Research Papers

Pseudo-Rigid-Body Model for the Flexural Beam With an Inflection Point in Compliant Mechanisms

[+] Author and Article Information
Shun-Kun Zhu

College of Mechanical Engineering and Applied
Electronics Technology,
Beijing University of Technology,
Beijing 100124, China

Yue-Qing Yu

College of Mechanical Engineering and Applied
Electronics Technology,
Beijing University of Technology,
Beijing 100124, China
e-mail: yqyu@bjut.edu.cn

1Corresponding author.

Manuscript received May 1, 2016; final manuscript received January 20, 2017; published online March 20, 2017. Assoc. Editor: Larry L Howell.

J. Mechanisms Robotics 9(3), 031005 (Mar 20, 2017) (8 pages) Paper No: JMR-16-1127; doi: 10.1115/1.4035986 History: Received May 01, 2016; Revised January 20, 2017

The pseudo-rigid-body model (PRBM) used to simulate compliant beams without inflection point had been well developed. In this paper, two types of PRBMs are proposed to simulate the large deflection of flexible beam with an inflection point in different configurations. These models are composed of five rigid links connected by three joints added with torsional springs and one hinge without spring representing the inflection point in the flexural beam. The characteristic radius factors of the PRBMs are determined by solving the objective function established according to the relative angular displacement of the two rigid links jointed by the hinge via genetic algorithm. The spring stiffness coefficients are obtained using a linear regression technique. The effective ranges of these two models are determined by the load index. The numerical result shows that both the tip locus and inflection point of the flexural beam with single inflection can be precisely simulated using the model proposed in this paper.

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Fig. 1

Flexural beam with an inflection point

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Fig. 2

Pseudo-rigid-body models for the flexural beam with an inflection point: (a) the RRHR PRBM and (b) the RHRR PRBM

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Fig. 3

Compliant link considered as two segments simulated and their PRBMs: (a) segment I, (b) segment II, (c) 2R PRBM of segment I, (d) 1R PRBM of segment II, (e) 1R PRBM of segment I, and (f) 2R PRBM of segment II

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Fig. 4

Configurations of flexural beam with the increasing κ

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Fig. 5

Flow chart of determining the objective function Ea

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Fig. 6

Max tip-locus error of two PRBMs with n = 0

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Fig. 7

Max tip-locus error of two PRBMs with n = 1

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Fig. 8

Max tip-locus error of two PRBMs with n = 2

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Fig. 9

Configuration of flexible beam and two PRBMs for various load indices κ




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