Singularity Design for RRSS Mechanisms

This paper explores the design of RRSS mechanisms with specified singular positions. The ultimate goal is to find an SS chain to couple a previously synthesized RR chain and to force the mechanism to become singular at intended positions. To this end, a system of equations including the closure equation and its derivative with respect to the joint values as well as a constraint imposing the prior design poses are utilized. This system acts as constraints for the optimization of an objective function to minimized the lengths of the links. The solution yields an SS chain that allows the mechanism to go through the task positions and to be singular at the selected positions.