.The kinematically redundant parallel manipulator obtains the functions of avoiding singularity,expanding the workspace,and improving the working performance.However,the introduction of kinematically redundant units increases the complexity of the manipulator,and its error sensitivity needs further study.Based on the above background,this paper uses a typical kinematically redundant planar parallel manipulator as the carrier to carry out the error sensitivity research of kinematically redundant planar parallel manipulator.This paper introduces the manipulator’s structure,analyzes the degree of freedom of the manipulator through the modified G-K formula and the screw theory,and proves that the manipulator is kinematically redundant.The inverse and forward kinematics solutions of the manipulator are calculated,the Jacobian analysis of the manipulator is carried out,and the correctness of the Jacobian matrix is verified.The workspace of the manipulator is calculated,the singularity analysis is completed,and the workspace and singular curve of the manipulator are drawn.A generalized method for error modeling of the planar 3-DOF parallel manipulator with three limbs is proposed.The error model of the manipulator is established.The correctness of the error model is verified,and the error sensitivity indexes and the distribution of the low error-sensitive workspace are analyzed.The error sensitivity of the manipulator to a single error is identified.The influence of the structure sizes on the accuracy is investigated.The error sensitivity is compared with that of the traditional planar 3-(?)RR parallel manipulator.The kinematic error analysis of the manipulator considering the joint clearance is carried out.The ideal dynamic model is established based on the Lagrangian equation of the first type using the local method.The change law of the driving torque,driving force and restraining force of each joint is studied.The simulation analysis of the dynamic performance of the manipulator with joint clearances is carried out.With the goal of maximizing the workspace and minimizing the error sensitivity,the multi-objective evolutionary algorithm is adopted to complete the optimization of the manipulator.The normalization method is used to integrate multiple error sensitivity indexes with different dimensions into a dimensionless index,which improves the optimization effect.The optimization results are analyzed from the error sensitivity indexes,the area of the workspace and the area of the low error sensitive workspace,and the output error,which proves the effectiveness of the optimization algorithm.The performance of two different trajectory planning methods is analyzed,and the best trajectory planning method is selected.Combined with the trajectory planning method,a singular avoidance strategy based on error sensitivity is proposed.Simulation analysis proves the effectiveness of the singular avoidance strategy in improving the accuracy of the mission path.A physical prototype is established to verify the feasibility of the singular avoidance strategy action.The actual positioning error of the mission path is measured by the three-coordinate measuring arm,which further proved the effectiveness of the singular avoidance strategy in reducing the positioning error.