Abstract: Because wires can only sustain tension, actuation redundancy is necessary for wire-driven parallel manipulators, which makes wire tension can’t be obtained in a trivial form. But real-time calculation of wire tension is necessary for motion control of the manipulators. To obtain the optimal tension solution, a new method proposed by Verhoeven is used, in which the optimal tension distribution problem is transformed into a non-linear optimization one on a convex polyhedra, I.e. the optimal solution is expressed by the linear combination of the lowest solution and the highest one. Owing to the discontinuity of the optimal solution in some cases, it is necessary to replace the infinity norm of the optimal solution by its p-norm ap-proximately. Finally, the algorithm of the method is stated in detail and a case study to solve the lowest and highest solutions of a 2-DOF wire-driven parallel manipulators with 4 wires is given.

Key words: Convex polyhedra, Non-linear optimization, p-norm, Tension distribution, Wire-driven parallel manipulators