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RESEARCH PAPERS

A New Approach to Shape Optimization for Closed Path Synthesis of Planar Mechanisms

[+] Author and Article Information
Ahmad Smaili1

Department of Mechanical and Mechatronics Engineering, Hariri Canadian University, P. O. Box 10 Damour, Chouf 2010, Lebanonsmailiaa@hcu.edu.lb

Nadim Diab

Department of Mechanical and Mechatronics Engineering, Hariri Canadian University, P. O. Box 10 Damour, Chouf 2010, Lebanon

1

Corresponding author.

J. Mech. Des 129(9), 941-948 (Oct 20, 2005) (8 pages) doi:10.1115/1.2753164 History: Received July 19, 2005; Revised October 20, 2005

A method for the synthesis of four-bar mechanisms to generate closed paths through shape optimization is herein introduced. The objective function is not based on Fourier descriptors, but rather on the cyclic angular deviation (CAD) vector associated with a set of desired points on the curve. A simple method is introduced to account for the starting point shift between the desired CAD and the generated one. Following shape optimization, a simple mathematical approach is devised to properly scale, rotate, and translate the mechanism to the desired configuration. Two case studies are presented to demonstrate the effectiveness and robustness of the proposed method.

Copyright © 2007 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Parameters of the four-bar linkage used in the text

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Figure 2

Flowchart for the ant search

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Figure 3

Angular deviations for a few points on a closed curve

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Figure 4

Original curve (a) and its scaled, rotated, and translated version (b)

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Figure 5

Circle passing through two desired points

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Figure 6

Desired trajectory and initial point chosen

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Figure 7

Shape-optimized mechanism and the generated and desired trajectories

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Figure 8

Shape-optimized mechanism and corresponding trajectories after rotation

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Figure 9

Shape-optimized mechanism and corresponding trajectories after rotation and translation operations

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Figure 11

Desired trajectory and initial point chosen

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Figure 12

Shape-optimized mechanism and corresponding desired and generated trajectories

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Figure 13

Shape-optimized mechanism and corresponding trajectory after scaling

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Figure 14

Shape-optimized mechanism and corresponding trajectory after scaling and rotation

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Figure 15

Final mechanism

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