On Mobility Analysis of Linkages Using Group Theory

Abstract

This paper presents a generalization of Kutzbach-Grübler criterion for mobility analysis of kinematic chains based on group theory. This new mobility criterion applies to exceptional linkages and reduces to a group theoretic representation of Kutzbach-Grübler criterion for trivial linkages. Furthermore, it is shown that using sets and groups of Euclidean displacements, one can distinguish between trivial, exceptional, and paradoxical linkages. Using these concepts, formal definitions of trivial, exceptional, and paradoxical linkages are presented and it is shown that there are two classes of paradoxical linkages. This work builds upon and extends the work of Hervé and Fanghella and Galletti in application of group theory to analysis of kinematic chains.