Virtual truss model for characterization of internal forces for multiple finger grasps

Internal force plays important roles in grasping and manipulation of objects by multiple fingers. It is well known that any internal force for three finger grasps with frictional point contacts can usually be decomposed into three pushing or pulling force components along the three lines joining the contact points. This paper studies the question of how far this intuitive decomposition can go for general multiple finger grasps. We propose a virtual truss model for the grasped object for characterizing the internal force and show that this characterization is valid for general multiple finger grasps under a non-degeneracy condition. We then discuss some degenerate cases and give a method of extending the virtual truss model to cope with these special cases. Based on this characterization, we give an explicit formulation of the categorization by Ponce et. al. (1993) of four finger grasps into concurrent, pencil, and regulus grasps. A method is also given for obtaining a non-redundant expression of all possible internal forces from this characterization