Force-closure analysis of general 6-DOF cable manipulators

This paper proposed a systematic method of verifying the force-closure condition for general 6-DOF cable manipulators with more than seven cables. Without explicitly solving the inverse dynamics problem, the method can determine, by examining the Jacobian matrix of the manipulator, whether a feasible force solution exists. The equivalence (i.e., necessity and sufficiency) of the proposed method to an existing force-closure theorem developed for the robot grasping problem is mathematically proven and hence, this work rigorously shows, for the first time, that the theory for grasping problem is also applicable to cable manipulators. Moreover, a convex-analysis based simplification of the method is discussed.