Object Spatial Impedance Achieved by a Multifinger Grasp With Hard-Point Contact

This article identifies the space of spatial impedance behaviors that can be achieved by a grasp of a multifinger hand in which each fingertip makes hard-point contact with the held object. The dimension of the space of realizable impedances for a given number of fingers is determined analytically. A set of necessary and sufficient conditions on impedance matrices that can be realized by a given grasp is developed and the physical significance of these conditions is identified. The space of impedances that can be achieved by a hard point grasp is a hyperplane in the space of all possible impedance behaviors. A process to achieve an arbitrary full-rank impedance in the hyperplane with a grasp having the minimum number of fingers is developed. With this process, any spatial impedance behavior in the hyperplane can be attained with a three-finger grasp by properly selecting: first, the locations where fingertips contact the held object, and second, the translational impedance provided by a finger at each of these locations.