Absbacf-This paper presents a method to determine stable pushing motions for a planar stack of polygonal parts The approach consists of solving a series of subproblems where each part in the stack is pushing the parts ahead of it. The solutions to these subproblems are sets of stable motions, and their intersection is the set of stable motions for the entire stack. The motion of multiple parts depends on the exact locations of the centers of m a s and the relative masses of the parts. If either or both of these is unknown, it is still possible to calculate a conservative set of motions guaranteed to be stable by using a center of mass uncertainty region.

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This paper presents a method to determine whether an assembly of planar parts will stay assembled as it is pushed over a support surface. For a given pushing motion, an assembly is classified into one of three categories: (P = possible) any force necessary to assure stability of the assembly can be generated by the pushing contacts; (I = impossible) stability of the assembly is impossible; and (U = undecided) pushing forces may or may not be able to stabilize the assembly. This classification is made based on the solution of linear constraint satisfaction problems. If the pushing contacts are frictionless, motions labeled P are guaranteed to preserve the assembly. The results are based on bounds on the possible support friction acting on individual parts in the face of indeterminacy in the distribution of support forces. Experimental results supporting the analysis are given.