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Research Papers

Optimum Synthesis of Planar Mechanisms for Path Generation Based on a Combined Discrete Fourier Descriptor

[+] Author and Article Information
Wen-Yi Lin

Department of Mechanical Engineering,
De Lin Institute of Technology,
1 Lane 380, Qingyan Road, Tucheng,
New Taipei City 23654, Taiwan
e-mail: wylin@dlit.edu.tw

1Corresponding author.

Manuscript received July 29, 2014; final manuscript received April 27, 2015; published online July 17, 2015. Assoc. Editor: Andrew P. Murray.

J. Mechanisms Robotics 7(4), 041023 (Nov 01, 2015) (11 pages) Paper No: JMR-14-1180; doi: 10.1115/1.4030584 History: Received July 29, 2014; Revised April 27, 2015; Online July 17, 2015

A two-phase synthesis method is described, which is capable of solving quite challenging path generation problems. A combined discrete Fourier descriptor (FD) is proposed for shape optimization, and a geometric-based approach is used for the scale–rotation–translation synthesis. The combined discrete FD comprises three shape signatures, i.e., complex coordinates (CCs), centroid distance (CD), and triangular centroid area (TCA), which can capture greater similarity of shape. The genetic algorithm–differential evolution (GA–DE) optimization method is used to solve the optimization problem. The proposed two-phase synthesis method, based on the combined discrete FD, successfully solves the challenging path generation problems with a relatively small number of function evaluations. A more accurate path shape can be obtained using the combined FD than the one-phase synthesis method. The obtained coupler curves approximate the desired paths quite well.

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Figures

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Fig. 1

Geared 5-bar mechanism in the global coordinate system

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Fig. 2

Final synthesis mechanism when the coupler curve (not shown) is similar to the mirror-image one of the desired curve

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Fig. 3

Desired path (triangle) and the coupler curve obtained using the proposed two-phase synthesis method for problem 1

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Fig. 4

Desired path (triangle) and the coupler curve obtained by Lin [30] using the one-phase synthesis method for problem 1

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Fig. 5

Desired path (asteroid) and the coupler curve obtained using the proposed two-phase synthesis method for problem 2

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Fig. 6

Desired path (asteroid) and the coupler curve obtained by Lin [30] using the one-phase synthesis method for problem 2

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Fig. 7

Desired path (ParamCurve) and the coupler curve obtained using the proposed two-phase synthesis method for problem 3

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Fig. 8

Desired path (ParaCurve) and the coupler curve obtained by Lin [30] using the one-phase synthesis method for problem 3

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Fig. 9

Mirror-image path and the coupler curve obtained using the proposed two-phase synthesis method for problem 4 (ArcofEllipse)

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Fig. 10

Desired path (ArcofEllipse) and the coupler curve obtained by Lin [30] using the one-phase synthesis method for problem 4

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Fig. 11

(a) Original synthesis mechanism and the corresponding coupler curve and (b) final synthesis mechanism and the corresponding coupler curve for problem 4

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Fig. 12

Desired path (GLetter) and the coupler curve obtained using the proposed two-phase synthesis method for problem 5

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Fig. 13

Desired path (GLetter) and the coupler curve obtained by Lin [30] using the one-phase synthesis method for problem 5

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