Difficulty of Kinematic Synthesis of Usable Constrained Planar 6R Robots

Abstract

In this paper we consider the difficulty of finding tasks for kinematic synthesis that result in usable constrained 6R planar serial chain. Kinematic synthesis consists of solving the constraint equations for articulated systems to determine the dimensions of the device the reaches a set of specified task positions. Our initial results show that the probability that an inventor finds a task that yields a usable constrained nR chain is approximately P = (1/36)n-1. For a constrained 6R chain this is one out of 60 million randomly selected tasks. We consider this to be a difficult kinematic synthesis problem.