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.

References

References
1.
Erdman
,
A. G.
, and
Sandor
,
G. N.
,
1991
,
Advanced Mechanism Design: Analysis and Synthesis
,
2nd ed.
, Vol.
2
,
Prentice Hall
,
Englewood Cliffs, NJ
.
2.
Nolle
,
H.
, and
Hunt
,
K. H.
,
1971
, “
Optimum Synthesis of Planar Linkages to Generate Coupler Curves
,”
J. Mech.
,
6
(
3
), p.
267
.
3.
Freudenstein
,
F.
,
1959
, “
Harmonic Analysis of Crank-and-Rocker Mechanisms With Application
,”
ASME J. Appl. Mech.
,
26
, pp.
673
675
.
4.
Ullah
,
I.
, and
Kota
,
S.
,
1997
, “
Optimal Synthesis of Mechanisms for Path Generation Using Fourier Descriptors and Global Search Methods
,”
ASME J. Mech. Des.
,
119
(
4
), pp.
504
510
.
5.
Mcgarva
,
J.
, and
Mullineux
,
G.
,
1993
, “
Harmonic Representation of Closed Curves
,”
Appl. Math. Modell.
,
17
(
4
), pp.
213
218
.
6.
Wu
,
J.
,
Ge
,
Q. J.
, and
Gao
,
F.
,
2009
, “
An Efficient Method for Synthesizing Crank-Rocker Mechanisms for Generating Low Harmonic Curves
,”
ASME
Paper No. DETC2009-87140.
7.
Wu
,
J.
,
Ge
,
Q. J.
,
Gao
,
F.
, and
Guo
,
W. Z.
,
2010
, “
On the Extension of a Fourier Descriptor Based Method for Four-Bar Linkage Synthesis for Generation of Open and Closed Paths
,”
ASME
Paper No. DETC2010-29028.
8.
Vasiliu
,
A.
, and
Yannou
,
B.
,
2001
, “
Dimensional Synthesis of Planar Mechanisms Using Neural Networks: Application to Path Generator Linkages
,”
Mech. Mach. Theory
,
36
(
2
), pp.
299
310
.
9.
Li
,
X.
,
Zhong
,
X.
, and
Ge
,
Q.
,
2015
, “
Parametrization-Independent Non-Uniform Fourier Approach to Path Synthesis of Four-Bar Mechanism
,”
14th World Congress in Mechanism and Machine Science
, Taipei, Taiwan, Oct. 25–30, pp.
440
448
.https://www.researchgate.net/publication/299410128_Parametrization-Independent_Non-Uniform_Fourier_Approach_to_Path_Synthesis_of_Four-Bar_Mechanism
10.
Li
,
X. Y.
, and
Chen
,
P.
,
2017
, “
A Parametrization-Invariant Fourier Approach to Planar Linkage Synthesis for Path Generation
,”
Math. Probl. Eng.
,
2017
, pp. 1–16.
11.
Li
,
X.
,
Wu
,
J.
, and
Ge
,
Q. J.
,
2016
, “
A Fourier Descriptor-Based Approach to Design Space Decomposition for Planar Motion Approximation
,”
ASME J. Mech. Rob.
,
8
(
6
), p.
064501
.
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