Research Papers: Design of Direct Contact Systems

Design of Multiple Operating Degrees-of-Freedom Planetary Gear Trains With Variable Structure

[+] Author and Article Information
Zeng-Xiong Peng, Tian-Li Xie, Chun-Wang Liu

National Key Laboratory of
Vehicular Transmission,
Beijing Institute of Technology,
Beijing 100081, China

Ji-Bin Hu

National Key Laboratory of
Vehicular Transmission,
School of Mechanical Engineering,
Room No. 414,
Building No. 9,
No. 5 Zhongguancun South Street,
Haidian District,
Beijing 100081, China
e-mail: bithjb@126.com

1Corresponding author.

Contributed by the Power Transmission and Gearing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received January 12, 2015; final manuscript received May 27, 2015; published online June 30, 2015. Assoc. Editor: Dar-Zen Chen.

J. Mech. Des 137(9), 093301 (Sep 01, 2015) (11 pages) Paper No: MD-15-1018; doi: 10.1115/1.4030856 History: Received January 12, 2015; Revised May 27, 2015; Online June 30, 2015

To obtain multiple speed ratios, a synthesis methodology of planetary gear trains (PGTs) with multiple operating degrees-of-freedom (DOFs) is proposed based on the variable structure method. Variable structure of PGT is accomplished by changing the fixed interconnection edge. First, PGTs with two operating DOFs are synthesized with a deduction method based on the relationship between the number of planetary gear sets (PGSs) and number of fixed interconnection edges. Next, connection characteristics of fixed interconnection edges are defined as frequency of utilization to construct original speed ratios of the two operating DOFs schemes. The connection characteristics are then obtained based on the power flow analysis. PGT graph model with connection characteristic is built to provide guidance in the design of varying structure. Finally, multispeed PGTs with multiple operating DOFs are synthesized based on the graph model and lever analogy. A design example for three-PGS PGTs is considered to highlight capabilities of the variable structure method.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Hwang, W. M., and Huang, Y. L., 2011, “Synthesis of a Six-Coaxial-Link Planetary Gear Train for Seven-Speed Automatic Transmissions,” J. Chin. Soc. Mech. Eng., 32(4), pp. 313–321.
Cooney, T. J., 1999, “The New Allison HD4070 Transmission—Design, Development and Applications,” SAE Paper No. 1999-01-3742. [CrossRef]
Ross, C. S., and Route, W. D., 1991, “A Method for Selecting Parallel-Connected, Planetary Gear Train Arrangements for Automotive Automatic Transmissions,” SAE Paper No. 911941. [CrossRef]
He, G. Q., 2004, “Study of the Mechanical Transmission Scheme for Automobile Automatic Transmission,” M.S. thesis, College of Mechanical Engineering, Tongji University, Shanghai, China (in Chinese).
Liu, X. J., 1998, Analysis of Vehicle Transmission System, National Defense Industry Press, Beijing, China (in Chinese).
Scherer, H., 2003, “ZF 6-Speed Automatic Transmission for Passenger Cars,” SAE Paper No. 2003-01-0596. [CrossRef]
Harmon, K. B., 1998, “The History of Allison Automatic Transmissions for On-Highway Trucks and Buses,” SAE Paper No. 982791. [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]
Chatterjee, G., and Tsai, L. W., 1994, “Enumeration of Epicyclic-Type Automatic Transmission Gear Trains,” SAE Paper No. 941012. [CrossRef]
Tsai, L. W., 2001, Mechanism Design: Enumeration of Kinematic Structures According to Function, CRC Press, New York.
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(1), pp. 10–16. [CrossRef]
Del Castillo, J. M., 2002, “Enumeration of 1DOF Planetary Gear Train Graphs Based on Functional Constraints,” ASME J. Mech. Des., 124(4), pp. 723–732. [CrossRef]
Tsai, L. W., Maki, E. R., Liu, T., and Kapil, N. G., 1988, “The Categorization of Planetary Gear Trains for Automatic Transmissions According to Kinematic Topology,” SAE Paper No. 885062. [CrossRef]
Becker, M., Amaral, D., and Dedini, F. G., 2003, “Tepiciclo—A Software to Help the Planetary Gear Trains Design,” SAE Technical Paper 2003-01-0679. [CrossRef]
Troha, S., Lovrin, N., and Milovančević, M., 2012, “Selection of the Two-Carrier Shifting Planetary Gear Train Controlled by Clutches and Brakes,” Trans. FAMENA, 3(36), pp. 1–12.
Bucknor, N. K., 2007, “Automatic Determination of Transmission Powerflow Mechanizability Using Graph Theory,” ASME Paper No. DETC2007-34018. [CrossRef]
Raghavan, M., Bucknor, N., Maguire, J., Hendrickson, J., and Singh, T., 2006, “The Design of Advanced Transmission,” FISITA, Yokohama, Japan.
Kahraman, A., Ligata, H., Kienzle, K., and Zini, D. M., 2004, “A Kinematics and Power Flow Analysis Methodology for Automatic Transmission Planetary Gear Trains,” ASME J. Mech. Des., 126(6), pp. 1071–1081. [CrossRef]
Kwon, H. S., Kahraman, A., Lee, H. K., and Suh, H. S., 2014, “An Automated Design Search for Single and Double-Planet Planetary Gear Sets,” ASME J. Mech. Des., 136(6), p. 061004. [CrossRef]
Tsai, L. W., 1987, “An Application of the Linkage Characteristic Polynomial to the Topological Synthesis of Epicyclic Gear Trains,” ASME J. Mech. Des., 109(3), pp. 329–336. [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]
Chatterjee, G., and Tsai, L. W., 1996, “Computer-Aided Sketching of Epicyclic-Type Automatic Transmission Gear Trains,” ASME J. Mech. Des., 118(3), pp. 405–411. [CrossRef]
Uicker, J. J., Jr., and Raicu, A., 1975, “A Method for the Identification and Recognition of Equivalence of Kinematic Chains,” Mech. Mach. Theory, 10(5), pp. 375–383. [CrossRef]
Wan, Y. Q., and Liu, T. L., 1997, Scheme Selection Theory and Optimization of Planetary Gearbox, National Defense Industry Press, Beijing, China (in Chinese).
Hsu, C. H., and Lam, K. T., 1992, “A New Graph Representation for the Automatic Kinematic Analysis of Planetary Spur-Gear Trains,” ASME J. Mech. Des., 114(3), pp. 196–200. [CrossRef]
Shim, H. T., 2005, “Power Train for 7-Speed Automatic Transmission for Vehicles,” U.S. Patent Nos. 20050202925 A1 and 2005-09-15.
Esmail, E. L., and Hassan, S. S., 2010, “An Approach to Power-Flow and Static Force Analysis in Multi-Input Multi-Output Epicyclic-Type Transmission Trains,” ASME J. Mech. Des., 132(1), p. 011009. [CrossRef]
Hopcroft, J., and Tarjan, R., 1974, “Efficient Planarity Testing,” J. ACM, 21(4), pp. 549–568. [CrossRef]
Li, X., and Schmidt, L., 2004, “Grammar-Based Designer Assistance Tool for Epicyclic Gear Trains,” ASME J. Mech. Des., 126(5), pp. 895–902. [CrossRef]


Grahic Jump Location
Fig. 1

Graph representation of PGTs: (a) PGT and (b) definition of weights

Grahic Jump Location
Fig. 2

Synthesis of two operating DOF PGTs

Grahic Jump Location
Fig. 3

Structure characteristic analysis: (a) 3P2N scheme, (b) composite lever, (c) edge (6, 8), (d) edge (5, 9) with 9-output, (e) edge (5, 9) with 5-output, (f) edge (4, 10) with 4-input, (g) edge (4, 10) with 10-input, and (h) edge (3, 7)

Grahic Jump Location
Fig. 4

Graph model and adjacency matrix of PGT with connection characteristics: (a) Graph model with connection characteristics and (b) the corresponding adjacency matrix

Grahic Jump Location
Fig. 5

Topology synthesis and analysis of multiple operating DOFs PGT: (a) Graph model and (b) properties matrix of scheme

Grahic Jump Location
Fig. 6

Six-speed 3DOF PGTs for scheme in Fig. 3



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