Principle of orthogonalization for completely restrained parallel wire driven robot

Parallel-wire driven robot utilizes light flexible wires instead of heavy rigid links, so it has some advantages such as high speed, heavy load and so on. Since wires can not push, but can pull an object, at least n + 1 wires are necessary in order to move an object in n-dimensional space for completely restrained parallel-wire driven system. A control scheme based on the wire length coordinates is very useful for the parallel-wire driven robots, since calculation of the inverse kinematics is generally easy as well as usual parallel-link robot. However the previous works could not prove the motion convergence of the system using more than n + 1 wires. In this paper, I investigate a principle of orthogonalization for completely restrained parallel-wire driven system. This principle clarifies the relation between wire tension and driving force-moment on the object. Using the principle of orthogonalization makes it possible to prove the motion convergence of the wire length feedback control utilizing more than n + 1 wires.