In this paper, we describe the use of turning functions to compare errors between the coupler and the target paths. The main reason to use turning functions is that the measured error does not depend on the mechanism scale or the position and rotation of the fixed link. Therefore, the searching space for the optimization algorithm is reduced. To carry out mechanism synthesis, we use an evolutionary algorithm. The effectiveness of the proposed method has been demonstrated in five synthesis examples.

References

1.
Han
,
C.
,
1966
, “
A General Method for the Optimum Design of Mechanisms
,”
J. Mech.
,
1
(
3–4
), pp.
301
313
.10.1016/0022-2569(66)90031-0
2.
Roston
,
G. D.
, and
Sturges
,
R. H.
,
1996
, “
Genetic Algorithm Synthesis of Four-Bar Mechanisms
,”
Artif. Intell. Eng. Des. Anal. Manuf.
,
10
(
5
), pp.
371
390
.10.1017/S0890060400001700
3.
Kunjur
,
A.
, and
Krishnamurty
,
S.
,
1997
, “
Genetic Algorithms in Mechanical Synthesis
,”
ASME J. Appl. Mech. Rob.
,
4
(
2
), pp.
18
24
.
4.
Cabrera
,
J. A.
,
Simon
,
A.
, and
Prado
,
M.
,
2002
, “
Optimal Synthesis of Mechanisms With Genetic Algorithms
,”
Mech. Mach. Theory
,
37
(
10
), pp.
1165
1175
.10.1016/S0094-114X(02)00051-4
5.
Cabrera
,
J. A.
,
Ortiz
,
A.
,
Nadal
,
F.
, and
Castillo
,
J. J.
,
2011
, “
An Evolutionary Algorithm for Path Synthesis of Mechanisms
,”
Mech. Mach. Theory
,
46
(
2
), pp.
127
141
.10.1016/j.mechmachtheory.2010.10.003
6.
Fox
,
R. L.
, and
Willmert
,
K. D.
,
1967
, “
Optimum Design of Curve-Generating Linkages With Inequality Constraints
,”
ASME J. Eng. Ind.
,
89
(
1
), pp.
144
152
.10.1115/1.3609986
7.
Angeles
,
J.
,
Alivizators
,
A.
, and
Akhras
,
A.
,
1988
, “
An Unconstrained Nonlinear Least-Square Method of Optimization of RRRR Planar Path Generators
,”
Mech. Mach. Theory
,
23
(
5
), pp.
343
353
.10.1016/0094-114X(88)90048-1
8.
Zhou
,
H.
, and
Cheung
,
H. M.
,
2001
, “
Optimal Synthesis of Crank-Rocker Linkages for Path Generation Using the Orientation Structural Error of the Fixed Link
,”
Mech. Mach. Theory
,
36
(
8
), pp.
973
982
.10.1016/S0094-114X(01)00029-5
9.
Watanabe
,
K.
,
1992
, “
Application of Natural Equations to the Synthesis of Curve Generating Mechanisms
,”
Mech. Mach. Theory
,
27
(
3
), pp.
261
273
.10.1016/0094-114X(92)90016-B
10.
Ullah
,
I.
, and
Kota
,
S.
,
1997
, “
Optimal Synthesis of Mechanism for Path Generation Using Fourier Descriptor and Global Search Methods
,”
ASME J. Mech. Des.
,
119
(
4
), pp.
504
510
.10.1115/1.2826396
11.
Zahn
,
C. T.
, and
Roskies
,
R. Z.
,
1972
, “
Fourier Descriptors for Plane Closed Curves
,”
IEEE Trans. Comput.
,
C-21
(
3
), pp.
269
281
.10.1109/TC.1972.5008949
12.
Wu
,
J.
,
Ge
,
Q. J.
,
Gao
,
F.
, and
Guo
,
W. Z.
,
2011
, “
On the Extension of a Fourier Descriptor Based Method for Planar Four-Bar Linkages Synthesis for Generation of Open and Closed Paths
,”
ASME J. Mech. Rob.
,
3
(
3
), p.
031002
.10.1115/1.4004227
13.
Galán
,
G.
,
Alonso
,
F. J.
, and
Del Castillo
,
J. M.
,
2009
, “
Shape Optimization for Path Synthesis of Crank-Rocker Using a Wavelet-Based Neural Network
,”
Mech. Mach. Theory
,
44
(
6
), pp.
1132
1143
.10.1016/j.mechmachtheory.2008.09.006
14.
Sedano
,
A.
,
Sancibrian
,
R.
,
de Juan
,
A.
,
Viadero
,
F.
, and
Egaña
,
F.
,
2012
, “
Hybrid Optimization Approach for the Design of Mechanisms Using a New Error Estimator
,”
Math. Probl. Eng.
,
2012
(3), pp. 1–20.10.1155/2012/151590
15.
Smaili
,
A.
, and
Diab
,
N.
,
2007
, “
A New Approach to Shape Optimization for Closed Path Synthesis of Planar Mechanisms
,”
ASME J. Mech. Des.
,
129
(
9
), pp.
941
948
.10.1115/1.2753164
16.
Buskiewicz
,
J.
,
2010
, “
Use of Shape Invariants in Optimal Synthesis of Geared Five-Bar Linkage
,”
Mech. Mach. Theory
,
45
(2), pp.
273
290
.10.1016/j.mechmachtheory.2009.09.004
17.
Damangir
,
S.
,
Jafarijashemi
,
G.
,
Mamduhi
,
M.
, and
Zohoor
,
H.
,
2006
, “
Optimum Synthesis of Mechanisms for Path Generation Using a New Curvature Based—Deflection Based Objective Function
,”
The 6th WSEAS International Conference on Simulation, Modelling and Optimization
, Lisbon, Portugal, September 22–24, 2006, pp.
672
676
.
18.
Nie
,
X.
, and
Krovi
,
V.
,
2005
, “
Fourier Methods for Kinematic Synthesis of Coupled Serial Chain Mechanism
,”
ASME J. Mech. Des.
,
127
(
2
), pp.
232
241
.10.1115/1.1829726
19.
Kramer
,
S. N.
, and
Sandor
,
G. N.
,
1975
, “
Selective Precision Synthesis. A General Method of Optimization for Planar Mechanisms
,”
ASME J. Eng. Ind.
,
97
(
2
), pp.
689
701
.10.1115/1.3438634
20.
Sohoni
,
V. N.
, and
Haug
,
E. J.
,
1982
, “
A State Space Technique for Optimal Design of Mechanisms
,”
ASME J. Mech. Des.
,
104
(
4
), pp.
792
798
.10.1115/1.3256438
21.
Fang
,
W. E.
,
1994
, “
Simultaneous Type and Dimensional Synthesis of Mechanisms by Genetic Algorithms
,” ASME, Design Engineering Division, 23rd Biennial Mechanisms Conference, Vol. 70, pp.
35
41
.
22.
Arkin
,
E. M.
,
Chew
,
L. P.
,
Huttenlocher
,
D. P.
,
Kedem
,
K.
, and
Mitchell
,
J. S. B.
,
1991
, “
An Efficiently Computable Metric for Comparing Polygonal Shapes
,”
IEEE Trans. Pattern Anal. Mach. Intell.
,
13
(
3
), pp.
209
216
.10.1109/34.75509
23.
Volotão
,
C. F. S.
,
Santos
,
R. D.
,
Erthal
,
G. J.
, and
Dutra
,
L. V.
,
2010
, “
Shape Characterization With Turning Functions
,”
IWSSIP 2010—17th International Conference on Systems, Signals and Image Processing
.
24.
McCreath
,
E. C.
,
2008
, “
Partial Matching of Planar Polygons Under Translation and Rotation,” CCCG 2008
, Montreal, Quebec, Aug. 13–15.
25.
Carvalho
,
J. D.
,
Guliato
,
D.
,
Santiago
,
S. A.
, and
Rangayyan
,
R. M.
,
2007
, “
Polygonal Modeling of Contours Using the Turning Angle Function
,”
Canadian Conference on Electrical and Computer Engineering
, pp.
1090
1093
.
26.
Latecki
,
L. J.
, and
Lakamper
,
R.
,
2002
, “
Application of Planar Shape Comparison to Object Retrieval in Image Databases
,”
Pattern Recognit.
,
35
(
1
), pp.
15
29
.10.1016/S0031-3203(01)00039-5
27.
Latecki
,
L. J.
, and
Lakamper
,
R.
,
1999
, “
Convexity Rule for Shape Decomposition Based on Discrete Contour Evaluation
,”
Comput. Vision Image Understandings
,
73
(
3
), pp.
441
454
.10.1006/cviu.1998.0738
28.
Storn
,
R.
, and
Price
,
K.
,
1997
, “
Differential Evolution. A Simple and Efficient Heuristic Scheme for Global Optimization Over Continuos Spaces
,”
J. Global Optim.
11
(
4
), pp.
341
359
.10.1023/A:1008202821328
29.
Yates
,
R. C.
,
1952
,
A Handbook on Curves and Their Properties
,
J. W.
Edwards
, ed., J. W. Edwards,
Ann Arbor, MI
.
30.
Freudenstein
,
F.
,
1954
, “
An Analytical Approach to the Design of Four-Link Mechanisms
,”
Trans. ASME
,
76
, pp.
483
492
.
31.
Acharyya
,
S. K.
, and
Mandal
,
M.
,
2009
, “
Performance of EAs for Four-Bar Linkage Synthesis
,”
Mech. Mach. Theory
,
44
(
9
), pp.
1784
1794
.10.1016/j.mechmachtheory.2009.03.003
You do not currently have access to this content.