This paper shows that the equilibria of a wide class of multibody systems with quasi-rigid, frictional, or frictionless supports correspond to local minima of their potential energy; hence they are stable against small perturbations of external forces. This is a generalization of a theorem by Howard and Kumar on the stability of a single rigid body held by a gripper. It is also demonstrated that ambiguous equilibria (those, which coexist with the possibility of accelerating motion) may be stable. These results help finding safe grasps on nonrigid objects and assessing the stability of quasi-static robots moving over complex terrains.

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