An elimination procedure for solving the geometric design of spatial 3R manipulators

In this paper the geometric design problem of serial-link robot manipulators with three revolute (R) joints when three precision points are specified is solved using an algebraic elimination method for the first time. Three spatial positions and orientations are defined and the dimensions of the geometric parameters of the 3R manipulator are computed so that the manipulator will be able to place its end-effector at these three prespecified locations. In this problem, six of the design parameters are set as free choices and their values are selected arbitrarily. For the specific case studied in this paper a 12 deg single variable polynomial is calculated that has eight roots that are the design solutions and the other four roots are extraneous solutions.