This paper discusses the active force closure (AFC) for 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, i.e., the first one where an arbitrary acceleration can be generated onto each one of the objects, and the second one where an arbitrary acceleration can be generated onto the center of balance of multiple objects without changing the relative position among objects. 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 just like a single rigid body if the second kind of AFC is satisfied. To explain these features of AFCs, numerical examples are shown for the grasp of three objects.
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