Star Parallel Manipulators Have More Than Two Assembly Modes

This paper presents a graphic solution method for the direct kinematic of Star translational parallel manipulators of general geometry. The method allows one to find all the position of the end-effector from a given set of actuated joint positions, which is equivalent to find the intersection points of three meridian-circular screw surfaces. Algebraically, this problem reduces to solve six nonlinear equations in six unknowns, from which it may exist more than two solutions.