Wrench Accuracy for Parallel Manipulators and Interval Dependency

In this paper, the wrench accuracy for parallel manipulators is examined under variations in parameters and data. The solution sets of actuator forces/torques are investigated utilizing interval arithmetic (IA). Implementation issues of interval arithmetic to analyze the performance of manipulators are addressed, including the consideration of dependencies in parameters and the design of input vectors to generate the required wrench. Specifically, the effect of the dependency within and among the entries of the Jacobian matrix is studied, and methodologies for reducing and/or eliminating the overestimation of solution set are presented. In addition, the subset of solution set that produces platform wrenches within the required lower and upper bounds is modeled. Furthermore, the formulation of solutions that provide any platform wrench within the defined interval is examined. Intersection of these two sets, if any, results in the given interval platform wrench. Implementation of the methods to identify the solution for actuator forces/torques is presented on example parallel manipulators.