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TECHNICAL PAPERS

Enumeration of 1-DOF Planetary Gear Train Graphs Based on Functional Constraints

[+] Author and Article Information
Jose M. del Castillo

Escuela de Ingenierias Industriales, Universidad de Extremadura, Avda. de Elvas s/n, 06071 Badajoz, Spain.e-mail: delcasti@unex.es

J. Mech. Des 124(4), 723-732 (Nov 26, 2002) (10 pages) doi:10.1115/1.1514663 History: Received January 01, 2001; Online November 26, 2002
Copyright © 2002 by ASME
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References

Buchsbaum,  F., and Freudenstein,  F., 1970, “Synthesis of Kinematic Structure of Geared Kinematic Chains and other Mechanisms,” J. Mech., 5, pp. 357–392.
Ravisankar,  R., and Mruthyunjaya,  T. S., 1985, “Computerized Synthesis of the Structure of Geared Kinematics Chains,” Mech. Mach. Theory, 20, pp. 367–387.
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.
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.
Shin,  J. K., and Krishnamurthy,  S., 1993, “Standard Code Technique in the Enumeration of Epicylic Gear Trains,” Mech. Mach. Theory, 28, pp. 347–355.
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.
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.
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.
Freudenstein,  F., 1971, “An Application of Boolean Algebra to the Motion of Epicyclic Drives,” ASME J. Ind., 93, pp. 176–182.
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.
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.
Hsu,  C. H., 1994, “Displacement Isomorphism of Planetary Gear Trains,” Mech. Mach. Theory, 29, pp. 513–523.
Hsu,  C. H., and Wu,  Y. C., 1997, “Automatic Detection of Embedded Structure in Planetary Gear Trains,” ASME J. Mech. Des., 119, 315–318.
Mathis,  R., and Rémond,  Y., 1999, “A New Approach to Solving the Inverse Problem for Compound Gear Trains,” ASME J. Mech. Des., 121, pp. 98–106.

Figures

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A planetary gear train and two possible graph representations
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Two 8-link base structures having identical link combinations
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Planet-carrier subgraphs for the link combination 2-3-3
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Assignment of gear pairs to planets of some planet-carrier subgraphs
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The four nonisomorphic planet-carrier subgraphs for the link combination 3-3-3 with jc=4
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Graphs of planetary gear trains with 4, 5 (top), 6 (middle) and 7 links (bottom)
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Graphs of planetary gear trains with 8 links
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Graphs of planetary gear trains with 9 links and link combinations 1-3-5 and 2-2-5
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Graphs of planetary gear trains with 9 links and link combination 2-3-4
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Graphs of planetary gear trains with 9 links and link combination 3-3-3
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Graphs of planetary gear trains with 9 links and link combination 3-3-3 (cont.)

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