Workspace determination of general 6-d.o.f. cable manipulators

This paper addresses workspace determination of general 6-d.o.f. cable-driven parallel manipulators with more than seven cables. The workspace under study is called force-closure workspace, which is defined as the set of end-effector poses satisfying the force-closure condition. Having force-closure in a specific end-effector pose means that any external wrench applied to the end-effector can be balanced through a set of non-negative cable forces under any motion condition of the end-effector. In other words, the inverse dynamics problem of the manipulator always has a feasible solution at any pose in the force-closure workspace. The workspace can be determined by the Jacobian matrix and, thus, it is consistent with the usual definition of workspace in the robotics literature. A systematic method of determining whether or not a given end-effector pose is in the workspace is proposed. Based on this method, the shape, boundary, dimensions and volume of the workspace of a 6-d.o.f., eight-cable manipulator are discussed. (C) Koninklijke Brill NV, Leiden and The Robotics Society of Japan, 2008.