0
Research Papers: Design of Direct Contact Systems

The Perimeter Loop-Based Method for the Automatic Isomorphism Detection in Planetary Gear Trains

[+] Author and Article Information
Wenjian Yang

School of Mechanical Engineering
and Electronic Information,
China University of Geosciences,
No. 388 LuMo Road, Hongshan District,
Wuhan 430074, China
e-mail: ywj19900125@163.com

Huafeng Ding

School of Mechanical Engineering
and Electronic Information,
China University of Geosciences,
No. 388 LuMo Road, Hongshan District,
Wuhan 430074, China
e-mail: dhf@ysu.edu.cn

1Corresponding author.

Contributed by the Power Transmission and Gearing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received March 10, 2018; final manuscript received September 18, 2018; published online October 19, 2018. Assoc. Editor: Mohsen Kolivand.

J. Mech. Des 140(12), 123302 (Oct 19, 2018) (10 pages) Paper No: MD-18-1205; doi: 10.1115/1.4041572 History: Received March 10, 2018; Revised September 18, 2018

Planetary gear trains (PGTs) are widely used in transmission systems. The structural synthesis of PGTs is an effective way to create novel and excellent transmissions. In the structural synthesis of PGTs, the isomorphism detection (ID) is an essential and especially important process. The ID aims to avoid duplication and guarantee the uniqueness of each PGT. The reliability of the ID method directly determines the accuracy of the synthesis result. Unfortunately, when the existing ID methods are used to synthesize PGTs, the synthesis results are not consistent with each other. A very important reason is that the ID methods fail to work in some cases. This fact gives rise to the need of an extremely reliable ID method, which may resolve the contradiction in the existing synthesis results in the future. In this paper, our previous perimeter loop-based ID method, which is applicable for linkage kinematic chains and has been proved to be reliable and efficient, is improved to detect isomorphic PGTs. The improvements relative to our previous method are discussed in detail. The present method is fully automated with the aid of a computer program, and verified by the atlas of PGTs with up to six links, as well as some PGTs with seven, eight, and ten links.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

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]
Yang, W. J. , Ding, H. F. , Zi, B. , and Zhang, D. , 2018, “ New Graph Representation for Planetary Gear Trains,” ASME J. Mech. Des., 140(1), p. 012303. [CrossRef]
Ravisankar, R. , and Mruthyunjaya, T. S. , 1985, “ Computerized Synthesis of the Structure of Geared Kinematic Chains,” Mech. Mach. Theory, 20(5), pp. 367–387. [CrossRef]
Tsai, L. W. , 1987, “ An Application of the Linkage Characteristic Polynomial to the Topological Synthesis of Epicyclic Gear Train,” ASME J. Mech., Transm. Autom. Des., 109(3), pp. 329–336. [CrossRef]
Tsai, L. W. , and Lin, C. C. , 1989, “ The Creation of Nonfractionated Two-Degree-of-Freedom Epicyclic Gear Trains,” ASME J. Mech., Transm. Autom. Des., 111(4), pp. 524–529. [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]
Shin, J. K. , and Krishnamurthy, S. , 1993, “ Standard Code Technique in the Enumeration of Epicyclic Gear Trains,” Mech. Mach. Theory, 28(3), pp. 347–355. [CrossRef]
Hsu, C. H. , and Lam, K. T. , 1993, “ Automatic Analysis of Kinematic Structure of Planetary Gear Trains,” ASME J. Mech. Des., 115(3), pp. 631–638. [CrossRef]
Del Castillo, J. M. , 2002, “ Enumeration of 1-DOF Planetary Gear Train Graphs Based on Functional Constraints,” ASME J. Mech. Des., 124(4), pp. 723–732. [CrossRef]
Hsu, C. H. , 1994, “ Displacement Isomorphism of Planetary Gear Trains,” Mech. Mach. Theory, 29(4), pp. 513–523. [CrossRef]
Hsu, C. H. , Lam, K. T. , and Yin, Y. L. , 1994, “ Automatic Synthesis of Displacement Graphs for Planetary Gear Trains,” Math. Comput. Modell., 19(11), pp. 67–81. [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]
Prasad Raju Pathapati, V. V. N. R. , and Rao, A. C. , 2002, “ A New Technique Based on Loops to Investigate Displacement Isomorphism in Planetary Gear Trains,” ASME J. Mech. Des., 124(4), pp. 662–675. [CrossRef]
Rao, A. C. , 2003, “ A Genetic Algorithm for Epicyclic Gear Trains,” Mech. Mach. Theory, 38(2), pp. 135–147. [CrossRef]
Rao, Y. V. D. , and Rao, A. C. , 2008, “ Generation of Epicyclic Gear Trains of One Degree of Freedom,” ASME J. Mech. Des., 130(5), p. 052604. [CrossRef]
Yang, P. , Pei, Z. H. , Liao, N. B. , and Yang, B. , 2007, “ Isomorphism Identification for Epicyclic Gear Mechanism Based on Mapping Property and Ant Algorithm,” Eng. Comput., 23(1), pp. 49–54. [CrossRef]
Kamesh, V. V. , Rao, K. M. , and Rao, A. B. S. , 2017, “ Topological Synthesis of Epicyclic Gear Trains Using Vertex Incidence Polynomial,” ASME J. Mech. Des., 139(6), p. 062304. [CrossRef]
Kamesh, V. , Rao, K. M. , and Rao, A. B. S. , 2017, “ An Innovative Approach to Detect Isomorphism in Planar and Geared Kinematic Chains Using Graph Theory,” ASME J. Mech. Des., 139(12), p. 122301. [CrossRef]
Ding, H. F. , and Huang, Z. , 2007, “ The Establishment of the Canonical Perimeter Topological Graph of Kinematic Chains and Isomorphism Identification,” ASME J. Mech. Des., 129(9), pp. 915–923. [CrossRef]
Ding, H. F. , Huang, P. , Yang, W. J. , and Kecskemethy, A. , 2016, “ Automatic Generation of the Complete Set of Planar Kinematic Chains With Up to Six Independent Loops and Up to 19 Links,” Mech. Mach. Theory, 96, pp. 75–93. [CrossRef]
Ding, H. F. , Yang, W. J. , Huang, P. , and Kecskemethy, A. , 2013, “ Automatic Structural Synthesis of Planar Multiple Joint Kinematic Chains,” ASME J. Mech. Des., 135(9), p. 091007. [CrossRef]
Ding, H. F. , Yang, W. J. , Zi, B. , and Kecskemethy, A. , 2016, “ The Family of Planar Kinematic Chains With Two Multiple Joints,” Mech. Mach. Theory, 99, pp. 103–116. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

(a) Three-dimensional model of the Simpson gear train, (b) schematic diagram, and (c) graph representation

Grahic Jump Location
Fig. 2

(a) Rotation graph of Fig. 1 and (b) displacement graph of Fig. 1

Grahic Jump Location
Fig. 3

(a) Adjacency matrix of Fig. 2(a) and (b) adjacency matrix of Fig. 2(b)

Grahic Jump Location
Fig. 4

(a) Displacement graph of a six-link 1DOF PGT and ((b) and (c)) canonical graphs

Grahic Jump Location
Fig. 5

(a) Perimeter loop graph of Fig. 2(b), (b) canonical graph, and (c) adjacency matrix

Grahic Jump Location
Fig. 6

C-code and C-graph of Fig. 2(b)

Grahic Jump Location
Fig. 7

Displacement graphs of two seven-link 2DOF PGTs

Grahic Jump Location
Fig. 8

Perimeter loop graphs of Fig. 7(a)

Grahic Jump Location
Fig. 9

Canonical graphs of Fig. 7(a)

Grahic Jump Location
Fig. 10

(a) C-graph of Fig. 7(a) and (b) C-graph of Fig. 7(b)

Grahic Jump Location
Fig. 11

Displacement graphs of two eight-link 1DOF PGTs

Grahic Jump Location
Fig. 12

Perimeter loop graphs for Fig. 11

Grahic Jump Location
Fig. 13

(a) C-graph of Fig. 11(a) and (b) C-graph of Fig. 11(b)

Grahic Jump Location
Fig. 14

Displacement graphs of two ten-link 1DOF PGTs

Grahic Jump Location
Fig. 15

Perimeter loop graphs for Fig. 14

Grahic Jump Location
Fig. 16

(a) C-graph of Fig. 14(a) and (b) C-graph of Fig. 14(b)

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In