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Research Papers

Elliptical-Arc-Fillet Flexure Hinges: Toward a Generalized Model for Commonly Used Flexure Hinges

[+] Author and Article Information
Guimin Chen

 School of Mechatronics, Xidian University, Xi’an, Shaanxi 710071, Chinagmchen@mail.xidian.edu.cn

Xiaoyuan Liu, Yunlei Du

 School of Mechatronics, Xidian University, Xi’an, Shaanxi 710071, China

J. Mech. Des 133(8), 081002 (Jul 27, 2011) (9 pages) doi:10.1115/1.4004441 History: Received June 24, 2010; Revised June 14, 2011; Accepted June 15, 2011; Published July 27, 2011; Online July 27, 2011

Flexure hinges have been used to produce frictionless and backlashless transmissions in a variety of precision mechanisms. Although there are many types of flexure hinges available, designers often chose a single type of flexure hinge (e.g., circular flexure hinges) without considering others in the design of flexure-based mechanisms. This is because the analytical equations are unique to each kind of flexure hinge. This work offers a solution to this problem in the form of a generalized flexure hinge model. We propose a new class of flexure hinges, namely, elliptical-arc-fillet flexure hinges, which brings elliptical arc, circular-arc-fillet, elliptical-fillet, elliptical, circular, circular-fillet, and right-circular flexure hinges together under one set of equations. The closed-form equations for all the elements in the compliance and precision matrices of elliptical-arc-fillet flexure hinges have been derived. The analytical results are within 10 percent error compared to the finite element results and within 8 percent error compared to the experimental results. The equations for evaluating the strain energy and stress level for elliptical-arc-fillet flexure hinges are also provided. This model can be used as a complementary model for the generalized model for conic flexure hinges.

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Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Diagram of an elliptical-arc-fillet flexure hinge. For clarity, the center of the flexure hinge, i.e., point “Q” is drawn on the outer profile.

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Figure 2

The relationship between flexure hinges of different cutout profiles. (a) Elliptical-arc-fillet hinge, (b) elliptical arc hinge, (c) circular-arc-fillet hinge, (d) elliptical-fillet hinge, (e) elliptical hinge, (f) circular hinge, (g) circular-fillet hinge, and (h) right-circular hinge.

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Figure 3

A Venn diagram showing the relationship between flexure hinges of different cutout profiles

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Figure 4

Analysis of hinge profile

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Figure 5

Finite element results for stress concentration factor (γ is the slenderness ratio of a flexure hinge and η the ellipticity of the elliptical-arc fillets)

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Figure 6

The finite element model for example 7

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Figure 7

The relative errors of the compliance factors between the analytical results and the finite element results shown in Table 2 (error = C/F – 1)

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Figure 8

The relative errors of the precision factors between the analytical results and the finite element results shown in Table 3 (error = C/F – 1)

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Figure 9

A flexure hinge sample (w = 10, t = 0.2, a = 4, b = 3, l = 2, θm  = 90°)

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