Stability analysis of 3D grasps by a multifingered hand

We discuss stability of 3D grasps by using a three-dimensional spring model (3D spring model). Many works have described stability of a frictionless grasp. These works used a one-dimensional spring model (1D spring model) for representation of frictionless contact as a matter of course. However, a 1D spring model involves the following problems: (i) displacement of a finger is restricted to one dimension along the initial normal at contact point; and (ii) it is not clearly considered that a finger generates contact force to the object along the normal direction only. To overcome the problems and provide accurate grasp stability, we introduce a 3D spring model. Then a finger´s displacement is relaxed and a finger´s contact force is precisely formulated. We analyze grasp stability from the viewpoint of the potential energy method. From numerical examples, we show that there exists an optimum contact force for stable grasp. Moreover, we also analyze a frictional grasp by using contact kinematics of pure rolling. By comparing frictional grasp stability with a frictionless one, we prove that friction enhances stability of a grasp.