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Abstract

A new approach to the analysis of statically indeterminate restraint of a rigid body with any arrangement of point contact is presented in this paper. The paper associates the elasticity at restraint contacts with geometric compatibility of the contact points and constructs elastic compatibility equations, which are complementary to the restraint equations. The equations so obtained are then used to augment the restraint equations and lead to an agumented Jacobian matrix. The new approach enables grasps to be analysed and synthesized in a constraint of combined elasticity and geometric compatibility, in addition to the force equilibrium condition. This gives a mathematical basis for the analysis of force distribution of the statically indeterminate restraint. Detailed reasoning and derivations are given followed by both planar and spatial examples.

Keywords

force distribution robotic grasps statically indeterminate restraint screw theory force equilibrium condition elasticity compatibility augmentation

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References

Salisbury

J. K.

Craig

J. J.

Articulated hands: force control and kinematic tissues. Int. J. Robotics Res., 1982, 1(1), 4–17.

Cutkosky

M. R.

Wright

P. K.

Friction, stability and the design of robotic fingers. Int. J. Robotics Res., 1986, 5(4), 20–37.

Reuleaux

Kinematics of machinery, 1965 (Reprinted at Dover, New York); German original: Theoretische Kinematik, 1875.

Lakshminarayana

Mechanics of form closure. ASME paper 78-DET-32, New York, 1978.

Salisbury

J. K.

Roth

Kinematic and force analysis of articulated mechanical hands. Trans. ASME J. Mechanisms Transmissions and Automation in Design, 1982, 105, 33–41.

Kerr

D. R.

Sanger

D. J.

The analysis of kinematic restraint. Proceedings of Sixth World Congress on The theory of machines and mechanisms, IFToMM, New Delhi, December 1983, pp. 299–303.

Nguyen

V. D.

Constructing stable grasps in 3D. Proceedings of 1987 IEEE Conference on Robotics and automations, Vol. 3, 1987, pp. 234–245.

Yoshikawa

Nagai

Manipulating and grasping forces in manipulation by multifingered robot hands. IEEE Trans. on Robotics and Automation, February 1991, 7(1), 67–77.

Cutkosky

M. R.

Robotic grasping and fine manipulation, 1985 (Kluwer Academic, Boston, Massachusetts).

10.

Kerr

D. R.

Sanger

D. J.

Restraint analysis of a rigid body using frictional elastic contacts. Trans. ASME J. Mechanisms Transmissions and Automation in Design, 1987, 105, 450–454.

11.

Kerr

D. R.

Griffis

Sanger

D. J.

Duffy

Redundant grasps, redundant manipulators, and their dual relationships. J. Robotics Systems, 1992, 459.

12.

Trinkle

J. C.

On the stability and instantaneous velocity of grasped frictionless objects. IEEE J. Robotics and Automation, October 1992, 8(5), 560–572.

13.

Dai

J. S.

Kerr

D. R.

Analysis and synthesis of planar grasping in an image space. Proceedings of Twenty-second ASME Mechanisms Conference Scottsdale Arizona September 1992, Vol. DE-45, pp. 283–292.

14.

Dai

J. S.

Kerr

D. R.

Synthesis of frictionless grasps in image space using affine augmentation. Presented at the Ninth World Congress on The theory of machines and mechanisms, Milano, Italy, August–September 1995.

15.

Brand

Vector and tensor analysis, 1947 (John Wiley, New York).

16.

Lipkin

Duffy

The elliptic polarity of screws. Trans. ASME J. Mechanisms Transmissions and Automation in Design, September 1982, 107, 377–387.

17.

Strang

Linear algebra and its applications, 2nd edition, 1980 (Academic Press, New York).

18.

Dai

J. S.

Screw image space and its application to robotic grasping. PhD Thesis, University of Salford, May 1993.

19.

Lang

Linear algebra, 3rd edition, 1989 (Springer-Verlag, New York).

Analysis of Force Distribution in Grasps Using Augmentation

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