A procedure for the enumeration of the graphs of 1-dof planetary gear trains is presented. The planetary gear trains enumerated have a single input shaft and a single output shaft. These gear trains should satisfy certain functional constraints that avoid the existence of idle links. These constraints are derived. The enumeration of the graphs exploits the resulting particular features of the structure of planetary gear trains by proceeding gradually through different levels of that structure. The procedure includes a check for isomorphism among the resulting graphs. Finally, the graphs of the planetary gear trains having up to 9 links are presented. Those graphs containing embedded structures are identified.

1.
Buchsbaum
,
F.
, and
Freudenstein
,
F.
,
1970
, “
Synthesis of Kinematic Structure of Geared Kinematic Chains and other Mechanisms
,”
J. Mech.
,
5
, pp.
357
392
.
2.
Ravisankar
,
R.
, and
Mruthyunjaya
,
T. S.
,
1985
, “
Computerized Synthesis of the Structure of Geared Kinematics Chains
,”
Mech. Mach. Theory
,
20
, pp.
367
387
.
3.
Tsai
,
L. W.
,
1987
, “
An Application of the Linkage Characteristic Polynomial to the Topological Synthesis of Epicyclic Gear Trains
,”
ASME J. Mech., Transm., Autom. Des.
,
109
, pp.
329
336
.
4.
Kim
,
J. U.
, and
Kwak
,
B. M.
,
1990
, “
Application of Edge Permutation Group to Structural Synthesis of Epicyclic Gear Trains
,”
Mech. Mach. Theory
,
25
, pp.
563
574
.
5.
Shin
,
J. K.
, and
Krishnamurthy
,
S.
,
1993
, “
Standard Code Technique in the Enumeration of Epicylic Gear Trains
,”
Mech. Mach. Theory
,
28
, pp.
347
355
.
6.
Hsu
,
C. H.
, and
Hsu
,
J. J.
,
1997
, “
An Efficient Methodology for the Structural Synthesis of Geared Kinematic Chains
,”
Mech. Mach. Theory
,
32
, pp.
957
973
.
7.
Olson
,
D. G.
,
Erdman
,
A. G.
, and
Riley
,
D. R.
,
1991
, “
Topological Analysis of Single-Degree-of-Freedom Planetary Gear Trains
,”
ASME J. Mech. Des.
,
113
, pp.
10
16
.
8.
Hsu
,
C. H.
, and
Lam
,
K. Y.
,
1992
, “
A New Graph Representation for the Automatic Kinematic Analysis of Planetary Spur-Gear Trains
,”
ASME J. Mech. Des.
,
114
, pp.
196
200
.
9.
Freudenstein
,
F.
,
1971
, “
An Application of Boolean Algebra to the Motion of Epicyclic Drives
,”
ASME J. Ind.
,
93
, pp.
176
182
.
10.
Gibson
,
D.
, and
Kramer
,
S.
,
1984
, “
Symbolic Notation and Kinematics Equation of Motion of the Twenty-two Basic Spur Planetary Gear Trains
,”
ASME J. Mech., Transm., Autom. Des.
,
106
, pp.
333
340
.
11.
Hsu
,
C. H.
, and
Lam
,
K. Y.
,
1993
, “
Automatic Analysis of Kinematic Structure of Planetary Gear Trains
,”
ASME J. Mech. Des.
,
115
, pp.
631
638
.
12.
Hsu
,
C. H.
,
1994
, “
Displacement Isomorphism of Planetary Gear Trains
,”
Mech. Mach. Theory
,
29
, pp.
513
523
.
13.
Hsu
,
C. H.
, and
Wu
,
Y. C.
,
1997
, “
Automatic Detection of Embedded Structure in Planetary Gear Trains
,”
ASME J. Mech. Des.
,
119
,
315
318
.
14.
Mathis
,
R.
, and
Re´mond
,
Y.
,
1999
, “
A New Approach to Solving the Inverse Problem for Compound Gear Trains
,”
ASME J. Mech. Des.
,
121
, pp.
98
106
.
You do not currently have access to this content.