This article discusses active force closure (AFC) for the manipulation of multiple objects. AFC for multiple objects is defined in such a way that the finger can generate an arbitrary acceleration onto a certain point of multiple objects. We define two kinds of AFC: in the first, an arbitrary acceleration can be generated onto each of the objects; in the second, an arbitrary acceleration can be generated onto the center of mass of multiple objects without changing the relative position of the

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... jects. We show that the grasped object cannot always be manipulated arbitrarily even if the first kind of AFC is satisfied. We also show that the grasped objects are manipulated like a single rigid body if the second kind of AFC is satisfied. To explain these features of AFCs, numerical examples for the grasp of three objects are shown.