Optimal Design of a Kinematically Redundant Planar Parallel Mechanism Based on Error Sensitivity and Workspace

In this paper, the dimensional optimization of a (2PRR)-R + 2RRR (P and R represent the prismatic and revolute joint, respectively, and the underline indicates that the joint is the actuator) kinematically redundant parallel mechanism is performed by taking the integrated error sensitivity index and workspace as the objectives. Based on the matrix method, a generalized method for error modeling of the planar three-degree-of-freedom (3-DOF) parallel mechanism is proposed. The process of the generalized error modeling method is explained, and the error model of the planar (2(sic)RR)-R + 29sic)RR kinematically redundant parallel mechanism is established. Based on the proposed error model, the error sensitivity indices of different dimension types are calculated. In order to reduce the error sensitivity and expand the workspace, the elitist non-dominated sorting genetic algorithm (NSGA-II) is used for multi-objective optimization of the mechanism. The comparative analysis between the optimized and the non-optimized mechanism is carried out from three aspects: error sensitivity, distribution of low-error sensitivity area, and area of the workspace. The results show that the optimization algorithm not only expands the workspace of the mechanism but also effectively reduces the error sensitivity in the workspace.