Static Grasp Stability Analysis of Multiple Spatial Objects

This paper analyzes grasp stability of multiple objects in three dimensions. Every finger is replaced with a translational linear spring model. The stability is formulated by a potential energy stored in the spring. The significant features are provided as follows: The contact surface geometry (metric tensor, curvature, and torsion) is included. Not only rolling contact but also sliding contact is investigated. In the case of rolling contact, partial derivatives of contact position parameters are derived in detail. In the case of sliding contact, novel independent parameters are introduced and their partial derivatives are derived. Finally, grasp force and moment vectors and grasp stiffness matrices are analytically derived. The results are clearer than those of the previous methods. Moreover, the problem on flat surfaces in the previous methods is overcome. Through numerical examples, the effectiveness of our proposed method is demonstrated.