Dimensional synthesis problem of 3R for three precision poses using dual quaternions

In this paper, three precision poses geometric synthesis problem of 3R serial manipulators is solved using a polynomial continuation method. Denavit-Hartenberg parameters and a new formulation using dual quaternions are used to formulate the problem and obtain the design equations. Upon choosing six of the design parameters arbitrarily, a system of thirteen polynomials in thirteen unknowns is derived. Four new types for selecting the free choices are introduced and their design equations are solved using polynomial homotopy continuation method. Numerical example is included in which the multi- homogeneous bounds for the solutions paths for the first type is 1152 and for the others are 9216.