A Contact Stress Model for Determining Forces in an Equilibrium Grasp

Most available methods that 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 statically 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. Also, these models sometimes lead to phenomenologically incorrect results which, while satisfactory from a purely mathematical viewpoint, are counterintuitive and not likely to be realized in practice. The model developed here utilizes a contact-stress analysis of an arbitrarily shaped object in a multi-fingered 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 non-linear constrained minimization problem. The total potential energy of the system is minimized, subject to the nonlinear, equality and inequality constraints on the system, using the Schittkowski algorithm. 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 application of the model to the grasp transfer maneuver.