This paper presents a model for analyzing the effect of global and local conformability on fixture-workpiece system static stability. Global conformability is defined as the geometric similarity between a workpiece and the smallest envelope fit over all contacts. Two conformability metrics, C1 and C2, are introduced to quantify only global, and global plus local conformability, respectively. The model considers all stiffness components of the fixture-workpiece system, including workpiece bulk stiffness. The effect of both conformability metrics on fixture-workpiece static stability is analyzed by means of examples. These examples show that static stability can either increase or decrease with conformability depending on the position of the fixturing elements with respect to the line of action of the externally applied loads. The model is experimentally validated using a pin-array type flexible machining fixture.

Issue Section:
Technical Papers
Keywords:
mechanical contact, mechanical stability, machining, robot dynamics, industrial manipulators
Topics:
Stability, Static stability, Stiffness, Stress, Machining, Modeling
1.
Montana
,
D. J.
,
1988
, “
The Kinematics of Contact and Grasp
,”
Int. J. Robot. Res.
,
7
, No.
3
, pp.
17
–
30
.
2.
Cutkosky, M. R., 1985, Robotic Grasping and Fine Manipulation, Kluwer Academic Publishers.
3.
Shimoga
,
K. B.
,
1996
, “
Robot Grasp Synthesis Algorithms: A Survey
,”
Int. J. Robot. Res.
,
15
, No.
3
, pp.
230
–
266
.
4.
Gandhi
,
M. V.
, and
Thompson
,
B. S.
,
1985
, “
Phase Change Fixturing for Flexible Manufacturing Systems
,”
J. Manuf. Syst.
,
4
, No.
1
, pp.
29
–
39
.
5.
Barozzi, G., 1988, U.S. Patent #4936560.
6.
Soderberg, M., Starr, R., Cook, L., and Thomas, R., 1998, U.S. Patent #5722646.
7.
Walczyk
,
D. F.
,
Lakshmikanthan
,
J.
, and
Kirk
,
D. R.
,
1998
, “
Development of a Reconfigurable Tool for Forming Body Panels
,”
J. Manuf. Syst.
,
17
, No.
4
, pp.
287
–
296
.
8.
Lee
,
J.
,
Hu
,
S. J.
, and
Ward
,
A. C.
,
1999
, “
Workspace Synthesis for Flexible Fixturing of Stampings
,”
ASME J. Manuf. Sci. Eng.
,
131
, No.
3
, pp.
478
–
484
.
9.
Shimoga, K. B., and Goldenberg, A. A., 1992, “Soft Materials for Robotic Fingers,” Proceedings of the IEEE International Conference on Robotics and Automation, Piscataway, NJ, pp. 1300–1305.
10.
Tomanik, E., 1996, “Piston Ring Conformability in a Distorted Bore,” SAE Special Publications, No. 1168, p. 169.
11.
Nguyen, V., 1986, “The Synthesis of Stable Grasps in the Plane,” Proceedings of the IEEE International Conference on Robotics and Automation, San Francisco, CA, pp. 884–889.
12.
Nguyen, V., 1987, “Constructing Stable Grasps in 3D,” Proceedings of the IEEE International Conference on Robotics and Automation, Raleigh, NC, pp. 234–239.
13.
Howard, W. S., and Kumar, V., 1994, “Stable Workpiece Fixturing,” ASME Advances in Design and Automation, Vol. 2, pp. 475–482.
14.
Howard
,
W. S.
, and
Kumar
,
V.
,
1996
, “
On the Stability of Grasped Objects
,”
IEEE Transactions on Robotics and Automation
,
12
, No.
6
, pp.
904
–
917
.
15.
Lin, Q., Burdick, J., and Rimon, E., 1997, “A Quality Measure for Compliant Grasps,” Proceedings of the IEEE International Conference on Robotics and Automation, pp. 86–92.
16.
Bruyninckx, H., Demey, S., and Kumar, V., 1998, “Generalized Stability of Compliant Grasps,” Proceedings of the IEEE International Conference on Robotics and Automation, pp. 2396–2402.
17.
Mortenson, M. E., 1985, Geometric Modeling, John Wiley & Sons.
18.
Preparata, F. P., and Shamos, M. I., 1985, Computational Geometry, An Introduction, Springer-Verlag.
19.
Timoshenko, S., 1972, Strength of Materials, Van Nostrand.
20.
Johnson, K. L., 1985, Contact Mechanics, Cambridge University Press.
21.
Richards, T. H., 1977, Energy Methods in Stress Analysis, John Wiley & Sons.
22.
Hurtado, J. F., and Melkote, S. N., 1998, “A Model for the Prediction of Reaction Forces in a 3-2-1 Machining Fixture,” Transactions of NAMRI/SME, Vol. 26, pp. 335–340.
23.
Kalker
,
J. J.
,
1977
, “
Variational Principles of Contact Elastostatics
,”
J. Inst. Math. Appl.
20
, pp.
199
–
219
.
24.
Matrix GmbH, X-Clamp Technical Data Sheet, matrix_gmbh@t-online.de, Stuttgart, Germany.
25.
Hurtado, J. F., and Melkote, S. N., 2001, “Experimental Study of the Effect of Conformability on Static Stability in a Flexible Machining Fixture,” Transactions of NAMRI/SME, Vol. 29, pp. 615–622.
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