Abstract
This paper discusses quasi-static grasp stability of frictionless enveloping grasps in two dimensions. The stability is investigated from the viewpoint of potential energy stored in the grasps. The system of the grasps is replaced with elastic property, in which joint position and link surface properties are represented by linear stiffness. The contact constraints between a grasped object and finger links are formulated. The potential energy of the grasp system is obtained from the stiffness and the joint and link surface displacements. A wrench (i.e., force and moment) vector and a stiffness matrix of the grasp system are derived from partial differentiations by the pose (i.e., translation and rotation) displacement of the object. The grasps are stable if both the wrench vector is zero and the matrix is positive definite. The stability is evaluated by the eigenvalues of the matrix. Since, in this paper, the wrench vector and the stiffness matrix are derived in an analytical way, the matrix is given as a function of grasp positions, grasp forces, local curvatures, joint and surface stiffnesses, and so on at contact points, explicitly. We investigate curvature and stiffness effects on the grasp system by partially differentiating the matrix by the curvatures and stiffnesses. The positive definiteness of the matrix differentiations is analyzed. Validity of our analysis is confirmed through numerical examples.
https://ror.org/024exxj48 
