Analyses of the stiffness and elastic deformation of a 2(3-SPR) serial—parallel manipulator

Abstract

Stiffness is one of the important indices for evaluating the performances of serial—parallel manipulators (S—PMs), particularly when the S—PMs are used as machine tools and the robot arm/leg, and higher stiffness allows higher machining speed with higher accuracy of the end-effector. In this article, the stiffness and the elastic deformation of a 2(3-SPR) S—PM are studied systematically. First, a 2(3-SPR) S—PM, including an upper 3-SPR parallel manipulator (PM) and a lower 3-SPR PM, is constructed, and its characteristics are analysed. Second, some formulae for solving the elastic deformation and the compliance matrix of the active legs are derived from the available kinematics/statics of this S—PM. Third, based on the principle of virtual work and the compliance matrix of the active legs, the elastic deformation and the total stiffness matrix of this S—PM are solved and analysed.