A Group Theoretical Derivation of a More General Mobility Criterion for Parallel Manipulators

Abstract

This contribution presents a group theoretical derivation of the mobility criterion applicable to parallel manipulators, which has been previously presented by the authors [1]. Unlike previously employed mobility criteria based on the well-known Kutzbach-Grübler criterion that often fails to provide the correct number of degrees of freedom of parallel manipulators, the mobility criterion, whose group theoretical derivation is presented here, provides the correct number of degrees of freedom for a wider class of parallel manipulators. In this reference the authors proved the mobility criterion by resorting to the Lie algebra, se(3), also known as screw algebra, of the Euclidean group; SE(3). In this contribution, the authors prove the same criterion but, in this case, by an analysis of the subgroups and subsets of the Euclidean group, SE(3).