Technical Brief

An Optimal Parametrization Scheme for Path Generation Using Fourier Descriptors for Four-Bar Mechanism Synthesis

[+] Author and Article Information
Shashank Sharma, Anurag Purwar, Q. Jeffrey Ge

Computer-Aided Design and Innovation Lab,
Department of Mechanical Engineering,
Stony Brook University,
Stony Brook, NY 11794-2300

1Corresponding author.

Contributed by the Computers and Information Division of ASME for publication in the JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Manuscript received March 29, 2018; final manuscript received September 21, 2018; published online October 18, 2018. Assoc. Editor: Joshua Summers.

J. Comput. Inf. Sci. Eng 19(1), 014501 (Oct 18, 2018) (5 pages) Paper No: JCISE-18-1079; doi: 10.1115/1.4041566 History: Received March 29, 2018; Revised September 21, 2018

Fourier descriptor (FD)-based path synthesis algorithms for generation of planar four-bar mechanisms require assigning time parameter values to the given points along the path. An improper selection of time parameters leads to poor fitting of the given path and suboptimal four-bar mechanisms while also ignoring a host of mechanisms that could be potentially generated otherwise. A common approach taken is to use uniform time parameter values, which does not take into account the unique harmonic properties of the coupler path. In this paper, we are presenting a nonuniform parametrization scheme in conjunction with an objective function that provides a better fit, leverages the harmonics of the four-bar coupler, and allows imposing additional user-specified constraints.

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Fig. 2

A planar four-bar mechanism showing dimensional parameters

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Fig. 1

Path generation of two four-bar mechanisms; one using uniform parametrization while the other using optimal nonuniform parametrization

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Fig. 5

Comparison of task curve speeds obtained with and without speed criteria

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Fig. 3

Synthesized solutions using different parametrizations: (a) uniform parametrization, (b) optimal parametrization, and (c) optimal parametrization with speed criteria

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Fig. 4

Comparison of task curve and coupler curve weighted FDs for uniform and optimal parametrization



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