Motions, efforts, and actuations in constrained dynamic systems: A multilink closed chain example

Abstract

The primary goal of this article is to examine various aspects of the motion–effort method for obtaining equations of motion and constraint of multibody systems. Gauge invariant transformations are used to recast the more commonly utilized dynamic equations into a dimensional gauge invariant form. Constraint elimination techniques based on singular value decompositions are then used to recast the invariant form of dynamic system equations into orthogonal sets of motion and effort equations. Desired motions and constraining efforts are partitioned into those ideally obtainable and unobtainable through the use of effort actuators. The actuation required to achieve these ideally obtainable constraining efforts and changes in motion are then found. The dynamic system performance resulting from the use of these ideal actuations is then evaluated. The method is compared to the more traditional augmented matrix, coordinate partitioning, and inverse dynamic solution approaches. A redundantly actuated multilinked closed chain linkage is used throughout the article as an example. ©1999 John Wiley & Sons, Inc.