New planetary gear trains (PGTs) are generated using graph theory. A geared kinematic chain is converted to a graph and a graph in turn is algebraically represented by a vertex-vertex adjacency matrix. Checking for isomorphism needs to be an integral part of the enumeration process of PGTs. Hamming matrix is written from the adjacency matrix, using a set of rules, which is adequate to detect isomorphism in PGTs. The present work presents the twin objectives of testing for isomorphism and compactness using the Hamming matrices and moment matrices.
Issue Section:
Power Transmissions and Gearing
Topics:
Chain,
Displacement,
Gears,
Planetary gears,
Rotation,
String,
Trains,
Kinematic chains,
Degrees of freedom
1.
Levai
, Z.
, 1968, “Structure and Analysis of Planetary Gear Trains
,” J. Mech.
0022-2569, 3
, pp. 131
–148
.2.
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
.3.
Ravishankar
, R.
, and Mruthyunjaya
, T. S.
, 1985, “Computerized Synthesis of Structure of Geared Kinematic Chains
,” Mech. Mach. Theory
0094-114X, 20
, pp. 367
–387
.4.
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.
0738-0666, 109
, pp. 329
–336
.5.
Hsu
, C. H.
, and Hsu
, J. J.
, 1997, “An Efficient Methodology for the Structural Synthesis of Geared Kinematic Chains
,” Mech. Mach. Theory
0094-114X, 32
, pp. 957
–973
.6.
Rao
, A. C.
, 1997, “Hamming Number Technique—I: Further Applications
,” Mech. Mach. Theory
0094-114X, 32
, pp. 477
–488
.7.
Rao
, A. C.
, and Varadaraju
, D.
, 1991, “Application of Hamming Number Technique to Detect Isomorphism Among Kinematic Chains and Inversions
,” Mech. Mach. Theory
0094-114X, 26
, pp. 55
–75
.8.
Freudenstein
, F.
, 1971, “An Application of Boolean Algebra to the Motion of Epicyclic Drives
,” ASME J. Eng. Ind.
0022-0817, 93
, pp. 176
–182
.9.
Hsu
, C.-H.
, and Lam
, K.-T.
, 1993, “Automatic Analysis of the Kinematic Structure of Planetary Gear Trains
,” ASME J. Mech. Des.
1050-0472, 115
, pp. 631
–638
.10.
Rao
, A. C.
, and Jagadeesh
, A.
, 1999, “Isomorphism, Inversions, Symmetry and Parallelism With Particular Reference to Manipulators
,” Journal of Institution of Engineers (I)
, 80
, pp. 70
–73
.11.
Kim
, J. U.
, and Kwak
, B. M.
, 1990, “Application of Edge Permutation Group to Structural Synthesis of Epicyclic Gear Trains
,” Mech. Mach. Theory
0094-114X, 25
, pp. 563
–573
.12.
Shin
, J. K.
, and Krishnamurthy
, S.
, 1993, “Standard Code Technique in Enumeration of Epicyclic Gear Trains
,” Mech. Mach. Theory
0094-114X, 28
, pp. 347
–355
.Copyright © 2008
by American Society of Mechanical Engineers
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