On the existence and synthesis of multifinger positive grips

Abstract

We study the criteria under which an object can be gripped by a multifingered dexterous hand, assuming no static friction between the object and the fingers; such grips are called positive grips. We study three cases in detail: (i) the body is at equilibrium, (ii) the body is under some constant external force/torque, and (iii) the body is under a varying external force/torque. In each case we obtain tight bounds on the number of fingers needed to obtain grip.We also present efficient algorithms to synthesize such positive grips for bounded polyhedral/polygonal objects; the number of fingers employed in the grips synthesized by our algorithms match the above bounds. The algorithms run in time linear in the number of faces/sides. The paper may be of independent interest for its presentation of algorithms arising in the study of positive linear spaces.

Minimal Fixturing of Frictionless Assemblies: Complexity and Algorithms

“…As a practical matter, determining if an assembly with fixture set F has robust stability is no harder than seeing if the assembly is merely directionally stable. Borrowing from Mishra et al [16]'s work on form-closure, we prove the following: …”

“…While the problem of synthesizing stable grasps for a single object has received considerable attention [9,10,13,18,16,12], stabilization of multiple bodies has only recently been a topic of interest [19,14]. In the single-object case, the emphasis has been on synthesizing a robust, stable grasp.…”

“…For example, Kirkpatrick et al [8] descibes the measure of stability of a grasp based on a geometric interpretation of Steinitz' theorem [16,5]. Trinkle [18] similarly proposes a stability measure that can be computed in terms of a linear program, and then extends The seemingly odd fixturing on object B is because object A slides down and leftward, attempting to force object B to rotate counterclockwise.…”

FixtureNet: interactive computer-aided design via the World Wide Web

“…FORM CLOSURE Reuleaux (1963) first described form closure which captures the intuitive requirement of a fixture: a part is held in form closure if it can resist arbitrary fo rces and torques. Lakshminarayana (1978) showed that seven frictionless contacts are necessary to hold a three-dimensional part in form closure; Mishra, Schwartz and Sharir (1987) showed that seven frictionless contacts are also sufficient. Goldman and Tucker (1956), in a purely mathematical paper on linear algebra.…”

Grasp analysis and synthesis of 2D articulated objects with n links

“…It must however, be remarked that when the object has rotational symmetry, frictionless contacts do not allow its immobilization. A detailed discussion about the number of contact points necessary for each case can be found in [3] [4].…”