Static Stability Analysis of a Single Planar Object Grasped by a Multifingered Hand

In this study, the static stability of the grasp of a single planar object is analyzed using the potential energy method. Inprevious papers, we considered cases in which individual fingers were replaced by a multidimensional translational spring model, inwhich each finger is constructed with prismatic joints. Human hands and the most developed mechanical hands are constructed withrevolute joints. In this paper, the effects of fingertip rotation and a revolute joint spring model are investigated. A grasp stiffness matrixis analytically derived by considering not only frictional rolling contact but also frictionless sliding contact. The difference between thefrictional stiffness matrix and the frictionless one is analytically obtained. The effect of local curvature at contact points is analyticallyderived. The grasp displacement directions affected by the change in curvature and the contact condition are also obtained. The derivedstiffness matrix of the revolute joint model is compared with that of the prismatic joint model, and then the stiffness relation is clarified.The gravity effect of the object is also considered. The effectiveness of our method is demonstrated through numerical examples. Thestability is evaluated by the eigenvalues of the grasp stiffness matrix, and the grasp displacement direction is obtained by thecorresponding eigenvectors. The effect of joint angle is also discussed.