Compliant four-bar mechanisms treated in previous works consisted of at least one rigid moving link, and such mechanisms synthesized for motion generation tasks have always comprised a rigid coupler link, bearing with the conventional definition of motion generation for rigid-link mechanisms. This paper introduces a new task called compliant-segment motion generation where the coupler is a flexible segment and requires a prescribed shape change along with a rigid-body motion. The paper presents a systematic procedure for synthesis of single-loop compliant mechanisms with no moving rigid-links for compliant-segment motion generation task. Such compliant mechanisms have potential applications in adaptive structures. The synthesis method presented involves an atypical inverse elastica problem that is not reported in the literature. This inverse problem is solved by extending the loop-closure equation used in the synthesis of rigid-links to the flexible segments, and then combining it with elastic equilibrium equation in an optimization scheme. The method is illustrated by a numerical example.

Issue Section:
Technical Papers
Keywords:
flexible structures, adaptive systems, inverse problems, elastic deformation
Topics:
Compliant mechanisms, Deformation, Equilibrium (Physics), Inverse problems, Optimization, Shapes, Stress, Displacement, Rotation, Boundary-value problems, Kinematics, Design, Computation
1.
Paros, J. M., and Weisbord, L., “How to Design Flexure Hinges,” Machine Design, Nov. 25, 1965, pp. 151–156.
2.
Burns, R. H., and Crossley, F. R. E., 1968, “Kinetostatic Synthesis of Flexible Link Mechanisms,” ASME Paper No. 68-MECH-36.
3.
Midha, A., 1993, “Chapter 9: Elastic Mechanisms,” Modern Kinematics—The Developments in the Last Forty Years, A. G. Erdman (Ed.), John Wiley and Sons Inc.
4.
Ananthasuresh, G. K., 1994, “A New Design Paradigm in Micro-Electromechanical Systems & Investigations on Compliant Mechanisms,” Ph.D. Dissertation, University of Michigan.
5.
Saggere, L., 1998, “Static Shape Control of Smart Structures: A New Approach Utilizing Compliant Mechanisms,” Ph.D. Dissertation, University of Michigan.
6.
Sevak, N. M., and McLarnan, C. W., 1974, “Optimal Synthesis of Flexible Link Mechanisms with Large Static Deflections,” ASME Paper No. 74-DET-83. (Also published in J. Eng. Ind., May 1975, pp. 520–526).
7.
Howell
,
L. L.
, and
Midha
,
A.
,
1994
, “
A Loop-Closure Theory for the Analysis and Synthesis of Compliant Mechanisms
,”
ASME J. Mech. Des.
,
118
, No.
1
, pp.
121
–
125
.
8.
Erdman, A. G., and Sandor, G. N., 1993, Mechanism Design: Analysis and Synthesis, Vol. 1, Prentice Hall, Inc., Englewood Cliffs, New Jersey.
9.
Midha
,
A.
,
Norton
,
T. W.
, and
Howell
,
L. L.
,
1994
, “
On the Nomenclature, Classification, and Abstractions of Complaint Mechanisms
,”
ASME J. Mech. Des.
,
116
, No.
1
, pp.
270
–
279
.
10.
Ghali, A., and Neville, A. M., 1978, Structural Analysis, Chapman and Hall Ltd., London.
11.
Shoup
,
T. E.
, and
McLarnan
,
C. W.
,
1971
, “
On the Use of the Undulating Elastica for the Analysis of Flexible Link Mechanisms
,”
ASME J. Ind.
,
93
, Feb. pp.
263
–
267
.
12.
Watson
,
L. T.
, and
Wang
,
C. Y.
,
1981
, “
A Homotopy Method Applied to Elastica Problems
,”
Int. J. Solids Struct.
,
17
, pp.
29
–
37
.
13.
Stack
,
K. D.
,
Benson
,
R. C.
, and
Diehl
,
T.
,
1994
, “
The Inverse Elastica Problem and its Application to Media Handling
,” Proceedings of the 1994 International Mechanical Engineering Congress and Exposition: Inverse Problems in Mechanics,
Proc. R. Soc. London, Ser. A
, ASME, AMD-Vol
186
, pp.
31
–
36
.
14.
Frisch-Fay, R., 1962, Flexible Bars, Butterworths, Washington.
15.
Banichuck, N. V., 1990, Chapter 7, Introduction to Optimization of Structures, Springer-Verlag, NY.
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 by ASME
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