Stiffness modeling of parallel manipulator with articulated traveling plate

Abstract

Parallel manipulator (PM) with articulated travelling plate (ATP) has drawn more and more attention from industry and academia. In order to characterize stiffness of PMs with ATP in an explicit and accurate manner, a semi-analytical stiffness modeling method is proposed. Resorting to superposition principle, compliance matrix of the whole PM can be formulated by the parallel limbs and ATP step-by-step. In the formulation of compliance of two substructures, n-DoF (n≤6) virtual springs are firstly applied to describe component deformations. Then, deformation superposition, twist/wrench mapping model, virtual work principle and Hooke’s Law are adopted. Wrenches of parallel limbs become single wrenches within each limb, combination wrenches from opposite limbs due to the effect of ATP. This stiffness modeling method is exemplified and verified by a one translational and three rotational (1T3R) PM with ATP. Results from finite element analysis software indicate that proposed stiffness modeling method is with high accuracy.