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Research Papers: Power Transmissions and Gearing

Generation of Epicyclic Gear Trains of One Degree of Freedom

[+] Author and Article Information
Y. V. Rao

 Mahaveer Institute of Science and Technology (MIST), 22-49/4, II Floor, SR Residency, V V Nagar, Dilsukhnagar, Hyderabad, Andhra Pradesh 500 060, India

A. C. Rao

 Disha Institute of Management and Technology, DIMT, Indore, India

J. Mech. Des 130(5), 052604 (Apr 08, 2008) (8 pages) doi:10.1115/1.2890107 History: Received April 24, 2007; Revised September 14, 2007; Published April 08, 2008

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.

Copyright © 2008 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

A simple gear train

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Figure 2

Functional diagram of a 3-link PGT in Fig. 1

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Figure 3

Graph of a 3-link PGT in Fig. 1

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Figure 4

Graph of a 4-link PGT

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Figure 5

Graph of a 5-link PGT

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Figure 6

Graph of another 5-link PGT

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Figure 7

Graph of third 5-link PGT

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Figure 8

Rotation graph of 5-link PGT in Fig. 7

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Figure 9

Graph of another 4-link PGT

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Figure 10

Graph of third 4-link PGT

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Figure 11

Rotation graph of 4-link PGT in Fig. 4

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Figure 12

Rotation graph of 4-link PGT in Fig. 9

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Figure 13

Graph of fourth 4-link PGT

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Figure 14

Rotation graph of 4-link PGT in Fig. 3

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Figure 15

Rotation graph of 4-link PGT in Fig. 1

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Figure 16

Graph of another 4-link PGT

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Figure 17

Graph of another 4-link PGT

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