AN INTERVAL ANALYSIS METHOD FOR WRENCH WORKSPACE DETERMINATION OF PARALLEL MANIPULATOR ARCHITECTURES

Abstract

This paper deals with the wrench workspace (WW) determination of parallel manipulators. The WW is the set of end-effector poses (positions and orientations) for which the active joints are able to balance a set of external wrenches acting at the end-effector. The determination of the WW is important when selecting an appropriate manipulator design since the size and shape of the WW are dependent on the manipulator’s geometry (design) and selected actuators. Algorithms for the determination of the reachable workspace and the WW are presented. The algorithms are applicable to manipulator architectures utilizing actuators with positive and negative limits on the force/torque they can generate, as well as cable-driven parallel manipulator architectures which require nonnegative actuator limits to maintain positive cable tensions. The developed algorithms are demonstrated in case studies applied to a cable-driven parallel manipulator with 2-degrees-of-freedom and three cables and to a 3-RRR parallel manipulator. The approaches used in this paper provide guaranteed results and are based on methods utilizing interval analysis techniques for the representation of end-effector poses and design parameters.