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Research Papers

Synthesis of Multistable Equilibrium Compliant Mechanisms Using Combinations of Bistable Mechanisms

[+] Author and Article Information
Young Seok Oh

Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109-2125ohys@umich.edu

Sridhar Kota

Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109-2125kota@umich.edu

J. Mech. Des 131(2), 021002 (Jan 06, 2009) (11 pages) doi:10.1115/1.3013316 History: Received January 23, 2008; Revised September 02, 2008; Published January 06, 2009

In this paper, we present a mathematical approach to synthesize multistable compliant mechanisms by combining multiple bistable equilibrium mechanisms. More specifically, we identify and categorize various types of bistabilities by characterizing the essential elements of their complicated deformation pattern. The behavior of a bistable compliant mechanism, in general, is highly nonlinear. Using combinations of such nonlinearities to capture the behavior of multistable (more than two stable positions) mechanisms can be quite challenging. To determine multistable behavior, our simplified mathematical scheme captures the essential parameters of bistability, such as the load-thresholds that cause the jump to the next stable position. This mathematical simplification enables us to characterize bistable mechanisms by using piecewise lower-order polynomials and, in turn, synthesize multistable mechanisms. Three case studies involving combinations of two, three, and four bistable behaviors are presented for the purpose of generating multistable mechanisms with up to 16 stable positions. The methodology enables us to design a compliant mechanism with a desired number of stable positions. A design example of a quadristable equilibrium rotational compliant mechanism consisting of two bistable submechanisms is presented to demonstrate the effectiveness of the approach.

Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Potential energy and load-displacement curves of a multistable equilibrium system

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Figure 2

A simple bistable equilibrium compliant mechanism

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Figure 3

Load-displacement curves of (a) solved using path following method, (b) solved using displacement-control method, and (c) solved using load-control method (ABAQUS )

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Figure 4

Illustration of the nonlinear behavior of a MSECM with four stable equilibria

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Figure 5

Piecewise-continuous function representing the key parameters (stable positions and actuation loads)

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Figure 6

(a) and (b) are two bistable equilibrium systems and (c) a combined multistable equilibrium system

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Figure 7

Load-displacement curves of two bistable behaviors (TYPE2121)

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Figure 8

Potential energy contour plot and PE path for TYPE2121. (b) represents the two axes (x1 and PE) isolated from the normal three axes, i.e., (x1, x2, PE). The vertical lines, in (b) correspond to the jumps of x2 in (a).

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Figure 9

Deformed configurations of BES1 (x1) and BES2 (x2) of TYPE2121 when x1 increases steadily

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Figure 10

Load-displacement curves of the combined multistability: (a) displacement-control and (b) load-control

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Figure 11

Potential energy contour plot and potential energy path for TYPE2112 and TYPE1221

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Figure 12

Combined multistable equilibrium system

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Figure 13

Load-displacement curves of three different bistable behaviors (TYPE312231)

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Figure 14

Potential energy versus displacement curve of combined multistable system behaviors (TYPE312231)

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Figure 15

Load-displacement curve of the combined multistability with controlling the load behaviors (TYPE312231)

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Figure 16

Load-displacement curves of four bistable behaviors

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Figure 17

Two bistable compliant mechanisms of different dimensions (size and proportion)

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Figure 18

Load-displacement curves for the bistable compliant mechanisms. (a) BiCM-inner and BiCM-outer, and (b) the combined results (ABAQUS ). Key parameters are marked as circles.

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Figure 19

Combined multistable equilibrium rotational compliant mechanism with four stable equilibria

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Figure 20

(a) Simplified mathematical functions of the two bistable behaviors and (b) the combined results (MAPLE ). Key parameters are marked as circles.

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Figure 21

Four stable configurations of the rotational MSECM

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