A Loop-Based Approach for Rigid Subchain Identification in General Mechanisms

The determination of rigid or overconstrained subsystems is an important task in the creative design of robotic mechanisms and in the processing of CAD-generated models. While for planar mechanisms with planar graphs a number of methods have been proposed, the case of general spatial mechanisms is still an open topic. In this paper, a novel method for identifying rigid subsystems is presented. The method uses the independent loops as building blocks of a graph, called kinematical network, which describes the overall transmission behavior. The detection of rigid subsystems can then be realized by finding the minimal cutsets in the solution flow of the kinematical network. The method is independent of the subspace in which the bodies are moving, i.e., it is possible to mix planar, spherical and spatial systems. Moreover, it is fast, as only the implicitly coupled loops need to be processed, which comprise much less elements than the number of bodies.