Persistent screw systems

When a mechanism moves, the twist system of the end-effector generally varies. In significant special cases, however, the end-effector twist space is a subalgebra of the Lie algebra se(3) of the special Euclidean group, and it remains constant. Accordingly, if the output twists of a serial linkage form a subalgebra of se(3) at one configuration, the space spanned by the end-effector twists remains unchanged under arbitrary joint motions away from singularities. This work investigates a generalization of this property, namely mechanisms whose end-effector twist system remains invariant up to a rigid displacement under arbitrary finite motions away from special configurations. In this case, the output screw system preserves its internal pattern and ‘shape’, but it moves in space like a rigid body. We say that a mechanism of this kind has a persistent screw system (PSS) of the end-effector. This paper introduces fundamental concepts and facts concerning PSSs. The phenomenon is illustrated with examples and its importance for mobility analysis and mechanism synthesis is discussed.