An Analytical Method for the Identification of Redundant Constraints in Multiple-Loop Spatial Mechanisms

Abstract

An analytical method for the explicit identification of redundant constraints in multiple-loop spatial mechanisms is presented. The kinematic constraint equations for each independent loop of multiple-loop mechanisms are developed. The independence of these equations is established and used to detect the presence of redundant constraints. The nature of the redundant constraints present is indicated by the type of redundant kinematic constraint equations present. Interaction of the constraints of adjacent loops in a multiple-loop mechanism also has to be taken into account. An example which illustrates the identification of redundant constraints in a cardan joint has been included to demonstrate the utility of this approach for real-world mechanism design problems. General guidelines for the elimination of redundant constraints, following their identification, are also provided.