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.>

The model developed 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 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.>

Grasping by a two-dimensional hand comprised of a palm and two hinged fingers is studied. The mathematics of frictionless grasping is presented and used in the development of a planner/simulator, The simulator computes the motion of the object using an active constraint set method and assuming exact knowledge of the physical properties of the polygonal object, hand, and support.

This paper examines the grasps attainable by mechanical hands with two opposing articulated fingers. Such grasps are called planar, since all forces lie in plane defined by the contact points and the center of mass of the object. Assuming the contact interaction can be modeled by point contact with friction we obtain the equilibrium equations parametrized by the magnitude of one of the applied normal forces. Thus a curve of possible grasps in friction angle space is obtained from which an optimum may be chosen. Three examples are discussed in detail.

The grasps attainable by mechanical hands with two opposing articulated fingers are examined. Such grasps are called planar, since all forces lie in plane defined by the contact points and the center of mass of the object. Assuming that the contact interaction can be modeled by point contact with Coulomb friction, the equilibrium equations for the grasped object are obtained. Satisfaction of force and moment equilibrium leads to the development of a compatability condition that relates object shape, contact locations and surface roughness as characterized by the coefficient of static friction μ. The set of all possible equilibrium grasps is determined for some examples and the results are presented as curves in a friction angle space. This representation permits choosing a grasp that is optimum in accordance with an independently developed criterion such as minimum dependence on friction forces.