Automatic characteristic analysis method of multi-degrees-of-freedom planetary gear train based on graph theory

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Year : 2026 | Volume : 04 | 02 | Page :
By

Ju Hyok Jong,

Su Gyong Ri,

Jong Chol Kil,

Thae Song Pak,

  1. Faculty, Department of Mechanical Engineering, Kim Chaek University of Technology, Pyongyang, DPR, Korea
  2. Faculty, Department of Mechanical Engineering, Kim Chaek University of Technology, Pyongyang, DPR, Korea
  3. Faculty, Department of Mechanical Engineering, Kim Chaek University of Technology, Pyongyang, DPR, Korea
  4. Faculty, Department of Mechanical Engineering, Kim Chaek University of Technology, Pyongyang, DPR, Korea

Abstract

The purpose of this paper is to develop a computer-aided analysis method of the planetary gear train (PGT) based on graph theory. In this paper, a novel graph model is developed to represent the structure of the PGTs. Then, according to the gear shift strategy, the characteristic analysis models are deduced for each operating mode. The structure of the graph model is efficiently described through several variations of the incidence matrix. The speeds and the torques of all structural components are calculated by using matrix operations. The efficiency of the transmission system is calculated through the torque method in each operating mode. Furthermore, the power flow analysis model of each operating mode is obtained to analyse the power flow in the transmission system. The components that do not participate in the power flow are detected and the directions of the    power flow through the components are assigned by using simple graph-based method. To verify the correctness and effectiveness of the proposed method, a novel hybrid transmission scheme is used. The results show that the proposed method can automatically calculate the characteristics of a PGT through efficient graph-based methods and matrix operations. Thus, this method provides a basis for automatic selection of the optimal solution for a PGT among a large number of schemes.

Keywords: Planetary gear train, characteristic analysis, graph-based method, optimal solution design, automation

How to cite this article: Ju Hyok Jong, Su Gyong Ri, Jong Chol Kil, Thae Song Pak. Automatic characteristic analysis method of multi-degrees-of-freedom planetary gear train based on graph theory. International Journal of Mechanical Dynamics and Systems Analysis. 2026; 04(02):-.
How to cite this URL: Ju Hyok Jong, Su Gyong Ri, Jong Chol Kil, Thae Song Pak. Automatic characteristic analysis method of multi-degrees-of-freedom planetary gear train based on graph theory. International Journal of Mechanical Dynamics and Systems Analysis. 2026; 04(02):-. Available from: https://journals.stmjournals.com/ijmdsa/article=2026/view=253481

References

  1. Xu XY, Dong P, Liu YF, Zhang H, et al. Progress in automotive transmission technology. Automot Innov. 2018;1:187-210.
  2. Kahraman A, Ligata H, Kienzle K, Zini D, et al. A kinematics and power flow analysis methodology for automatic transmission planetary gear trains. J Mech Des. 2004;126(6):1071-1081.
  3. Karhula H, Nicolai M. Towards automated synthesis of automatic transmission designs. Int J Autom Eng. 2018;9(4):244-251.
  4. Dong P, Liu YF, Tenberge P, et al. Design and analysis of a novel multi-speed automatic transmission with four degrees-of-freedom. Mech Mach Theory. 2017;108:83-96.
  5. Xie TL, Hu JB, Peng ZX, et al. Synthesis of seven-speed planetary gear trains for heavy-duty commercial vehicles. Mech Mach Theory. 2015;90:230-239.
  6. Pennestri E, Belfore NP. On Crossley’s contribution to the development of graph based algorithms for the analysis of mechanisms and gear trains. Mech Mach Theory. 2015;89:92-106.
  7. Tsai LW. Mechanism design: enumeration of kinematic structures according to function. Boca Raton (FL): CRC Press; 2001.
  8. Chatterjee G, Tsai LW. Computer-aided sketching of epicyclic-type automatic transmission gear trains. J Mech Des. 1996;118(3):405-411.
  9. Yang WJ, Ding HF, Zi B, et al. New graph representation for planetary gear trains. J Mech Des. 2018;140(1):012303.
  10. Juber AH, Esmail EL, Ali TN. Graph representation of planetary gear trains: a review. Al-Qadisiyah J Eng Sci. 2022;14:227-231.
  11. Sun W, Li RH, Kong JY, et al. A new method for isomorphism identification of planetary gear trains. Mech Sci. 2021;12:193-202.
  12. Yang WJ, Ding HF. Automatic detection of degenerate planetary gear trains with different degrees of freedom. Appl Math Model. 2018;64:320-332.
  13. Ali TN, Esmail EL, Nafeh H. A graph-based approach for detection of degenerate structures in multi-planetary gear trains. Cogent Eng. 2022;9:2034266.
  14. Nafeh HA, Esmail EL, Abdali SH. Automatic structural synthesis of planetary geared mechanisms using graph theory. J Appl Comput Mech. 2023;9(2):384-403.
  15. Bucknor NK. Automatic determination of transmission powerflow mechanizability using graph theory. In: Proceedings of the ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference; 2007 Sep 4-7; Las Vegas, NV, USA. New York (NY): ASME; 2007. Paper DETC2007-34018.
  16. Hwang WM, Huang YL. Connecting clutch elements to planetary gear trains for automotive automatic transmissions via coded sketches. Mech Mach Theory. 2011;46:44-52.
  17. Ding HF, Cai CW, Chen ZM, et al. Configuration synthesis and performance analysis of 9-speed automatic transmissions. Chin J Mech Eng. 2020;33(1):50.
  18. Hsieh HI, Tsai LW. Kinematic analysis of epicyclic-type transmission mechanisms using the concept of fundamental geared entities. J Mech Des. 1996;118:294-299.
  19. Hsieh HI, Tsai LW. The selection of a most efficient clutching sequence associated with automatic transmission mechanisms. J Mech Des. 1998;120:514-519.
  20. Del Castillo JM. The analytical expression of the efficiency of planetary gear trains. Mech Mach Theory. 2002;37(2):197-214.
  21. Esmail EL, Hassan SS. An approach to power-flow and static force analysis in multi-input multi-output epicyclic type transmission trains. J Mech Des. 2010;132:10.
  22. Gao MF, Hu JB. Kinematic analysis of planetary gear trains based on topology. J Mech Des. 2018;140(1):012302.
  23. Esmail EL, Hassan SS. Nomographs for kinematics, statics and power flow analysis of epicyclic gear trains. In: Proceedings of the ASME 2009 International Mechanical Engineering Congress and Exposition; 2009 Nov 13-19; Lake Buena Vista, FL, USA. New York (NY): ASME; 2009. Paper IMECE2009-10789.
  24. Esmail EL. Nomographs and feasibility graphs for enumeration of Ravigneaux-type automatic transmissions. Adv Mech Eng. 2013;2013:120324.
  25. Schulz M. Circulating mechanical power in a power-split hybrid electric vehicle transmission. Proc Inst Mech Eng Part D J Automob Eng. 2004;218(12):1419-1425.
  26. Cui YH, Gao J, Ji XM, et al. The multi-attribute topological graph method and its application on power flow analysis in closed planetary gear trains. Adv Mech Eng. 2018;10(8):1-9.
  27. Yang FC, Feng JX, Zhang HC. Power flow and efficiency analysis of multi-flow planetary gear trains. Mech Mach Theory. 2015;92:86-99.
  28. Du M, Yang L. A basis for the computer-aided design of the topological structure of planetary gear trains. Mech Mach Theory. 2020;145:103690.
  29. Xue H, Li L. Motion, static force, and efficiency analysis of planetary gear transmission based on graph theory. Appl Sci. 2023;13(19):10983.
Ahead of Print Subscription Original Research
Volume 04
02
Received 25/03/2026
Accepted 17/08/2026
Published 27/08/2026
Publication Time 155 Days

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