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Research Papers

Bistable Buckled Beam: Modeling of Actuating Force and Experimental Validations

[+] Author and Article Information
Paul Cazottes

Institut Jean Le Rond d’Alembert, UPMC Univ Paris 06, CNRS-UMR 7190, F-75005 Paris, France; Laboratoire d’Interfaces Sensorielles, CEA List, F-92265 Fontenay-aux-Roses, Francecazottes@lmm.jussieu.fr

Amâncio Fernandes

Institut Jean Le Rond d’Alembert, UPMC Univ Paris 06, CNRS-UMR 7190, F-75005 Paris, Franceamancio.fernandes@upmc.fr

Joël Pouget1

Institut Jean Le Rond d’Alembert, UPMC Univ Paris 06, CNRS-UMR 7190, F-75005 Paris, Francepouget@lmm.jussieu.fr

Moustapha Hafez

Laboratoire d’Interfaces Sensorielles, CEA List, F-92265 Fontenay-aux-Roses, Francemoustapha.hafez@cea.fr

1

Corresponding author.

J. Mech. Des 131(10), 101001 (Sep 02, 2009) (10 pages) doi:10.1115/1.3179003 History: Received December 14, 2007; Revised April 20, 2009; Published September 02, 2009

Compliant bistable mechanisms are a class of mechanical systems that benefit from both compliance, allowing easy manufacturing on a small scale, and bistability, which provides two passive and stable positions. These properties make them first-class candidates not only for microswitches but also several other robotic appliances. This paper investigates the actuation of a simple bistable mechanism, the bistable buckled beam. It is pointed out that the position of the actuation has a significant impact on the behavior of the system. A new model is proposed and discussed, with experimental validations to compare central and offset loading, highlighting the strengths of each.

Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

A clamped-clamped bistable mechanism. A force allows the system to snap from one stable position to the other one.

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Figure 2

Compression of the beam. The first buckling mode appears and during actuation, the second unstable mode is triggered.

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Figure 3

Topological decomposition of the deflection, using a general solution (modes 1 and 2) and a particular solution

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Figure 4

The first and second modes of buckling for a clamped-clamped beam. These first two modes coexist during the snapping process.

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Figure 5

Energy of the system depending on coefficients a1 and a2, drawn for an external force of 10 N (central actuation)

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Figure 6

The five configurations of equilibrium for an actuation force of 10 N, for a centrally actuated beam

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Figure 7

Performance indices: switching point (S), apparent stiffness (A.S.), average apparent stiffness (a.A.S.) both on point P1, stroke, and stable domains

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Figure 8

f-d curve for a central actuation depending on parameter P

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Figure 9

Full range f-d curve for a central actuation with a high ηP parameter (ηP=42, used from the following simulations). The positive stiffness line appears representing the particular solution behavior. The actual f-d curves are obtained by cutting this curve to the useful force values, here F=−40 N to F=40 N as in Fig. 1.

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Figure 10

Snapping sequences for a typical clamped-clamped beam. Mode 2 buckling is used to help the switch from one position to the other.

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Figure 11

f-d curve for a central actuation clamped-clamped beam

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Figure 12

fn-d curve for a central actuation clamped-clamped beam

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Figure 13

Coefficients a1 (cross) and a2 (circles) versus displacement curves for a central actuation clamped-clamped beam

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Figure 14

Switching sequences with a shifted force actuator, the snapping is delayed

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Figure 15

f-d curve for a clamped-clamped beam with a shifted (40%) actuation

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Figure 16

fn-d curve for a shifted actuation clamped-clamped beam

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Figure 17

Coefficients a1 (cross) and a2 (circles) versus displacement curves for a shifted actuation clamped-clamped beam

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Figure 18

Full range f-d curve for a shifted (40%) actuation

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Figure 19

f-d curve for a central actuation beam with 3 free parameters a1, a2, and a3

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Figure 20

Test bench for force-displacement measurement. On the left is the Vishay console and on the right is the mechanical setup.

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Figure 21

Test bench for force-displacement measurement

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Figure 22

f-d curve for a central actuation clamped-clamped beam, with experimental points in cross

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Figure 23

f-d curve for a shifted (40%) actuation clamped-clamped beam, with experimental points (cross)

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Figure 24

f-d theoretical curve with a 40% actuation shift (points), compared with experimental measurements (line)

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Figure 25

f-d curve for a clamped-clamped beam with a slightly shifted (49.5%) actuation, with central actuation experimental points (cross)

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Figure 26

Energy used and actuator total energy for a central actuation clamped-clamped beam. The ratio is about 25%.

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Figure 27

Energy used and actuator total energy for a shifted (40%) actuation clamped-clamped beam. The ratio is much increased compared with the central actuation.

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