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TECHNICAL BRIEFS

Synthesis of Bistable Compliant Four-Bar Mechanisms Using Polynomial Homotopy

[+] Author and Article Information
Hai-Jun Su

Mechanical Engineering Department, University of Maryland Baltimore County, 1000 Hilltop CircleBaltimore, MD 21250haijun@umbc.edu

J. Michael McCarthy

Robotics and Automation Laboratory, University of California,Irvine, CA 92697jmmccart@uci.edu

J. Mech. Des 129(10), 1094-1098 (Sep 06, 2006) (5 pages) doi:10.1115/1.2757192 History: Received October 28, 2005; Revised September 06, 2006

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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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Synthesis of a rigid-body four-bar to reach n specified task positions

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Figure 2

Synthesis of a compliant four-bar to reach n specified equilibrium positions

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Figure 3

The solutions to the synthesis of a compliant mechanism with three specified equilibrium points

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Figure 4

Energy curves of the solutions 1–6 for equilibrium point synthesis

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