The identification of link adjacency and joint incidence of kinematic chains and mechanisms is important and essential prior to the task of conceptual mechanism design. A careful observation method can be done in general; however, a computational approach is particularly needed for the design automation and algorithmic enumeration. This paper proposes a systematic approach for this goal in which a pseudogenetic concept is employed. The graph identification is then generalized from which the identifications of kinematic chains and mechanisms are automatically mapped. The illustrative examples show that the computation is simple and easily programmable. This development is helpful for the automated structural synthesis of mechanisms.

1.
Freudenstein
,
F.
, and
Dobrjanskyj
,
L.
, 1964, “
On a Theory for the Type Synthesis of Mechanisms
,”
Proceedings of 11th International Conference Applied Mechanics
, pp.
420
428
.
2.
Crossley
,
F. R. E.
, 1965, “
The Permutations of Kinematic Chains of Eight Member or Less from the Graph-Theoretic Viewpoint
,”
Developments in Theoretical and Applied Mechanisms
,
W. A.
Shaw
ed.,
Pergamon
,
Oxford
, Vol.
2
, pp.
467
486
.
3.
Johnson
,
R. C.
, 1967, “
Creative Design of Epicyclic Gear Chains Using Number Synthesis
,”
ASME J. Eng. Ind.
0022-0817,
89
, pp.
309
314
.
4.
Woo
,
L.
, 1967, “
Type Synthesis of Planar Linkages
,”
ASME J. Eng. Ind.
0022-0817,
89
, pp.
159
172
.
5.
Buchsbaum
,
F.
, and
Freudenstein
,
F.
, 1970, “
Synthesis of Kinematic Structure of Geared Kinematic Chains and Other Mechanisms
,”
J. Mech.
0022-2569,
5
, pp.
357
392
.
6.
Huang
,
M.
, and
Soni
,
A. H.
, 1973, “
Application of Linear and Nonlinear Graphs in Structural Synthesis of Kinematic Chains
,”
ASME J. Eng. Ind.
0022-0817,
95
, pp.
525
532
.
7.
Freudenstein
,
F.
, and
Maki
,
E. R.
, 1979, “
The Creation of Mechanisms According to Kinematic Structure and Function
,”
Environ. Plann. B
0308-2164,
6
, pp.
375
391
.
8.
Erdman
,
A. G.
,
Nelson
,
E.
,
Peterson
,
J.
, and
Bowen
,
J.
, 1981, “
Type and Dimensional Synthesis of Casement Window Mechanisms
,” ASME Paper No. 80-DET-78.
9.
Yan
,
H. S.
, and
Hsu
,
C. H.
, 1983, “
A Method for the Type Synthesis of New Mechanisms
,”
J. Chin. Soc. Mech. Eng. (Taiwan)
,
4
(
1
), pp.
11
23
.
10.
Yan
,
H. S.
, and
Chen
,
J. J.
, 1985, “
Creative Design of a Wheel Damping Mechanism
,”
Mech. Mach. Theory
0094-114X,
20
(
6
), pp.
597
600
.
11.
Yan
,
H. S.
, and
Hwang
,
Y. W.
, 1991, “
The Specialization of Mechanisms
,”
Mech. Mach. Theory
0094-114X,
26
(
6
), pp.
541
551
.
12.
Yan
,
H. S.
, 1992, “
A Methodology for Creative Mechanism Design
,”
Mech. Mach. Theory
0094-114X,
27
(
3
), pp.
235
242
.
13.
Yan
,
H. S.
, and
Hung
,
C. C.
, 2006, “
Identifying and Counting the Number of Mechanisms From Kinematic Chains Subject to Design Constraints
,”
ASME J. Mech. Des.
1050-0472,
128
(
5
), pp.
1177
1182
.
14.
Hung
,
C. C.
,
Yan
,
H. S.
, and
Pennock
,
G. R.
, 2008, “
A Procedure to Count the Number of Planar Mechanisms Subject to Design Constraints from Kinematic Chains
,”
Mech. Mach. Theory
0094-114X,
43
(
6
), pp.
676
694
.
15.
Lu
,
Y.
, and
Leinonen
,
T.
, 2005, “
Type Synthesis of Unified Planar-Spatial Mechanisms by Systematic Linkage and Topology Matrix-Graph Technique
,”
Mech. Mach. Theory
0094-114X,
40
(
10
), pp.
1145
1163
.
16.
Mruthyunjaya
,
T. S.
, and
Raghavan
,
M. R.
, 1979, “
Structural Analysis of Kinematic Chains and Mechanisms Based on Matrix Representation
,”
ASME J. Mech. Des.
1050-0472,
101
(
3
), pp.
488
494
.
17.
Uicker
,
J. J.
, and
Raicu
,
A.
, 1975, “
A Method for the Identification of and Recognition of Equivalence of Kinematic Chains
,”
Mech. Mach. Theory
0094-114X,
10
(
5
), pp.
375
383
.
18.
Yan
,
H. S.
, and
Hall
,
A. S.
, 1981, “
Linkage Characteristic Polynomials: Definitions, Coefficients by Inspection
,”
ASME J. Mech. Des.
1050-0472,
103
(
3
), pp.
578
584
.
19.
Yan
,
H. S.
, and
Hall
,
A. S.
, 1982, “
Linkage Characteristic Polynomials: Assembly, Theorems, Uniqueness
,”
ASME J. Mech. Des.
1050-0472,
104
(
1
), pp.
11
20
.
20.
Yan
,
H. S.
, and
Hwang
,
W. M.
, 1984, “
Linkage Path Code
,”
Mech. Mach. Theory
0094-114X,
19
(
4–5
), pp.
425
429
.
21.
Sohn
,
W. J.
, and
Freudenstein
,
F.
, 1986, “
An Application of Dual Graphs to the Automatic Generation of the Kinematic Structures of Mechanisms
,”
ASME J. Mech., Transm., Autom. Des.
0738-0666,
108
(
3
), pp.
392
398
.
22.
Ambekar
,
A. G.
, and
Agrawal
,
V. P.
, 1987, “
Canonical Numbering of Kinematic Chains and Isomorphism Problem: Min Code
,”
Mech. Mach. Theory
0094-114X,
22
(
5
), pp.
453
461
.
23.
Shin
,
J. K.
, and
Krishnamurty
,
S.
, 1992, “
Development of a Standard Code for Colored Graphs and Its Application to Kinematic Chains
,”
ASME J. Mech. Des.
1050-0472,
114
(
1
), pp.
189
196
.
24.
Rao
,
A. C.
, and
Varada
,
R. D.
, 1991, “
Application of the Hamming Number Technique to Detect Isomorphism Among Kinematic Chains and Inversion
,”
Mech. Mach. Theory
0094-114X,
26
(
1
), pp.
55
75
.
25.
Rao
,
A. C.
, and
Rao
,
C. N.
, 1993, “
Loop Based Pseudo Hamming Values-1 Testing Isomorphism and Rating Kinematic Chains
,”
Mech. Mach. Theory
0094-114X,
28
(
1
), pp.
113
127
.
26.
Rao
,
A. C.
, and
Rao
,
C. N.
, 1993, “
Loop Based Pseudo Hamming Values-2 Inversions, Preferred Frames and Actuator
,”
Mech. Mach. Theory
0094-114X,
28
(
1
), pp.
129
143
.
27.
Chu
,
J. K.
, and
Cao
,
W. Q.
, 1994, “
Identification of Isomorphism Among Kinematic Chains and Inversions Using Link’s Adjacent Chain Table
,”
Mech. Mach. Theory
0094-114X,
29
(
1
), pp.
53
58
.
28.
He
,
P. R.
,
Zhang
,
W. J.
,
Li
,
Q.
, and
Wu
,
F. X.
, 2003, “
A New Method for Detection of Graph Isomorphism Based on the Quadratic Form
,”
ASME J. Mech. Des.
1050-0472,
125
(
3
), pp.
640
642
.
29.
Pavan Sunkari
,
R.
, and
Schmidt
,
L. C.
, 2006, “
Reliability and Efficiency of the Existing Spectral Methods for Isomorphism Detection
,”
ASME J. Mech. Des.
1050-0472,
128
(
6
), pp.
1246
1252
.
30.
Ding
,
H.
,
Huang
,
Z.
, and
Cao
,
Y.
, 2006, “
Topological Graphs Creation Automatically of Kinematic Chains and Atlas Database Establishment
,”
Chin. J. Mech. Eng.
0577-6686,
42
(
4
), pp.
32
36
.
31.
Ding
,
H.
, and
Huang
,
Z.
, 2007, “
The Establishment of the Canonical Perimeter Topological Graph of Kinematic Chains and Isomorphism Identification
,”
ASME J. Mech. Des.
1050-0472,
129
(
9
), pp.
915
923
.
32.
Ding
,
H.
, and
Huang
,
Z.
, 2007, “
A Unique Representation of the Kinematic Chain and the Atlas Database
,”
Mech. Mach. Theory
0094-114X,
42
(
6
), pp.
637
651
.
33.
Rao
,
A. C.
, 2000, “
A Genetic Algorithm for Topological Characteristics of Kinematic Chains
,”
ASME J. Mech. Des.
1050-0472,
122
(
2
), pp.
228
231
.
34.
Rao
,
A. C.
, 2003, “
A Genetic Algorithm for Epicyclic Gear Trains
,”
Mech. Mach. Theory
0094-114X,
38
(
2
), pp.
135
147
.
35.
Rao
,
A. C.
, 2006, “
Pseudogenetic Algorithm for Evaluation of Kinematic Chains
,”
Mech. Mach. Theory
0094-114X,
41
(
4
), pp.
473
485
.
36.
West
,
D. B.
, 2001,
Introduction to Graph Theory
, 2nd ed.,
Prentice Hall
,
Upper Saddle River, NJ
.
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