In this paper we formulate and solve the synthesis equations for a compliant four-bar linkage with three specified equilibrium configurations in the plane. The kinematic synthesis equations as for rigid-body mechanisms are combined with equilibrium constraints at the flexure pivots to form design equations. These equations are simplified by modeling the joint angle variables in the equilibrium equations using sine and cosine functions. Polynomial homotopy continuation is applied to compute all of the design candidates that satisfy these design equations, which are refined using a Newton-Raphson technique. A numerical example demonstrates design methodology in which the homotopy solver obtained eight real solutions. Two of them provide two stable and one unstable equilibrium, and hence, can be used as the prototype of bistable compliant mechanisms.
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e-mail: haijun@umbc.edu
e-mail: jmmccart@uci.edu
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October 2007
Technical Briefs
Synthesis of Bistable Compliant Four-Bar Mechanisms Using Polynomial Homotopy
Hai-Jun Su,
Hai-Jun Su
Mechanical Engineering Department,
e-mail: haijun@umbc.edu
University of Maryland Baltimore County,
1000 Hilltop CircleBaltimore, MD 21250
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J. Michael McCarthy
J. Michael McCarthy
Robotics and Automation Laboratory,
e-mail: jmmccart@uci.edu
University of California
,Irvine, CA 92697
Search for other works by this author on:
Hai-Jun Su
Mechanical Engineering Department,
University of Maryland Baltimore County,
1000 Hilltop CircleBaltimore, MD 21250e-mail: haijun@umbc.edu
J. Michael McCarthy
Robotics and Automation Laboratory,
University of California
,Irvine, CA 92697e-mail: jmmccart@uci.edu
J. Mech. Des. Oct 2007, 129(10): 1094-1098 (5 pages)
Published Online: September 6, 2006
Article history
Received:
October 28, 2005
Revised:
September 6, 2006
Citation
Su, H., and McCarthy, J. M. (September 6, 2006). "Synthesis of Bistable Compliant Four-Bar Mechanisms Using Polynomial Homotopy." ASME. J. Mech. Des. October 2007; 129(10): 1094–1098. https://doi.org/10.1115/1.2757192
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