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Research Papers: Mechanisms and Robotics

Kinetostatic Modeling of Fully Compliant Bistable Mechanisms Using Timoshenko Beam Constraint Model

[+] Author and Article Information
Guimin Chen

School of Electro-Mechanical Engineering,
Xidian University,
Xi'an, Shaanxi 710071, China
e-mail: guimin.chen@gmail.com

Fulei Ma

School of Electro-Mechanical Engineering,
Xidian University,
Xi'an, Shaanxi 710071, China

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received November 6, 2013; final manuscript received October 20, 2014; published online November 26, 2014. Assoc. Editor: Kazuhiro Saitou.

J. Mech. Des 137(2), 022301 (Feb 01, 2015) (10 pages) Paper No: MD-13-1513; doi: 10.1115/1.4029024 History: Received November 06, 2013; Revised October 20, 2014; Online November 26, 2014

Fully compliant bistable mechanisms (FCBMs) have numerous applications in both micro- and macroscale devices, but the nonlinearities associated with the deflections of the flexible members and the kinetostatic behaviors have made it difficult to design. Currently, the design of FCBMs relies heavily on nonlinear finite element modeling. In this paper, an analytical kinetostatic model is developed for FCBMs based on the beam constraint model (BCM) that captures the geometric nonlinearities of beam flexures that undergo relatively small deflections. An improved BCM (i.e., Timoshenko BCM (TBCM)) is derived based on the Timoshenko beam theory in order to include shear effects in the model. The results for three FCBM designs show that the kinetostatic model can successfully identify the bistable behaviors and make reasonable predictions for the locations of the unstable equilibrium points and the stable equilibrium positions. The inclusion of shear effects in the TBCM model significantly improves the prediction accuracy over the BCM model, as compared to the finite element analysis (FEA) results.

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Figures

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Fig. 1

Photographs of a FCBM prototype at its as-fabricated position and second stable equilibrium position. This prototype contains six identical bistable fixed-guided limbs (Nl = 6).

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Fig. 2

A simple beam flexure subject to combined force and moment loads. Δx(L) and Δx(L) are denoted as Δx and Δx for convenience, respectively.

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Fig. 3

Deflections of beam flexures subject to pure transverse forces predicted using BCM and TBCM (with the value of the ratio YTBCM/BCM for each flexure shown)

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Fig. 4

Schematic showing the parameterization of a bistable fixed-guided limb. The out-of-plane thickness of the mechanism is denoted as w.

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Fig. 5

The free body diagram of a bistable limb. The positive directions of the forces and the deflections are indicated by the reference arrows.

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Fig. 6

The kinetostatic behaviors of design 1

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Fig. 7

The kinetostatic behaviors of design 2

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Fig. 8

Prototype photographs of design 1 at its two stable positions

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Fig. 10

The axial and the transverse forces of beam flexure 1 at different deflected positions and their contributions to shear deflections along the Y1-axis

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Fig. 11

Fixed-guided bistable compliant mechanism

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Fig. 12

The kinetostatic behaviors of design 3

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