It is of great importance in the conceptual creative design of mechanical systems to synthesize as many feasible kinematic structures of mechanisms as possible. However, the methods for the structural synthesis of multiple joint kinematic chains are seldom addressed in literature even though they are widely used in various mechanical products. This paper proposes an automatic method to synthesize planar multiple joint kinematic chains. First, the bicolor topological graph and the bicolor contracted graph are introduced to represent the topological structures of multiple joint kinematic chains. Then, the characteristic number string of bicolor topological graphs is proposed and used to efficiently detect isomorphism in the synthesis progress. Finally, a systematic method for the synthesis of kinematic chains with one multiple joint is proposed, and the whole families of multiple joint kinematic chains with up to 16 links and all possible degrees of freedom are synthesized for the first time.

Issue Section:
Research Papers
Keywords:
multiple joint kinematic chain, structural synthesis, bicolor topological graph, characteristic number string, isomorphism identification
Topics:
Kinematic chains

References

1.
Yan
,
H. S.
,
1998
,
Creative Design of Mechanical Devices
,
Springer-Verlag
,
Singapore Pte. Ltd
.
2.
Mruthyunjaya
,
T. S.
,
2003
, “
Kinematic Structure of Mechanisms Revisited
,”
Mech. Mach. Theory
,
38
(
4
), pp.
279
–
320
.10.1016/S0094-114X(02)00120-9
3.
Kong
,
X.
, and
Gosselin
,
C.
,
2007
,
Type Synthesis of Parallel Mechanisms
,
Springer
,
New York
.
4.
Huang
,
Z.
,
Li
,
Q. C.
, and
Ding
,
H. F.
,
2012
,
Theory of Parallel Mechanisms
,
Springer
,
New York
.
5.
Manolescu
,
N. I.
,
1968
, “
For a United Point of View in the Study of the Structural Analysis of Kinematic Chains and Mechanisms
,”
J. Mech.
,
3
(
3
), pp.
149
–
169
.10.1016/0022-2569(68)90353-4
6.
Assur
,
L. V.
,
1913
, “
Investigation of Plane Hinged Mechanisms With Lower Pairs From the Point of View of Their Structure and Classification (in Russian): Part I, II
,”
Bull. Petrograd Polytech. Inst.
,
20
, pp.
329
–
386
.
7.
Assur
,
L. V.
,
1914
, “
Investigation of Plane Hinged Mechanisms With Lower Pairs From the Point of View of Their Structure and Classification (in Russian): Part I, II
,”
Bull. Petrograd Polytech. Inst.
21–23
, pp.
187
–
283
.
8.
Davies
,
T. H.
, and
Crossley
,
F. R. E.
,
1966
, “
Structural Analysis of Plane Linkages by Franke's Condensed Notation
,”
J. Mech.
,
1
(
2
), pp.
171
–
183
.10.1016/0022-2569(66)90021-8
9.
Soni
,
A. H.
,
1971
, “
Structural Analysis of Two General Constraint Kinematic Chains and Their Practical Application
,”
ASME J. Eng. Ind.
,
93B
(
1
), pp.
231
–
238
.10.1115/1.3427881
10.
Crossley
,
F. R. E.
,
1965
,
The Permutations of Kinematic Chains of Eight Members or Less From the Graph-Theoretic View Point
,”
Developments in Theoretical and Applied Mechanics
, Vol.
2
,
Pergamon
,
Oxford
, pp.
467
–
486
.
11.
Woo
,
L. S.
,
1967
, “
Type Synthesis of Plane Linkages
,”
ASME J. Eng. Ind.
,
89B
, pp.
159
–
172
.10.1115/1.3609989
12.
Dobrjanskyj
,
L.
, and
Freudenstein
,
F.
,
1967
, “
Some Applications of Graph Theory to the Structural Analysis of Mechanisms
,”
ASME J. Eng. Ind.
,
89B
, pp.
153
–
158
.10.1115/1.3609988
13.
Manolescu
,
N. I.
,
1973
, “
A Method Based on Baranov Trusses and Using Graph Theory to Find the Set of Planar Jointed Kinematic Chains and Mechanisms
,”
Mech. Mach. Theory
,
8
(
1
), pp.
3
–
22
.10.1016/0094-114X(73)90003-7
14.
Mruthyunjaya
,
T. S.
,
1979
, “
Structural Synthesis by Transformation of Binary Chains
,”
Mech. Mach. Theory
,
14
(
4
), pp.
221
–
231
.10.1016/0094-114X(79)90009-0
15.
Tuttle
,
E. R.
,
Peterson
,
S. W.
, and
Titus
,
J. E.
,
1989
, “
Further Application of Group Theory to the Enumeration and Structural Analysis of Basis Kinematic Chains
,”
ASME J. Mech., Transm., Autom. Des.
,
111
, pp.
494
–
497
.10.1115/1.3259027
16.
Tuttle
,
E. R.
,
Peterson
,
S. W.
, and
Titus
,
J. E.
,
1989
, “
Enumeration of Basis Kinematic Chains Using the Theory of Finite Groups
,”
ASME J. Mech., Transm., Autom. Des.
,
111
, pp.
498
–
503
.10.1115/1.3259028
17.
Tuttle
,
E. R.
,
1996
, “
Generation of Planar Kinematic Chains
,”
Mech. Mach. Theory
,
31
(
6
), pp.
729
–
748
.10.1016/0094-114X(95)00083-B
18.
Sohn
,
W. J.
, and
Freudenstein
,
F.
, “
An Application of Dual Graphs to the Automatic Generation of the Kinematic Structure of Mechanisms
,”
American Society of Mechanical Engineers (Paper)
(
1986
) 86-DET-1.
19.
Rao
,
A. C.
,
1997
, “
Hamming Number Technique-I: Further Applications
,”
Mech. Mach. Theory
,
32
(
4
), pp.
477
–
488
.10.1016/S0094-114X(96)00064-X
20.
Rao
,
A. C.
,
1997
, “
Hamming Number Technique-II: Generation of Planar Kinematic Chains
,”
Mech. Mach. Theory
,
32
(
4
), pp.
489
–
499
.10.1016/S0094-114X(96)00065-1
21.
Yan
,
H. S.
, and
Hwang
,
Y. W.
,
1990
, “
Number Synthesis of Kinematic Chains Based on Permutation Groups
,”
Math. Comput. Modell.
,
13
(
8
), pp.
29
–
42
.10.1016/0895-7177(90)90069-Y
22.
Yan
,
H. S.
,
1992
, “
A Methodology for Creative Mechanism Design
,”
Mech. Mach. Theory
,
27
(
3
), pp.
235
–
242
.10.1016/0094-114X(92)90013-8
23.
Hwang
,
W. M.
, and
Hwang
,
Y. W.
,
1992
, “
Computer-Aided Structural Synthesis of Planar Kinematic Chains With Simple Joints
,”
Mech. Mach. Theory
,
27
(
2
), pp.
189
–
199
.10.1016/0094-114X(92)90008-6
24.
Butcher
,
E. A.
, and
Hartman
,
C.
,
2005
, “
Efficient Enumeration and Hierarchical Classification of Planar Simple-Jointed Kinematic Chains: Application to 12- and 14-Bar Single Degree-of-Freedom Chains
,”
Mech. Mach. Theory
,
40
(
9
), pp.
1030
–
1050
.10.1016/j.mechmachtheory.2004.12.015
25.
Ding
,
H. F.
,
Hou
,
F. M.
,
Kecskeméthy
,
A.
, and
Huang
,
Z.
,
2012
, “
Synthesis of the Whole Family of Planar 1-DOF Kinematic Chains and Creation of Their Atlas Databases
,”
Mech. Mach. Theory
,
47
(
1
), pp.
1
–
15
.10.1016/j.mechmachtheory.2011.08.011
26.
Ding
,
H. F.
,
Cao
,
W. A.
,
Kecskeméthy
,
A.
, and
Huang
,
Z.
,
2012
, “
Complete Atlas Database of 2-DOF Kinematic Chains and Creative Design of Mechanisms
,”
ASME J. Mech. Des.
,
134
(
3
), p.
0310061
.10.1115/1.4005866
27.
Hsu
,
C. H.
,
1992
, “
Enumeration of Basic Kinematic Chains With Simple and Multiple Joints
,”
J. Franklin Inst.
,
329
(
4
), pp.
775
–
789
.10.1016/0016-0032(92)90088-X
28.
Chu
,
J. K.
, and
Cao
,
W. Q.
,
1998
, “
Systemics of Assur Groups With Multiple Joints
,”
Mech. Mach. Theory
,
33
(
8
), pp.
1127
–
1133
.10.1016/S0094-114X(97)00117-1
29.
Song
,
L.
, and
Yang
,
J.
,
2004
, “
Combination Method of Type Synthesis for Planar Kinematic Chain With Multiple Joints
,”
Chin. J. Mech. Eng.
,
40
(
2
), pp.
37
–
41
.10.3901/JME.2004.02.037
30.
Ding
,
H. F.
,
Zhao
,
J.
, and
Huang
,
Z.
,
2009
, “
Unified Topological Representation Models of Planar Kinematic Chains
,”
ASME J. Mech. Des.
,
131
(
11
),
p. 114503
.10.1115/1.4000215
31.
Ding
,
H. F.
,
Zhao
,
J.
, and
Huang
,
Z.
,
2010
, “
Unified Structural Synthesis of Planar Simple and Multiple Joint Kinematic Chains
,”
Mech. Mach. Theory
,
45
(
4
), pp.
555
–
568
.10.1016/j.mechmachtheory.2009.10.012
32.
Ding
,
H. F.
,
Huang
,
Z.
, and
Mu
,
D. J.
,
2008
, “
Computer-aided Structure Decomposition Theory of Kinematic Chains and Its Applications
,”
Mech. Mach. Theory
,
43
(
12
), pp.
1596
–
1609
.10.1016/j.mechmachtheory.2007.12.011
33.
Tsai
,
L. W.
,
2001
,
Mechanism Design: Enumeration of Kinematic Structures According to Function
,
CRC Press
,
Boca Raton, FL
.
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