Modeling and performance analysis of elastostatic stiffness of kinematically redundant parallel mechanisms

An analytical elastostatic stiffness modeling approach for kinematically redundant parallel mechanisms (KR-PMs) according to screw theory and the second theorem of Castigliano is proposed. The 2-UPR/PRPU and 2-PUPR/PRPU KR-PMs are used as two examples of KR-PMs to validate the precision of the proposed approach. The relative error is less than 1.55% when the theoretical model is compared to the FEA model. The PM's stiffness performance is assessed using the minimum linear displacement stiffness performance index, which is based on the theoretical model. By integrating Particle Swarm Optimization (PSO) with polynomial fitting technology, an analytical mapping model of the response surface between the optimal actuating distances and the moving platform (MP)'s given position and orientation is established. It is demonstrated that 2-UPR/PRPU and 2-PUPR/PRPU KR-PMs can significantly enhance the stiffness performance when compared to the stiffness performance of 2-UPR/RPU PM.