Many-objective Optimization Design of a 2PRU-PRUR Parallel Mechanism Without Parasitic Motion

A novel 2PRU-PRUR parallel mechanism with one translational and two rotational (1T2R) degrees of freedom and without parasitic motion, and its mobility and motion characteristic were analyzed by means of the screw theory. The output axis of the moving platform designed as the deviation type can enhance the orientation capability of the mechanism. The orientation of the end-effector output axis was depicted by using the spherical attitude angles (the azimuth and tilt angles), and the symbolic solutions for the inverse displacement analysis were proposed. The screw theory was used as a mathematical tool to establish the definitions and computing methods for the local and global transmission performances indices of the mechanism. Based on the performance evaluation and workspace analysis, a constrained many-objective optimization model was constructed to formulate the design problem of dimensional parameters, and multi-objective evolutionary algorithms were employed to solve this problem. To enhance the optimization performance of the algorithm for solving the problem, a vector-angle-based many-objective differential evolution (VaDE) algorithm was proposed, which can balance comprehensively the convergence and distribution of the individuals. At the same time, the VaDE was utilized to solve the many-objective optimization problem, and multiple Pareto optimal solutions were obtained. The research results can provide reference for the dimensional synthesis and practical application of the proposed mechanism.