0
Technical Brief

Bi-BCM: A Closed-Form Solution for Fixed-Guided Beams in Compliant Mechanisms

[+] Author and Article Information
Fulei Ma

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

Guimin Chen

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

1Corresponding author.

Manuscript received March 10, 2016; final manuscript received October 4, 2016; published online November 23, 2016. Assoc. Editor: Venkat Krovi.

J. Mechanisms Robotics 9(1), 014501 (Nov 23, 2016) (8 pages) Paper No: JMR-16-1065; doi: 10.1115/1.4035084 History: Received March 10, 2016; Revised October 04, 2016

A fixed-guided beam, with one end is fixed while the other is guided in that the angle of that end does not change, is one of the most commonly used flexible segments in compliant mechanisms such as bistable mechanisms, compliant parallelogram mechanisms, compound compliant parallelogram mechanisms, and thermomechanical in-plane microactuators. In this paper, we split a fixed-guided beam into two elements, formulate each element using the beam constraint model (BCM) equations, and then assemble the two elements' equations to obtain the final solution for the load–deflection relations. Interestingly, the resulting load–deflection solution (referred to as Bi-BCM) is closed-form, in which the tip loads are expressed as functions of the tip deflections. The maximum allowable axial force of Bi-BCM is the quadruple of that of BCM. Bi-BCM also extends the capability of BCM for predicting the second mode bending of fixed-guided beams. Besides, the boundary line between the first and the second modes bending of fixed-guided beams can be easily obtained using a closed-form equation. Bi-BCM can be immediately used for quick design calculations of compliant mechanisms utilizing fixed-guided beams as their flexible segments (generally no iteration is required). Different examples are analyzed to illustrate the usage of Bi-BCM, and the results show the effectiveness of the closed-form solution.

FIGURES IN THIS ARTICLE
<>
Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Fig. 1

Illustration of different compliant mechanisms that employ fixed-guided beams: (a) a bistable mechanism, (b) a thermomechanical in-plane microactuator, (c) a compound compliant parallelogram mechanism, and (d) a double parallelogram mechanism

Grahic Jump Location
Fig. 2

Schematic of a fixed-guided beam

Grahic Jump Location
Fig. 3

Free body diagrams for the two element of a fixed-guided beam end remains zero

Grahic Jump Location
Fig. 4

Illustration of two possible deflected configurations corresponding to the second mode bending (configuration I corresponding to solution (a) and configuration II corresponding to solution (b))

Grahic Jump Location
Fig. 5

Schematic of a fixed-guided beam in a bistable mechanism

Grahic Jump Location
Fig. 6

The force–deflection curves of the bistable mechanism

Grahic Jump Location
Fig. 7

The boundary between first and second mode bending according to Eq. (42) for the fixed-guided beam. Several deflected beam configurations are also shown.

Grahic Jump Location
Fig. 8

Comparison of the two deflected configurations obtained by Bi-BCM solution and the experimental results in Ref. [10]

Grahic Jump Location
Fig. 9

Schematic of a fixed-guided beam taken from a compliant parallelogram mechanism

Grahic Jump Location
Fig. 10

The force–deflection curves of the compliant parallelogram mechanism

Grahic Jump Location
Fig. 11

Schematic of a deflected TIM leg

Grahic Jump Location
Fig. 12

The force–displacement relationship of the thermomechanical in-plane microactuator

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In