A Mobility Determination Method for Parallel Platforms Based on the Lie Algebra of SE(3) and Its Subspaces

Abstract

This contribution presents a screw theory-based method for determining the mobility of fully parallel platforms. The method is based on the application of three stages. The first stage involves the application of the intersection of subalgebras of Lie algebra, se(3), of the special Euclidean group, SE(3), associated with the legs of the platform. The second stage analyzes the possibility of the legs of the platform generating a sum or direct sum of two subalgebras of the Lie algebra, se(3). The last stage, if necessary, considers the possibility of the kinematic pairs of the legs satisfying certain velocity conditions; these conditions reduce the platform’s mobility analysis to one that can be solved using one of the two previous stages. Several examples are illustrated.