An Explicit Method for Determining the Force-Moment Capabilities of Redundantly Actuated Planar Parallel Manipulators

A new explicit methodology for the determination of the force-moment capabilities of nonredundantly and redundantly actuated planar parallel manipulators (PPMs) is presented. This methodology is based on properly adjusting the actuator outputs to their maximum capabilities. As a result, the wrench to be applied or sustained is maximized. For a nonredundantly actuated PPM, one actuator can be maximized, while for a redundantly actuated PPM, one actuator, beyond the one of the nonredundant case, may be maximized for every degree of redundancy added to the mechanism. This methodology is compared to a previous work that required an optimization algorithm. The new method yields more accurate and reliable results and is considerably more efficient. Four studies of force-moment capabilities are considered: maximum force with prescribed moment, maximum applicable force, maximum moment with a prescribed force, and maximum applicable moment. The methodology is used to generate the force-moment capabilities of an existing PPM throughout its workspace.