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.

This paper formulates the static equilibrium equations for grasping a general solid object using a three fingered mechanical hand. The contact between the fingers and the object is modeled as point contact with friction. The primary result of this work is a procedure which allows the computation of the friction forces required to satisfy equilibrium for a known set of contact normal forces. By comparing these friction forces to the maximum sustainable between the contacting surfaces, we can determine if the object will slip from the grasp and further we have the twist which characterizes the slipping mode. Two examples are solved in detail to illustrate the procedure.

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.

A procedure is presented for computing the friction forces required to satisfy static equilibrium, given a set of normal contact forces exerted by a three-fingered mechanical hand. The contact between the fingers and the object is modeled as "point contact with friction. "This means the fingertip is free to rotate about the point of contact, but sliding along its surface is resisted by a friction force. Comparing these friction forces to the maximum friction force, which can be sustained between the contacting surfaces, it must be determined whether the object slips from the grasp and further the instantaneous motion of the impending movement. Two examples are solved in detail to illustrate the procedure.