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.

Persistent screw systems

CARRICATO, MARCO;
2014

Abstract

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.
MECHANISM AND MACHINE THEORY
Marco Carricato; Dimiter Zlatanov
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11585/216059
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