A More General Mobility Criterion for Parallel Platforms

This contribution presents a more general mobility criterion applicable to parallel platforms, 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 introduced in this contribution provides the correct number of degrees of freedom for a wider class of parallel manipulators. Furthermore, the analysis provides insight into why the criteria based on the Kutzbach-Grübler criterion often fails. Moreover, the recently developed criterion computes the passive degrees of freedom in parallel platforms and the mobility of some classes of kinematically defficient parallel platforms. Finally, it is important to note that this criterion is based on an analysis of the subalgebras of the Lie algebra, $se$(3), also known as screw algebra, of the Euclidean group, $SE$(3). Moreover, it should be emphasized that, unlike other attempts to develop a criterion, the criterion developed in this contribution does not require any consideration of reciprocal screws. As is common in many areas of kinematics, the criterion presented here can be also obtained by an analysis of the subgroups of the Euclidean group.