Error Sensitivity Analysis of a 1T2R Kinematically Redundant Parallel Mechanism with Closed-Loop Chain

Abstract In this paper, a generalized method for error modeling of the spatial 1T2R three degrees of freedom (DOFs) kinematically redundant parallel mechanism with a closed-loop chain is proposed, which is based on the matrix differential method. Firstly, the detailed process of generalized error modeling and error analysis are described. Based on the proposed method, the error model of the spatial 3PRR(RR)S-P (“P,” prismatic joint; “R,” revolute joint; “S,” spherical joint; and the underline indicates that the joint is the actuator) kinematically redundant parallel mechanism is established as an example, and the correctness of the error model is verified by combining forward with inverse kinematics. Then, the patterns affecting the output error of the moving platform are discussed for the case where the mechanism contains only static error or dynamic error, respectively. In addition, the error sensitivity indices are defined to evaluate the error sensitivity of the moving platform to different redundant parameters L4 under a certain pose. Finally, in order to identify the key error terms, the sensitivity of the output error of the mechanism to a single error term is analyzed. The results show that the error sensitivity of the spatial kinematically redundant parallel mechanism can be effectively reduced by adjusting the kinematically redundant parameters, so that the mechanism can maintain a low error sensitivity in a certain pose.