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TECHNICAL PAPERS

Synthesis of Planar, Compliant Four-Bar Mechanisms for Compliant-Segment Motion Generation

[+] Author and Article Information
L. Saggere, S. Kota

Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor, MI 48109

J. Mech. Des 123(4), 535-541 (Apr 01, 1999) (7 pages) doi:10.1115/1.1416149 History: Received April 01, 1999
Copyright © 2001 by ASME
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References

Paros, J. M., and Weisbord, L., “How to Design Flexure Hinges,” Machine Design, Nov. 25, 1965, pp. 151–156.
Burns, R. H., and Crossley, F. R. E., 1968, “Kinetostatic Synthesis of Flexible Link Mechanisms,” ASME Paper No. 68-MECH-36.
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.
Ananthasuresh, G. K., 1994, “A New Design Paradigm in Micro-Electromechanical Systems & Investigations on Compliant Mechanisms,” Ph.D. Dissertation, University of Michigan.
Saggere, L., 1998, “Static Shape Control of Smart Structures: A New Approach Utilizing Compliant Mechanisms,” Ph.D. Dissertation, University of Michigan.
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).
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.
Erdman, A. G., and Sandor, G. N., 1993, Mechanism Design: Analysis and Synthesis, Vol. 1, Prentice Hall, Inc., Englewood Cliffs, New Jersey.
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.
Ghali, A., and Neville, A. M., 1978, Structural Analysis, Chapman and Hall Ltd., London.
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.
Watson,  L. T., and Wang,  C. Y., 1981, “A Homotopy Method Applied to Elastica Problems,” Int. J. Solids Struct., 17, pp. 29–37.
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-Vol186, pp. 31–36.
Frisch-Fay, R., 1962, Flexible Bars, Butterworths, Washington.
Banichuck, N. V., 1990, Chapter 7, Introduction to Optimization of Structures, Springer-Verlag, NY.

Figures

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Illustration of the compliant-segment motion generation task
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Complaint four-bar mechanism for motion generation
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Boundary conditions set-up for dimensional synthesis of the segments
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Sign convention for slope-deflection equation. (a) Positive directions of end-rotations αN and αF, and chord rotation φ. (b) End-moments caused by a unit rotation at N. (c) End-moments caused by a unit rotation at F.
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Design parameters involved in synthesis of the segment A-B
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Model of curved beam using torsional springs and rigid elements
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Comparison of the static deformation of a flexible member using conventional beam elements (-+-) and the spring-model (-0-)
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Notation for the computational scheme of the finite-link model
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A schematic illustrating the design specifications
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A schematic illustrating the computed end-moments and end-forces
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Results of synthesis of segment AB
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Results of synthesis of segment CD
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Finite element analysis of the resulting complete mechanism after synthesizing the three segments: A-B, B-C, and C-D. (A-B-C-D represents the initial undeformed position of the mechanism, and A-b-c-D represents its final deformed position obtained by a finite-element analysis).

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