Dual Quaternion Synthesis of Constrained Robots

This paper presents a synthesis methodology for robots that have less than six degrees of freedom, termed constrained robots. The goal is to determine the physical parameters of the chain that fit its workspace to a given set of spatial positions. Our formulation uses the dual quaternion form of the kinematics equations of the constrained robot. Here we develop the theory and formulate the synthesis equations for the spatial RPR robot. Their solution ensures that the three dimensional workspace of this robot contains a given set of four spatial positions.