Force/Motion Transmissibility Analysis of Six Degree of Freedom Parallel Mechanisms

Abstract

Drawing mainly on the concepts of dual space and dual basis in linear algebra and on existing screw theory, this paper presents a novel and systematic approach for the force/motion transmissibility analysis of 6DOF parallel mechanisms. By taking the reciprocal product of a wrench on a twist as a linear functional, the property exhibited by the dual basis allows the formulation of the force/motion transmissibility between the joint space and operation space in an accurate and concise manner. The consistency between the force/motion transmissibility and the minimum singular value of the Jacobian for singularity identification is rigorously proved. This leads to the development of a set of homogeneously dimensionless local and global transmission indices for measuring the closeness to singular configurations as well as for kinematic performance evaluation over a given workspace. A Stewart platform is employed an exemplar to illustrate the effectiveness of the approach.