Abstract: The properties of the wrench-closure workspace of 6 degree-of-freedom completely restrained and redundant restrained wire-driven parallel manipulators are investigated. The necessary and sufficient conditions to test whether a pose of the end-effector driven by an arbitrary number of wires belongs to the wrench-closure workspace of the manipulators are proposed and proved, and the geometric characters of structure matrices satisfying the definition of the wrench-closure are illustrated. A criteria theorem to determine the wrench-closure workspace of the manipulators is concluded. The theorem indicates that the rank of structure matrices of the manipulators should be full, and a column vector existing in structure matrices should be inside the six-dimensional convex polyhedral cone generated by six linearly independent column vectors of structure matrices at their opposite direction, and the sums of the correlative coefficients should be positive. According to the theorem and properties, an analytic expression of the boundary of the wrench-closure workspace is developed for 6 degree-of-freedom completely restrained and redundant restrained wire-driven parallel manipulators. An efficient algorithm that determines the boundary of the wrench-closure workspace is introduced. The numerical examples demonstrate the effectiveness of the proposed algorithm.

Key words: Configuration parameters, Wire-driven parallel manipulator, Wrench-closure workspace