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Research Papers

Modeling Large Planar Deflections of Flexible Beams in Compliant Mechanisms Using Chained Beam-Constraint-Model1

[+] Author and Article Information
Fulei Ma

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

Guimin Chen

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

1Paper presented at the ASME 2014 Design Engineering Technical Conferences and Computers and Information in Engineering Conference (DETC2014), Aug. 17–20, 2014, Buffalo, NY.

2Corresponding author.

Manuscript received April 6, 2015; final manuscript received June 12, 2015; published online November 24, 2015. Assoc. Editor: Larry L. Howell.

J. Mechanisms Robotics 8(2), 021018 (Nov 24, 2015) (11 pages) Paper No: JMR-15-1082; doi: 10.1115/1.4031028 History: Received April 06, 2015; Revised June 12, 2015; Accepted July 01, 2015

Modeling large deflections has been one of the most fundamental problems in the research community of compliant mechanisms. Although many methods are available, there still exists a need for a method that is simple, accurate, and can be applied to a vast variety of large deflection problems. Based on the beam-constraint model (BCM), we propose a new method for modeling large deflections called chained BCM (CBCM), which divides a flexible beam into a few elements and models each element by BCM. The approaches for determining the strain energy stored in a deflected beam and the stress distributed on it are also presented within the framework of CBCM. Several typical examples were analyzed and the results show CBCMs capabilities of modeling various large deflections of flexible beams in compliant mechanisms. Generally, CBCM can serve as an efficient and versatile tool for solving large deflection problems in a variety of compliant mechanisms.

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References

Figures

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Fig. 1

A simple beam subject to combined force and moment loads at its free end

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Fig. 3

The beam shape when subjected to pure vertical end force

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Fig. 4

Deflected configurations when beam subject to an end moment (the stars correspond to the nodes)

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Fig. 5

Tip errors compared to results of Eq. (16)

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Fig. 6

A partially compliant four-bar mechanism containing a fixed–fixed flexible beam DQ

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Fig. 7

Free-body diagrams of the mechanism

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Fig. 8

Force displacement relationship of partial compliant four-bar mechanism

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Fig. 9

Strain energy in partially compliant four-bar mechanism

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Fig. 10

Deflected configurations of the partial compliant four-bar mechanism at different θ1

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Fig. 11

Maximum stress in partially compliant four-bar mechanism

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Fig. 12

Diagram of fixed-guided beam

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Fig. 13

Deflected configurations of the fixed-guided beam

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Fig. 14

Force deflection relationships of fixed-guided mechanism

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Fig. 15

Comparison of strain energy of the fixed-guided beam

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Fig. 16

Maximum stress along the fixed-guided beam

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Fig. 17

Circular-guided compliant mechanism

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Fig. 18

Kinetostatic behavior of circular-guided mechanism

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Fig. 19

Deflected configurations of circular-guided mechanism

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Fig. 20

Strain energy stored in circular-guided mechanism

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Fig. 21

Maximum stress on flexible beam in circular-guided mechanism

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Fig. 22

Geometry of cross-axis flexural pivot

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Fig. 23

Free-body diagrams of cross-axis flexural pivot

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Fig. 24

Kinetostatic behaviors and deflected configurations of cross-axis flexural pivot

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Fig. 25

Comparison of strain energy in cross-axis flexural pivot

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Fig. 26

Maximum stress of the total mechanism

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