Analytical Methods for Solution Sets of Interval Wrench

Abstract

Methodologies for calculating the solution set of actuator inputs, in the presence of uncertainty/error in parameters/data, are investigated. The enclosure for the vector of actuator torques is formulated utilizing the interval forms of the Jacobian matrix and external wrench. Two analytical methods are utilized to identify the solution set; one method generates the rays that bound the solution set in each orthant, and the other one is based on parameterizing the interval entries of the Jacobian matrix and wrench. For the parametric method, the existence of dominant parameter groups to produce the whole solution set (or a subset of solution set) is examined. Implementation of these methods on example parallel manipulators are presented to identify the solution set for the actuator torques, and the results are verified with the discrete method.