Workspace Analysis of Mechanical Manipulators Using Polynomial Discriminants

Abstract

A new method, for the investigation of manipulator workspace, based on polynomial displacement equations and their discriminants is proposed in this paper. The approach followed enables one to obtain (a ) analytical expressions describing the workspace boundary surfaces in Cartesian coordinates, (b ) the distribution of the number of ways to position the hand inside the workspace, and (c ) the conditions on kinematic parameters when the motion of the hand degenerates. Joint limitations are incorporated in the method. In the present paper and a companion paper [17], the method is rigorously applied to eight types of manipulators with various combinations of revolute and prismatic pairs having the last three revolute axes intersect orthogonally at at point. A numerical example is presented for illustration.