Designing Positive Tension for Wire-Actuated Parallel Manipulators

Abstract

For wire-actuated parallel manipulators, the minimum 2-norm solution for the vector of wire tensions, calculated utilizing the Moore-Penrose generalized inverse of the Jacobian matrix, could result in negative tension for wires. In this paper, a methodology for generating the minimum 2-norm non-negative wire tension vector, when the null space basis of the Jacobian matrix of these manipulators is spanned by one or more vectors, is presented. Two planar parallel manipulators, a four-wire 2 degrees of freedom and a six-wire 3 degrees of freedom, are simulated to illustrate the proposed methodologies.