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Research Papers: Design of Direct Contact Systems

Detection of Degenerate Structure in Single Degree-of-Freedom Planetary Gear Trains

[+] Author and Article Information
Vinjamuri Venkata Kamesh

Mechanical Engineering Department,
University College of Engineering,
JNTUK,
East Godavari District,
Kakinada 533003, Andhra Pradesh, India
e-mail: kameshvv@gmail.com

Kuchibhotla Mallikarjuna Rao

Professor
Mechanical Engineering,
University College of Engineering,
JNTUK,
East Godavari District,
Kakinada 533003, Andhra Pradesh, India
e-mail: rangaraokuchibhotla@gmail.com

Annambhotla Balaji Srinivasa Rao

Professor
Mechanical Engineering,
Sri Vasavi Institute of Engineering
and Technology,
Krishna District, Pedana Mandal,
Nandamuru 534329, Andhra Pradesh, India
e-mail: absrao71@gmail.com

Contributed by the Power Transmission and Gearing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received January 13, 2017; final manuscript received April 24, 2017; published online June 15, 2017. Assoc. Editor: Dar-Zen Chen.

J. Mech. Des 139(8), 083302 (Jun 15, 2017) (5 pages) Paper No: MD-17-1032; doi: 10.1115/1.4036782 History: Received January 13, 2017; Revised April 24, 2017

Graph theory is a powerful tool in structural synthesis and analysis of planetary gear trains (PGTs). In this paper, a new algorithm has been developed for detecting degenerate structure in planetary gear trains. The proposed algorithm is based on the concept of fundamental circuits' rotation graphs. Detection of degeneracy is entirely based on finding one key element. The key element or link that makes planetary gear train into two groups is found in this work. The main advantage of the proposed method lies in the drastic reduction in the required combinatorial analysis compared to other methods available.

Copyright © 2017 by ASME
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References

Del Castillo, J. M. , 2002, “ Enumeration of 1-DOF Planetary Gear Trains Graphs Based on Functional Constraints,” ASME J. Mech. Des., 124(4), pp. 723–732. [CrossRef]
Salgado, D. R. , and Del Castillo, J. M. , 2005, “ A Method for Detecting Degenerate Structures in Planetary Gear Trains,” Mech. Mach. Theory, 40(8), pp. 948–962. [CrossRef]
Buchsbaum, F. , and Freudenstein, F. , 1970, “ Synthesis of Kinematic Structure of Geared Kinematic Chains and Other Mechanisms,” J. Mech., 5(3), pp. 357–392. [CrossRef]
Hsu, C. H. , and Hsu, J. J. , 1997, “ An Efficient Methodology for the Structural Synthesis of Geared Kinematic Chains,” Mech. Mach. Theory, 32(8), pp. 957–973. [CrossRef]
Ravisankar, R. , and Mruthyunjaya, T. S. , 1985, “ Computerized Synthesis of the Structure of Geared Kinematics Chains,” Mech. Mach. Theory, 20(5), pp. 367–387. [CrossRef]
Kim, J. U. , and Kwak, B. M. , 1990, “ Application of Edge Permutation Group to Structural Synthesis of Epicyclic Gear Trains,” Mech. Mach. Theory, 25(5), pp. 563–574. [CrossRef]
Tsai, L. W. , 1987, “ An Application of the Linkage Characteristic Polynomial to the Topological Synthesis of Epicyclic Gear Trains,” J. Mech. Transm. Autom. Des., 109(3), pp. 329–336. [CrossRef]
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(1), pp. 196–200. [CrossRef]
Hsu, C. H. , and Wu, Y. C. , 1997, “ Automatic Detection of Embedded Structure in Planetary Gear Trains,” ASME J. Mech. Des., 119(2), pp. 315–318. [CrossRef]
Rao, A. C. , 2003, “ A Genetic Algorithm for Planetary Gear Trains,” Mech. Mach. Theory, 38(2), pp. 135–147. [CrossRef]

Figures

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Fig. 1

A six-link 1DOF PGT and two representations of its graph

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Fig. 2

Flow chart for the proposed algorithm

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Fig. 3

PGT 8430a in Appendix I, which is available under the “Supplemental Materials” tab for this paper on the ASME Digital Collection

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Fig. 4

Rotation graph part 1

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Fig. 5

Rotation graph part 2

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Fig. 6

Rotation graph part 3

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Fig. 7

PGT 8332Bb in Appendix I, which is available under the “Supplemental Materials” tab for this paper on the ASME Digital Collection

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Fig. 8

Rotation graph part 1

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Fig. 9

Rotation graph part 2

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Fig. 10

Rotation graph part 3

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Fig. 11

Code 9430d in Appendix I, which is available under the “Supplemental Materials” tab for this paper on the ASME Digital Collection

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Fig. 12

Rotation graph part 1

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Fig. 13

Rotation graph part 2

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Fig. 14

Rotation graph part 3

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Fig. 15

Code 9431Bf in Appendix I, which is available under the “Supplemental Materials” tab for this paper on the ASME Digital Collection

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Fig. 16

Rotation graph part 1

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Fig. 17

Rotation graph part 2

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Fig. 18

Rotation graph part 3

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