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Research Papers: Design of Mechanisms and Robotic Systems

Dynamic Analysis of Planar Mechanisms With Fuzzy Joint Clearance and Random Geometry

[+] Author and Article Information
Dongyang Sun

College of Aerospace Engineering,
Chongqing University,
Chongqing 400044, China
e-mail: dongyangsunnuaa@gmail.com

Yan Shi

State Key Laboratory of Mechanics and
Control of Mechanical Structures,
Nanjing University of
Aeronautics and Astronautics,
Nanjing 210016, China
e-mail: yshi@nuaa.edu.cn

Baoqiang Zhang

School of Aerospace Engineering,
Xiamen University,
Xiamen 361005, China
e-mail: bqzhang@xmu.edu.cn

1Corresponding author.

2D. Sun and Y. Shi contributed equally to this work.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received April 1, 2018; final manuscript received November 19, 2018; published online January 11, 2019. Assoc. Editor: Joo H. Kim.

J. Mech. Des 141(4), 042301 (Jan 11, 2019) (9 pages) Paper No: MD-18-1273; doi: 10.1115/1.4042111 History: Received April 01, 2018; Revised November 19, 2018

The dynamic characteristics of planar mechanisms with fuzzy joint clearance and random geometry are studied in this paper. The dynamics model for the mechanism is constructed by utilizing Baumgarte approach in which the clearance size is a fuzzy number, while the geometry parameters are assumed as random variables. A hybrid contact force model, which consists of the Lankarani–Nikravesh model, improved Winkler elastic foundation model and modified Coulomb friction force model, is applied to construct revolute clearance joint. In order to solve the dynamics model, two methodologies are developed: confidence region method for quantification of random and fuzzy uncertainties (CRMQRFU) and confidence region method with transformation method (CRMTM). In the CRMQRFU, fuzzy numbers are first decomposed into intervals under the given membership level. Then, a general framework is proposed for quantification of random and interval uncertainties in the mechanism. In the CRMTM, a transformation method is applied to transform intervals into deterministic arrays, while probability theory is used to obtain the confidence regions under the given fuzzy values. The confidence region, considering random and fuzzy uncertainties, is obtained by fuzzy set theory. Finally, two examples are used to demonstrate the validity and feasibility of these methods.

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Figures

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Fig. 1

Schematic illustration of revolute clearance joint

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Fig. 2

The modified Coulomb friction force model

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Fig. 3

The α-cut for a triangular fuzzy number with membership function μà at membership level

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Fig. 4

Slider-crank mechanism with clearance

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Fig. 5

Slider displacement errors with different uncertain parameters at α-cut 0

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Fig. 6

Slider displacement errors for isosceles triangular membership function and nonlinear membership function at cases of (a) α-cut 0, (b) α-cut 0.5, and (c) α-cut 1, respectively

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Fig. 7

Slider displacement error for nSE  =  10, 50, and 200 obtained by CRMQRFU at cases of (a) α-cut 0, (b) α-cut 0.5, and (c) α-cut 1, respectively

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Fig. 8

Slider displacement error for m = 4, 6, and 10 obtained by CRMTM at cases of (a) α-cut 0, (b) α-cut 0.5, and (c) α-cut 1, respectively

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Fig. 9

Slider displacement error obtained by CRMQRFU, CRMTM at α-cut 0 and 50 random samples

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Fig. 10

Circle trajectory tracking of the deployable mechanism with clearance joint

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Fig. 11

Trajectory errors of the mechanism for different uncertainty situations in (a) the X-direction and (b) the Y-direction, respectively

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