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Research Papers

On the Extension of a Fourier Descriptor Based Method for Planar Four-Bar Linkage Synthesis for Generation of Open and Closed Paths

[+] Author and Article Information
Jun Wu

 Computational Design Kinematics Lab, Department of Mechanical Engineering, Stony Brook University, Stony Brook, NY 11794-2300

Q. J. Ge1

 Computational Design Kinematics Lab, Department of Mechanical Engineering, Stony Brook University, Stony Brook, NY 11794-2300Qiaode.Ge@stonybrook.edu

Feng Gao, W. Z. Guo

 State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai 200240, China

1

Corresponding author.

J. Mechanisms Robotics 3(3), 031002 (Jul 12, 2011) (8 pages) doi:10.1115/1.4004227 History: Received April 11, 2010; Revised March 27, 2011; Accepted April 13, 2011; Published July 12, 2011; Online July 12, 2011

In an earlier work, we have presented an efficient method for synthesizing crank-rocker mechanisms that are capable of generating perceptually simple and smooth low harmonic closed curves. In this paper, we seek to extend this approach to the synthesis of planar four-bar linkages for the generation of open curves. Instead of using Fourier transform that requires a function to be defined over the entire period, we combine finite Fourier series in a curve fitting scheme for the approximation of periodic as well as nonperiodic paths. This yields a general method for planar four-bar path generation that is applicable to both closed and open paths.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

A crank-rocker mechanism

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Figure 2

The flow chart of the synthesis algorithm

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Figure 3

(a) The given closed path; (b) the synthesized four-bar linkage and the path it generates

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Figure 4

Structural error I as a function of the initial input angle

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Figure 5

(a) The given open path; (b) the synthesized four-bar linkage and the path it generates

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Figure 6

The synthesized mechanisms for the generation of low harmonic curve segment and line-segment. The given paths and the synthesized curves are represented by circular dots and solid curves, respectively. (a) The structural error I is 0.0677. The running time is 22.0938 s. (b) The structural error I is 0.0049. The running time is 21.8281 s. (c) The structural error I is 0.0016. The running time is 28.5000 s. (d) The structural error I is 0.0017, and the running time is 52.7813 s. (e) The structural error I is 0.0016, and the running time is 58.2656 s. (f) The structural error I is 0.0015, and the running time is 178.75 s.

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