Static Stability Analysis of a Planar Object Grasped by Multifingers with Three Joints

This paper discusses static stability of a planar object grasped by multifingers with three joints. Each individual joint (prismatic joint or revolute joint) is modeled as a linear spring stiffness. The object mass and the link masses are also included. We consider not only pure rolling contact but also frictionless sliding contact. The grasp stability is investigated using the potential energy method. This paper makes the following contributions: (i) Grasp wrench vectors and grasp stiffness matrices are analytically derived not only for the rolling contact but also for the sliding contact; (ii) It is shown in detail that the vectors and the matrices are given by functions of grasp parameters such as the contact conditions (rolling contact and sliding contact), the contact position, the contact force, the local curvature, the link shape, the object mass, the link masses, and so on; (iii) By using positive definiteness of the difference matrix of the grasp stiffness matrices, it is analytically proved that the rolling contact grasp is more stable than the sliding contact grasp. The displacement direction affected by the contact condition deviation is derived; (iv) By using positive definiteness of the differential matrix with respect to the local curvatures, it is analytically proved that the grasp stability increases when the local curvatures decrease. The displacement direction affected by the local curvature deviation is also derived; (v) Effects of the object mass and the joint positions are discussed using numerical examples. The numerical results are reinforced by analytical explanations. The effect of the link masses is also investigated