Dimensional synthesis for a Rec4 parallel mechanism with maximum transmission workspace

Abstract

A 4-RUPaR parallel mechanism (named as Rec4) with Schöenflies motion has been taken as the research object, and its dimensional synthesis problem has been solved by intelligence algorithms. Using screw theory as a mathematical tool, this paper establishes two indices (i.e., the input transmission index and the output transmission index) to evaluate motion and force transmission performance of mechanism, and presents the definition and numerical calculation method of effective transmission positional workspace (ETPW). A constrained optimization model is constructed to formulate the design problem of dimensional parameters on the maximizing volume of ETPW, and differential evolution (DE) algorithm is employed to solve this problem. A real case of dimensional optimization design is given, and the results show that the proposed model and algorithm are feasible and effective. Furthermore, a comparative test on global optimization capability to solve the dimensional design case is carried out with genetic algorithm (GA), particle swarm optimization (PSO), and DE algorithm, and the numerical experiments demonstrate that DE outperforms GA and PSO in terms of performance indices.