Accuracy Analysis of Redundantly Actuated and Overconstrained Parallel Mechanisms With Actuation Errors

Abstract

A general accuracy analysis method of redundantly actuated and overconstrained parallel mechanisms is proposed. Coupled effects of actuation errors and internal elastic forces arose from the elastic deformation are both considered. The accuracy analysis approach is based on the Lie-group theory and screw theory, and it includes three steps. First, stiffness matrices of serial legs are obtained. Second, the movement of each leg is modeled based on group theory and the elastic forces arose from the deformation are represented using the stiffness matrices, following which the multiclosed-loop structure constraint and self-balanced force constraint are modeled. Finally, the error pose is estimated. The proposed method is illustrated by the accuracy study of a redundantly actuated and overconstrained Stewart platform. The error modeling is easy as the use of stiffness matrix can model the passive joint motions and deformation together. Moreover, the proposed method is computationally cheap as all computations are linear.