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Research Papers: Mechanisms and Robotics

A Compliant Bistable Mechanism Design Incorporating Elastica Buckling Beam Theory and Pseudo-Rigid-Body Model

[+] Author and Article Information
Ümit Sönmez1

Department of Mechanical Engineering,  Istanbul Technical University (İTÜ), Gümüşsuyu, 34437 Istanbul, Turkeyusonitu@gmail.com

Cem C. Tutum2

Department of Manufacturing Engineering and Management,  Technical University of Denmark, Produktionstorvet, 2800 Kgs. Lyngby, Denmarkcem@ipl.dtu.dk

1

Corresponding author.

2

Formerly Graduate Student at İTÜ, Department of Mechanical Engineering, Istanbul, Turkey.

J. Mech. Des 130(4), 042304 (Feb 28, 2008) (14 pages) doi:10.1115/1.2839009 History: Received August 30, 2006; Revised April 23, 2007; Published February 28, 2008

In this work, a new compliant bistable mechanism design is introduced. The combined use of pseudo-rigid-body model (PRBM) and the Elastica buckling theory is presented for the first time to analyze the new design. This mechanism consists of the large deflecting straight beams, buckling beams, and a slider. The kinematic analysis of this new mechanism is studied, using nonlinear Elastica buckling beam theory, the PRBM of a large deflecting cantilever beam, the vector loop closure equations, and numerically solving nonlinear algebraic equations. A design method of the bistable mechanism in microdimensions is investigated by changing the relative stiffness of the flexible beams. The actuation force versus displacement characteristics of several cases is explored and the full simulation results of one of the cases are presented. This paper demonstrates the united application of the PRBM and the buckling Elastica solution for an original compliant mechanism kinematic analysis. New compliant mechanism designs are presented to highlight where such combined kinematic analysis is required.

Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

A ball on a curved surface

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Figure 2

(a) Proposed compliant bistable mechanism design and (b) the same design with several shoulder and arm beams, which does not require a track to follow

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Figure 3

Pinned-pinned buckling Elastica attached to a slider

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Figure 4

Buckling of the pin-pin beam; the exact Elastica solution and the corresponding fourth order fit

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Figure 5

Pin-pin buckling beam shape factor k versus normalized deflection

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Figure 6

Buckled shapes of the pinned-pinned Elastica as the beam deflects

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Figure 7

Initially straight large deflecting cantilever beam with force at the free end

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Figure 8

Tip paths of large deflecting fixed-free beam for different loading conditions

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Figure 9

PRBM of a fixed-free beam

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Figure 10

Stiffness coefficient Kθ versus force coefficient (n or −s)

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Figure 11

Characteristic radius factor (γ) versus force coefficient (n or −s)

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Figure 12

Vector loop closure

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Figure 13

Representation of the half model before buckling

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Figure 14

Representation of the buckling beam as a nonlinear spring member

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Figure 15

Limit cases representing the relative stiffness effect of the compliant bistable mechanism

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Figure 16

Actuation load versus slider displacement considering shoulder beam in-plane thickness effect

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Figure 17

Actuation load versus slider displacement considering shoulder beam out-of-plane width

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Figure 18

Actuation load versus slider displacement considering shoulder beam length effect

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Figure 19

Actuation load versus slider displacement. Arm beam in-plane thickness effect.

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Figure 20

Actuation load versus slider displacement considering arm beam initial angle effect

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Figure 21

Load deflection plot of the candidate mechanism

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Figure 22

Shoulder angle (θ2) versus displacement

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Figure 23

Arm angle (θ3) versus displacement

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Figure 24

Arm load compared to the critical buckling load versus displacement

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Figure 25

Arm beam length (R3) versus displacement

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Figure 26

Shoulder beam tip path obtained from mechanism analysis and Elastica theory

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Figure 27

New compliant mechanism designs to be modeled by the PRBM and buckling Elastica theory

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