This paper investigates the soft-finger contact by presenting the contact with a set of line springs based on screw theory, reveals the rotational effects, and identifies the stiffness properties of the contact. An elastic model of a soft-finger contact is proposed and a generalized contact stiffness matrix is developed by applying the congruence transformation and by introducing stiffness mapping of the line springs in translational directions and rotational axes. The effective stiffnesses along these directions and axes are hence obtained and the rotational stiffnesses are revealed. This helps create a screw representation of a six-dimensional soft-finger contact and produce an approach of analyzing and synthesizing a robotic grasp without resorting to the point contact representation. The correlation between the rotational stiffness, the number of equivalent point contacts and the number of equivalent contours is given and the stiffness synthesis is presented with both modular and direct approaches. The grasp thus achieved from the stiffness analysis contributes to both translational and rotational restraint and the stiffness matrix so developed is proven to be symmetric and positive definite. Case studies are presented with a two-soft-finger grasp and a three-soft-finger grasp. The grasps are analyzed with a general stiffness matrix which is used to control the fine displacements of a grasped object by changing the preload on the contact.
Issue Section:
Technical Papers
1.
Dimentberg, F. M., 1965, “The Screw Calculus and its Applications in Mechanics,” Technical Report FTD-HT-23-1632-67, Foreign Technology Division, Wright-Patterson Air Force Base.
2.
Loncaric, J., 1985, “Geometrical Analysis of Compliant Mechanisms in Robotics,” Ph.D. dissertation, Harvard University.
3.
Kerr
, D. R.
, and Sanger
, D. J.
, 1986
, “Restraint Analysis of a Rigid Body Using Frictional Elastic Contacts
,” ASME J. Mech. Des.
, 105
, pp. 450
–454
.4.
Ghafoor
, A.
, and Kerr
, D. R.
, 1992
, “In-Grasp Robotic Fine Motion With Frictionless Elastic Point Contacts
,” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
, 206
, pp. 41
–47
.5.
Dai, J. S., and Kerr, D. R., 1992, “Analysis and Synthesis of Grasping in an Image Space,” Proc. 22nd ASME Mechanisms Conference, DE-Vol. 45, pp. 283–292.
6.
Holzmann
, W.
, and McCarthy
, J. M.
, 1985
, “Computing the Friction Forces Associated with a Three-Fingered Grasp
,” IEEE J. Rob. Autom.
, RA-1
(4
), pp. 206
–210
.7.
Griffis
, M.
, and Duffy
, J.
, 1993
, “Global Stiffness Modelling of a Class of Simple Compliant Coupling
,” Mech. Mach. Theory
, 28
(2
), pp. 207
–224
.8.
Ciblank, N., and Lipkin, H., 1994, “Asymmetric Cartesian Stiffness for the Modelling of Compliant Robotic Systems,” Proc. ASME 23rd Biennial Mech. Conf., Des. Eng., Vol. 72, New York, NY.
9.
Ciblank, N., and Lipkin, H., 1998, “Synthesis of Stiffness by Springs,” 1998 ASME Design Technical Conference, Sept. 11–14, Atlanta, GA.
10.
Zefran
, M.
, Kumar
, V.
, and Croke
, C.
, 1999
, “Metrics and Connections for Rigid Body Kinematics
,” Int. J. Robot. Res.
, 18
(2
), pp. 243
–258
.11.
Zefran
, M.
, and Kumar
, V.
, 2002
, “A Geometrical Approach to the Study of the Cartesian Stiffness Matrix
,” ASME J. Mech. Des.
, 124
, pp. 30
–38
.12.
Sugar
, T. G.
, and Kumar
, V.
, 2002
, “Design and Control of a Compliant Parallel Manipulator
,” ASME J. Mech. Des.
, 124
, pp. 676
–683
.13.
Kao
, I.
, and Cutkosky
, M. R.
, 1992
, “Dextrous Manipulation With Compliance and Sliding
,” Int. J. Robot. Res.
, 11
(1
), pp. 20
–40
.14.
Kao
, I.
, and Ngo
, C.
, 1999
, “Properties of the Grasp Stiffness Matrix and Conservative Control Strategies
,” Int. J. Robot. Res.
, 18
(2
), pp. 159
–167
.15.
Huang, S., and Schimmels, J. M., 1997, “The Realizable Space of Spatial Stiffness Achieved With a Parallel Connection of Springs,” IEEE Trans. Rob. Autom.
16.
Huang
, S.
, and Schimmels
, J. M.
, 1998
, “The Bounds and Realization of Spatial Stiffnesses Achieved With Simple Springs Connected in Parallel
,” IEEE Trans. Rob. Autom.
, 14
(3
), pp. 466
–475
.17.
Whitney
, D. E.
, Gilbert
, O. L.
, and Jastrzebski
, M.
, 1994
, “Representation of Geometric Variations Using Matrix Transforms for Statistical Tolerance Analysis in Assemblies
,” J. Res. Eng. Design-Theory Appl. Concurrent Eng.
, 6
(4
), pp. 191
–210
.18.
Cutkosky, M. R., and Wright, P. K., 1984, “
Active Control of a Compliant Wrist in Manufacturing Tasks,” Proceedings of the 14th International Symposium on Industrial Robots and the 7th International Conference on Industrial Robot Technology, IFS, Kempston, UK, pp. 517–528.
19.
Huang
, C.
, and Roth
, B.
, 1993
, “Dimensional Synthesis of Closed-Loop Linkages to Match Force and Position Specifications
,” ASME J. Mech. Des.
, 115
(2
), pp. 194
–198
.20.
Fasse, E. D., 1996, “A Spatial Compliance Controller for Spatial Manipulators,” Proc. ASME IMEC, Dyn. Syst. Contr. Div.
21.
Ghafoor
, A.
, Dai
, J. S.
, and Duffy
, J.
, 2000
, “Fine Motion Control Based on Constraint Criteria Under Pre-Loading Configurations
,” J. Rob. Syst.
, 17
(4
), pp. 171
–185
.22.
Cutkosky, M. R., 1985, Robotic Grasping and Fine Manipulation, Kluwer Academic, Boston, Massachusetts.
23.
Mussa-Ivaldi
, F. A.
, Hogan
, N.
, and Bizzi
, E.
, 1985
, “Neural Mechanical, and Geometric Factors Subserving Arm Posture in Humans
,” J. Neurosci.
, 10
(5
), pp. 2732
–2743
.24.
Kearney
, R. E.
, and Hunter
, I. W.
, 1990
, “System Identification of Human Joint Dynamics, Critical Review
,” Biomed. Eng.
, 18
(1
), pp. 55
–87
.25.
Kao, I., 1994, “Stiffness Control and Calibration of Robotic and Human Hands and Fingers,” Proceedings of the IEEE Conf. on Robot. and Automat., Washington, DC, pp. 399–406.
26.
Lu
, Z.
, and Goldenberg
, A. A.
, 1995
, “Robust Impedance Control and Force Regulation: Theory and Experiments
,” Int. J. Robot. Res.
, 14
(3
), pp. 225
–254
.27.
Kao
, I.
, Cutkosky
, M. R.
, and Johansson
, R. S.
, 1997
, “Robotic Stiffness Control and Calibration as Applied to Human Grasping Tasks
,” IEEE Trans. Rob. Autom.
, 13
(4
), pp. 557
–566
.28.
Dai
, J. S.
, and Kerr
, D. R.
, 2000
, “A Six-Component Contact Force Measurement Device Based on the Stewart Platform
,” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
, 214
(C5
), pp. 687
–697
.29.
Hertz, H., 1882, On the Contact of Rigid of Elastic Solids and on Hardness, New York, Macmillan.
30.
Flugge, W., and Lubkin, J. L., 1962, Contact Problems, Handbook of Engineering Mechanics, McGraw-Hill, New York, sec 42-1.
31.
Xydas
, N.
, and Kao
, I.
, 1999
, “Modelling of Contact Mechanics and Friction Limit Surface for Soft Fingers in Robotics, With Experimental Results
,” Int. J. Robot. Res.
, 18
(8
), pp. 947
–950
.32.
Zeienkiewicz, O. C., and Taylor, R. L., 1994, The Finite Element Method, McGraw Hill.
33.
Dai
, J. S.
, and Zhao
, T.
, 2002
, “Stiffness Characteristics and Kinematics Analysis of Two-Link Elastic Underactuated Manipulators
,” J. Rob. Syst.
, 19
(4
), pp. 169
–176
.34.
Dai, J. S., 1993, “Screw Image Space and Its Application to Robotic Grasping,” PhD Thesis, University of Salford, UK.
35.
Kerr
, D. R.
, Griffis
, M.
, Sanger
, D. J.
, and Duffy
, J.
, 1992
, “Redundant Grasps, Redundant Manipulators and Their Dual Relationships
,” J. Rob. Syst.
, 9
(7
), pp. 973
–1000
.36.
Dai
, J. S.
, and Rees Jones
, J.
, 2001
, “Interrelationship Between Screw Systems and Corresponding Reciprocal Systems and Applications
,” Mech. Mach. Theory
, 36
(5
), pp. 633
–651
.37.
Dai
, J. S.
, and Rees Jones
, J.
, 2002
, “Null Space Construction Using Cofactors From a Screw Algebra Context
,” Proc. R. Soc., Math. Physic. Eng. Sci.
, 458
(2024
), pp. 1845
–1866
.38.
Dai
, J. S.
, Holland
, N.
, and Kerr
, D. R.
, 1995
, “Finite Twist Mapping and Its Application to Planar Serial Manipulators With Revolute Joints
,” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
, 209
(C4
), pp. 263
–272
.39.
Lipkin
, H.
, and Duffy
, J.
, 1985
, “The Elliptic Polarity of Screws
,” ASME J. Mech. Trans. Autom. Des.
, 107
, pp. 377
–387
.40.
Dai
, J. S.
, and Kerr
, D. R.
, 1996
, “Analysis of Force Distribution in Grasps Using Augmentation
,” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
, 210
(C1
), pp. 15
–22
.41.
Hanafusa, H., and Asada, H., 1977, “A Robot Hand With Elastic Fingers and Its Application to Assembly Process,” Proc. IFAC Symposium on Information Control Problems in Manufacturing Technology, Tokyo, pp. 127–138.
42.
Nguyen
, V.
, 1989
, “Constructing Stable Grasp
,” Int. J. Robot. Res.
, 8
(1
), pp. 26
–37
.Copyright © 2004
by ASME
You do not currently have access to this content.
