Controllable workspace of cable driven redundant parallel manipulator with more than one degree of redundancy

Controllable workspace analysis is one of the most important issues in the cable-driven parallel manipulator design. This paper introduces a set of extended fundamental wrenches that opens new horizons for physical interpretation of controllable workspace of cable driven redundant parallel manipulators with more than one degree of redundancy. Based on extended fundamental wrench properties, attractive theorems are presented in order to analyze the controllable workspace of cable-driven parallel manipulator with more than one degree of redundancy. Moreover, an analytical method is developed to determine the controllable workspace of redundant cable-driven parallel manipulators based on extended fundamental wrenches. The proposed method is generally applicable to any cable redundant manipulators as long as its Jacobian matrix is of full rank. In the proposed method, an analytic approach is employed based on linear algebra in order to derive the boundary of controllable workspace. Finally, the simulation result for a spatial manipulator is given.