Force-closure analysis of 6-DOF cable manipulators with seven or more cables

A cable manipulator controls its end-effector by a number of cables. If the cables can balance any external and inertia wrenches at a certain pose of the end-effector, the cable manipulator is said to have a force-closure at this pose. Since a cable can work only in tension, the force-closure at a specific pose may not exist. Thus, how to check the existence of force-closure at a given pose is an important issue for design and control of cable manipulators. This paper describes a systematic method of verifying the existence of force-closure at a specific pose of a general 6-DOF cable manipulator with seven or more cables. By examining the Jacobian matrix of the manipulator, the method can determine whether a force-closure exists at the pose corresponding to the Jacobian matrix. The necessity and sufficiency of the proposed method are mathematically proven. Moreover, a convex-analysis-based simplification of the method for manipulators with more than seven cables is also discussed.