On the Solution Set for Positive Wire Tension With Uncertainty in Wire-Actuated Parallel Manipulators

Abstract

The solution for positive wire tension vector in the presence of uncertainties in design parameters and error in data is investigated for parallel manipulators. The minimum 2-norm non-negative solution and enclosures for the vector of wire tensions are formulated utilizing the perturbed and the interval forms of Jacobian matrix and platform wrench. Methodologies for calculating the minimum 2-norm non-negative solution set of wire tension vector, for interval Jacobian matrix and interval external wrench, are presented. Example parallel manipulators are simulated to investigate the implementation and effectiveness of these methodologies while relating their results.