In an earlier work, we have combined a curve fitting scheme with a type of shape descriptor, Fourier descriptor (FD), to develop a unified method to the synthesis of planar four-bar linkages for generation of both open and closed paths. In this paper, we aim to extend the approach to the synthesis of planar four-bar linkages for motion generation in an FD-based motion fitting scheme. Using FDs, a given motion is represented by two finite harmonic series, one for translational component of the motion and the other for rotational component. It is shown that there is a simple linear relationship between harmonic content of the rotational component and that of the translational component for a planar four-bar coupler motion. Furthermore, it is shown that the rotational component of the given motion identifies a subset of design parameters of a four-bar linkage including link ratios, while the translational component determines the rest of the design parameters such as locations of the fixed pivots. This leads naturally to a decomposed design space for four-bar mechanism synthesis for approximate motion generation.

References

References
1.
Wu
,
J.
,
Ge
,
Q. J.
,
Gao
,
F.
, and
Guo
,
W. Z.
,
2011
, “
On the Extension of a FD Based Method for Planar Four-Bar Linkage Synthesis for Generation of Open and Closed Paths
,”
ASME J. Mech. Rob.
,
3
(
3
), p.
031002
.
2.
Freudenstein
,
F.
,
1959
, “
Harmonic Analysis of Crank-and-Rocker Mechanisms With Application
,”
ASME J. Appl. Mech.
,
26
, pp.
673
675
.
3.
Funabashi
,
H.
, and
Freudenstein
,
F.
,
1979
, “
Performance Criteria for High-Speed Crank-and-Rocker Linkages—Part I: Plane Crank-and-Rocker Linkages
,”
ASME J. Mech. Des.
,
101
(
1
), pp.
20
25
.
4.
Fanhang
,
K.
,
Midha
,
A.
, and
Bajaj
,
A.
,
1988
, “
Synthesis of Harmonic Motion Generating Linkages—Part I: Function Generation
,”
ASME J. Mech. Transm. Autom. Des.
,
110
(
1
), pp.
16
21
.
5.
Fanhang
,
K.
,
Midha
,
A.
, and
Bajaj
,
A.
,
1988
, “
Synthesis of Harmonic Motion Generating Linkages—Part II: Path and Motion Generation
,”
ASME J. Mech. Transm. Autom. Des.
,
110
(
1
), pp.
22
27
.
6.
Chu
,
J.
, and
Cao
,
W.
,
1993
, “
Synthesis of Coupler Curves of Planar Four-Bar Linkages Through Fast Fourier Transform
,”
Chin. J. Mech. Eng.
,
29
(
5
), pp.
117
122
.
7.
McGarva
,
J.
, and
Mullineux
,
G.
,
1993
, “
Harmonic Representation of Closed Curves
,”
Appl. Math. Modell.
,
17
(
4
), pp.
213
218
.
8.
McGarva
,
J.
,
1994
, “
Rapid Search and Selection of Path Generating Mechanisms From a Library
,”
Mech. Mach. Theory
,
29
(
2
), pp.
223
235
.
9.
Ullah
,
L.
, and
Kota
,
S.
,
1997
, “
Optimal Synthesis of Mechanisms for Path Generation Using Fourier Descriptor and Global Search Methods
,”
ASME J. Mech. Des.
,
119
(
4
), pp.
504
510
.
10.
Chu
,
J. K.
, and
Wang
,
L. D.
,
2004
, “
Relationship Between Properties of Coupler Curve and Link Dimensions in 4-Bar Mechanisms
,”
Sci. Chin. Ser. E: Technol. Sci.
,
347
, pp.
753
762
.
11.
Nie
,
X.
, and
Krovi
,
V.
,
2005
, “
Fourier Methods for Kinematic Synthesis of Coupled Serial Chain Mechanisms
,”
ASME J. Mech. Des.
,
127
(
1
), pp.
232
241
.
12.
Chu
,
J.
, and
Sun
,
J.
,
2010
, “
A New Approach to Dimensional Synthesis of Spatial Four-Bar Linkage Through Numerical Atlas Method
,”
ASME J. Mech. Rob.
,
2
(
4
), p.
041004
.
13.
Chu
,
J.
, and
Sun
,
J.
,
2010
, “
Numerical Atlas Method for Path Generation of Spherical Four-Bar Mechanism
,”
Mech. Mach. Theory
,
45
(
6
), pp.
867
879
.
14.
Sun
,
J.
, and
Chu
,
J.
,
2010
, “
Fourier Series Representation of the Coupler Curves of Spatial Linkages
,”
Appl. Math. Model.
,
34
(
5
), pp.
1396
1403
.
15.
McCarthy
,
J. M.
,
1990
,
Introduction to Theoretical Kinematics
,
MIT
,
Cambridge, MA
.
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