Geometric design of 3R manipulators for three precision poses using dual quaternions

Three precision poses, geometric synthesis problem of 3R serial manipulators is the subject of the present work. Denavit-Hartenberg parameters and unit dual quaternions are used to formulate the problem so that the design equations are polynomial with reduced degree. Upon choosing some of the design parameters arbitrarily, a system of twelve polynomials in twelve unknowns whose degrees are at most 2 is derived. Less degree results in less complexity and easy approach to solution. Five new types for selecting the free choices are introduced and their design equations are solved using polynomial homotopy continuation. In a numerical example, we will show that the multi-homogeneous bounds for the solutions paths for all the types are 576.