Finite Motion Validation for Parallel Manipulators: A Differential Geometry Approach

Type synthesis of low (3-5) degree of freedom (Dof) spatial parallel manipulators is well documented in literature. Recent approaches such as proposed in J.M. Herve and F. Sparacino (1991) - Z. Huang and Q.C. Li (2003) showed some systematic design capability, but did not develop an equally effective means to check for prescribed finite motion. In this paper, we studied the finite motion set of parallel manipulators from a general input-affine nonlinear system viewpoint. Differential geometry tools for controllability (reachability) analysis of nonlinear system on a differential manifold are utilized together with lie group theory. Our techniques are shown to be effective by applying to a systematic type synthesis method proposed in M. Jian, et al. (2005) and W. Yuanqing, et al. (2005)

I. Introduction

Systematic modeling and type synthesis of low DOF parallel manipulator has been addressed by several authors([1]–[4]).i)Screw theory and ii) Lie group algebraic tool are extensively utilized in kinematics modeling of parallel manipulators since they are embedded with good geometric underlying.