A CONTACT STRESS MODEL FOR MULTIFINGERED GRASPS OF ROUGH OBJECTS

Most available methods to predict the forces necessary to grasp an arbitrary object treat the object and the fingers as rigid bodies and the finger/object interface as a point contact with Coulomb friction. For statistically indeterminate grasps, therefore, while it is possible to find grasps that are stable, there is no unique determination of the actual forces at the contact points and equilibrium grasps are determined as many-parameter families of solutions. Rigid contact-Coulomb friction models sometimes also lead to ambigious solutions. The model developed here utilizes a contact-stress analysis of an arbitrarily shaped object in a multifingered grasp. The fingers and the object are all treated as elastic bodies, and the region of contact is modeled as a deformable surface patch. The relationship between the friction and normal forces is now nonlocal and nonlinear in nature and departs from the Coulomb approximation. The nature of the constraints arising out of conditions for compatibility and static equilibrium motivated the formulation of the model as a nonlinear constrained minimization problem. The model is able to predict the magnitude of the inwardly directed normal forces and both the magnitude and direction of the tangential (friction) forces at each finger/object interface for grasped objects in static equilibrium. Examples in two and three dimensions are presented along with an application of the model to the grasp transfer maneuver.