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Research Papers

Modeling and Experimental Validation of Actuating a Bistable Buckled Beam Via Moment Input

[+] Author and Article Information
Jonathon Cleary

Department of Mechanical and
Aerospace Engineering,
The Ohio State University,
Columbus, OH 43210
e-mail: cleary.77@osu.edu

Hai-Jun Su

Department of Mechanical and
Aerospace Engineering,
The Ohio State University,
Columbus, OH 43210
e-mail: su.298@osu.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received December 23, 2014; final manuscript received March 16, 2015; published online March 31, 2015. Assoc. Editor: Taher Saif.

J. Appl. Mech 82(5), 051005 (May 01, 2015) (7 pages) Paper No: JAM-14-1602; doi: 10.1115/1.4030074 History: Received December 23, 2014; Revised March 16, 2015; Online March 31, 2015

Bistable mechanisms have two stable equilibrium positions separated by a higher energy unstable equilibrium position. They are well suited for microswitches, microrelays, and many other macro- and micro-applications. This paper discusses a bistable buckled beam actuated by a moment input. A theoretical model is developed for predicting the necessary input moment. A novel experimental test setup was created for experimental verification of the model. The results show that the theoretical model is able to predict the maximum necessary input moment within 2.53%. This theoretical model provides a guideline to design bistable compliant mechanisms and actuators. It is also a computational tool to size the dimensions of buckled beams for actuating a specific mechanism.

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References

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Figures

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Fig. 1

A clamped–clamped bistable beam with applied moment to actuate from one stable position to the other

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Fig. 2

Buckling modes of a clamped–clamped bistable buckled beam

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Fig. 3

A clamped–clamped bistable beam with applied distributed moment to actuate from one stable position to the other

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Fig. 4

A set of continuous beam shape solutions for actuation at 23.33% along the length of the beam and a precompression of η = 2%

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Fig. 5

Moment versus displacement plot for actuation at 23.33% along the length of the beam. The x-axis is displacement in m, the y-axis is moment in N m.

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Fig. 6

Critical actuation moment versus position of applied moment along the beam's length. The x-axis is percent of the beams length, the y-axis is moment in N m. Starting from the bottom curve up to the top, the precompressions are η = 2%,η = 3%,η = 4%, and η = 5%.

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Fig. 7

Moment versus displacement plot for actuation at 23.33% along the length of the beam. The solid line is the theoretical results and the dashed line is the FEA results.

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Fig. 8

The platform and moment application apparatus. (a) The beam to be tested, (b) the clamping device attached to the location where the moment is to be applied, (c) the beam end clamps that determine both L0 and L, (d) the wheel apparatus used to apply the moment to the beam, (e) the y-axis shuttle for free translation in the y-direction, and (f) the x-axis shuttle for free translation in the x-direction.

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Fig. 9

Schematic of the x-shuttle with representative beam and wheel/thread moment input device. (a) The air bed, (b) the beam end clamps, (c) the actuation wheel and threads, and (d) the beam. Note the markers on the wheel and the beam's ends for data acquisition.

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Fig. 10

The clamping conditions for the beam end and moment application

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Fig. 11

Overview of the full test setup. (a) The bistable buckled beam, (b) the xy air bearing platform, (c) the force sensor mounted on the CNC bed, (d) the force sensor readout, (e) the camera, (f) the computer, and (g) the stationary bar where one of the wheel threads is attached.

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Fig. 12

Representative photo for data acquisition. The force data are collected by Pasco force sensor with a resolution 0.002 N. Three color beads (pointed to by arrows) are attached to the beam. The beam shape is captured by using a high resolution camera.

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Fig. 13

Plot of the analytical prediction and experimental data for an actuation at 23.33% along the length of the beam

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Fig. 14

Critical actuation moment versus position of applied moment along the beam's length for a beam with η=2% precompression. The x-axis is percentage of the beams length, the y-axis is moment in N m. The curve is the analytical model, the data points are experimental results.

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