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We discuss the stability of assemblies consisting of arbitrary configurations of rigid bodies considering Coulomb friction under uniform gravity. We give a method to calculate the set of all stable orientations of an assembly considering the frictional properties. The presented algorithm is a new method for automatically determining all stable orientations of assemblies considering friction. The potential stability criterion describes a necessary but not a sufficient condition for the stability of assemblies. To compute the potential stability of an assembly we consider the forces which arise at contact points of objects touching each other. Constraints which must be satisfied for a set of valid contact forces are expressed by linear inequalities; we use linear programming to determine such valid contact forces. Beside this we describe a method based on the concepts of the enumeration of vertices of polyhedra to compute the set of stable orientations considering Coulomb friction even in the case of degeneracy in the linear program, Furthermore, we discuss the space and time complexity of the underlying algorithm.
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Mosemann et al. (1997) studied this question.
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