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Technical Brief

Accuracy Assessment of Pseudo-Rigid-Body Model for Dynamic Analysis of Compliant Mechanisms

[+] Author and Article Information
Na Li

Department of Mechanical and Electrical Engineering,
Hebei Agricultural University,
Baoding 071001, China;
Department of Mechanical and Aerospace Engineering,
The Ohio State University,
Columbus, OH 43210

Hai-Jun Su

Department of Mechanical and Aerospace Engineering,
The Ohio State University,
Columbus, OH 43210
e-mail: su.298@osu.edu

Xian-Peng Zhang

Department of Mechanical and Electrical Engineering,
Hebei Agricultural University,
Baoding 071001, China

1Corresponding author.

Manuscript received January 4, 2017; final manuscript received June 16, 2017; published online August 4, 2017. Assoc. Editor: James J. Joo.

J. Mechanisms Robotics 9(5), 054503 (Aug 04, 2017) (10 pages) Paper No: JMR-17-1004; doi: 10.1115/1.4037186 History: Received January 04, 2017; Revised June 16, 2017

Dynamic characteristics analysis is very important for the design and application of compliant mechanisms, especially for dynamic and control performance in high-speed applications. Although pseudo-rigid-body (PRB) models have been extensively studied for kinetostatic analysis, their accuracy for dynamic analysis is relatively less evaluated. In this paper, we first evaluate the accuracy of the PRB model by comparing against the continuum model using dynamic simulations. We then investigate the effect of mass distribution on dynamics of PRB model for compliant parallel-guided mechanisms. We show that when the beam mass is larger than 10% of the motion stage, the error is significant. We then propose a new PRB model with a corrected mass distribution coefficient which significantly reduces the error of the PRB model. And the dynamic responses are also analyzed according to the corrected mass distribution coefficient. At last, a compliant double parallel-guiding mechanism is used as a case study for validation of the new PRB model for dynamics of compliant mechanisms.

Copyright © 2017 by ASME
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Figures

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Fig. 1

(a) The structural parameters of a compliant parallel guide mechanism. The beams have a uniform cross section. The second moment of area is I, and the elastic modulus of the material is E. (b) The continuum model in abaqus. The beams are modeled using Beam21 elements in continuum model. (c) The PRB model in adams. The parallel guide mechanism is equivalent to a parallel four-bar linkage with four torsional springs in PRB model.

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Fig. 2

The frequency of PRB model fPRB and continuum model fc versus the mass ratio of stage and beams χ

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Fig. 3

The error distribution of frequency between the continuum model and the PRB model versus the mass ratio χ

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Fig. 4

The relationship between mass distribution coefficient η and mass ratio χ∈[0  1000]

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Fig. 5

The relationship between mass distribution coefficient η and mass ratio χ∈[0  10]

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Fig. 6

The main parameters of PRB model with correction coefficient of mass distribution. The characteristic radius factor γ = 0.85. The mass distribution coefficient η is given in Eq. (5).

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Fig. 7

The frequency comparison between the PRB model with and without the application of correction mass coefficient and continuum model (a) and the error of frequency (b)

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Fig. 8

The displacement comparison between the PRB model with and without the application of correction mass coefficient and continuum model with different mass ratio

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Fig. 9

The velocity comparison between the PRB model with and without the application of correction mass coefficient and continuum model with different mass ratio

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Fig. 10

The acceleration comparison between the PRB model with and without the application of correction mass coefficient and continuum model with different mass ratio

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Fig. 11

The PRB model of compliant double parallel-guiding mechanism for dynamics

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Fig. 12

The frequencies of second stage during dynamic analysis based on the PRB model and continuum model

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Fig. 13

The frequency error of the PRB model without correction mass distribution coefficient (left) and with the correction mass distribution coefficient (right) comparing against with the continuum model

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Fig. 14

The displacement comparison of compliant double parallel-guiding mechanism between the PRB model with and without the application of correction mass coefficient and continuum model with different mass ratio

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Fig. 15

The velocity comparison of compliant double parallel guiding mechanism between the PRB model with and without the application of correction mass coefficient and continuum model with different mass ratio

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Fig. 16

The acceleration comparison of compliant double parallel-guiding mechanism between the PRB model with and without the application of correction mass coefficient and continuum model with different mass ratio

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