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RESEARCH PAPERS

Characteristics of Beam-Based Flexure Modules

[+] Author and Article Information
Shorya Awtar1

Precision Engineering Research Group, Massachusetts Institute of Technology, Cambridge, MA 01239shorya@mit.edu

Alexander H. Slocum

Precision Engineering Research Group, Massachusetts Institute of Technology, Cambridge, MA 01239slocum@mit.edu

Edip Sevincer

 Omega Advanced Solutions Inc., Troy, NY 12108sevincer@omegaadvanced.com

1

Corresponding author.

J. Mech. Des 129(6), 625-639 (May 29, 2006) (15 pages) doi:10.1115/1.2717231 History: Received December 29, 2005; Revised May 29, 2006

The beam flexure is an important constraint element in flexure mechanism design. Nonlinearities arising from the force equilibrium conditions in a beam significantly affect its properties as a constraint element. Consequently, beam-based flexure mechanisms suffer from performance tradeoffs in terms of motion range, accuracy and stiffness, while benefiting from elastic averaging. This paper presents simple yet accurate approximations that capture the effects of load-stiffening and elastokinematic nonlinearities in beams. A general analytical framework is developed that enables a designer to parametrically predict the performance characteristics such as mobility, over-constraint, stiffness variation, and error motions, of beam-based flexure mechanisms without resorting to tedious numerical or computational methods. To illustrate their effectiveness, these approximations and analysis approach are used in deriving the force–displacement relationships of several important beam-based flexure constraint modules, and the results are validated using finite element analysis. Effects of variations in shape and geometry are also analytically quantified.

Copyright © 2007 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

(a) Lumped-compliance and (b) distributed-compliance multi-parallelogram mechanisms

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Figure 2

Generalized beam flexure

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Figure 3

Normalized compliance terms: actual (solid lines) and approximate (dashed lines)

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Figure 4

Transverse elastic stiffness coefficients

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Figure 5

Transverse geometric stiffness coefficients

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Axial kinematic coefficients

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Axial elastokinematic coefficients

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Figure 8

Axial elastic stiffness coefficient

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Figure 9

Parallelogram flexure and free body diagram

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Figure 10

Parallelogram flexure stage rotation: CFA (lines), FEA (circles)

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Figure 11

Parallelogram flexure transverse displacement: CFA (lines), FEA (circles)

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Figure 12

Parallelogram and double parallelogram flexures transverse stiffness: CFA (lines), FEA (circles)

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Figure 13

Parallelogram and double parallelogram flexures axial stiffness: CFA (lines), FEA (circles)

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Figure 14

“Nonidentical beam” parallelogram flexure stage rotation: CFA (lines), FEA (circles)

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Figure 15

Tilted-beam flexure

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Tilted-beam flexure transverse elastic stiffness: CFA (lines), FEA (circles)

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Figure 17

Tilted-beam flexure stage rotation: CFA (lines), FEA (circles)

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Figure 18

Tilted-beam flexure kinematic axial displacement: CFA (lines), FEA (circles)

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Figure 19

Tilted-beam flexure axial stiffness: CFA (lines), FEA (circles)

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Figure 20

Double parallelogram flexure

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Figure 21

Double parallelogram flexure primary stage rotation: CFA (lines), FEA (circles)

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Figure 22

Double tilted-beam flexure

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Figure 23

Double tilted-beam flexure axial stiffness: CFA (lines), FEA (circles)

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