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A model that utilizes a contact-stress analysis of an arbitrarily shaped object in a multifingered grasp is developed. 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.>
Sinha et al. (Wed,) studied this question.