Determining contact force distribution for enveloping grasps: subspace structure and dynamical balance

This paper addresses one of standard problems in enveloping grasp analysis, the so-called contact force distribution. First, a subspace structure is analyzed using projection matrices into four subspaces of contact force space. Motivated by an example demonstrating that a careless definition of contact force subspaces leads to completely invalid result, we propose a proper set of projection matrices using a special weighted pseudo-inverse. Next, an example of statical ambiguity is provided in obtaining contact force distribution, which implies that contact forces can not be determined in light of statical viewpoint. To resolve such ambiguity, we propose the notion of dynamical balance. By presenting a tool for identification of dynamically balanced motions and forces, we can have a complete characterization of the force distribution for a general enveloping grasp system