Kinematic Synthesis of RPS Serial Chains

Abstract

This paper examine the geometric design of the five degree-of-freedom RPS serial chain. This constrained robot can be designed to reach an arbitrary set of ten spatial positions. It is often convenient to consider tasks with fewer positions, and here we study the cases of seven through ten position synthesis. A generalized eigenvalue elimination technique yields analytical solutions for cases seven and eight. While cases nine and ten are solved numerically using homotopy continuation. An numerical example is provided for an eight position task.