Finding infinitesimal motions of objects in assemblies using Grassmann-Cayley algebra

Abstract

We present a method for deriving the set of allowed infinitesimal motions of a polyhedron in contact with a polyhedral assembly without breaking the established basic contacts. The result is obtained, under the frictionless assumption, by describing each basic contact by means of the Grassmann-Cayley algebra and using cycle conditions over closed kinematic chains between the polyhedron and the assembly. Although, in practice, subparts of assemblies need to be moved completely and not only infinitesimally, the obtained results constitute a very useful information for an assembly sequence planner [Thomas et al. 1992], [Staffetti et al. 1998]. We also apply the proposed technique to solve infinitesimal mobility analysis problems of general multiloop spatial mechanisms.