Saoud, F., Abdali, S., Esmail, E. (2026). Structural synthesis and classification of planetary gear-cam mechanisms using graph theory. , 19(1), 11-19. doi: 10.30772/qjes.2023.142157.1015
Farah Mohammed Saoud; Sajad Hussein Abdali; Essam Esmail. "Structural synthesis and classification of planetary gear-cam mechanisms using graph theory". , 19, 1, 2026, 11-19. doi: 10.30772/qjes.2023.142157.1015
Saoud, F., Abdali, S., Esmail, E. (2026). 'Structural synthesis and classification of planetary gear-cam mechanisms using graph theory', , 19(1), pp. 11-19. doi: 10.30772/qjes.2023.142157.1015
Saoud, F., Abdali, S., Esmail, E. Structural synthesis and classification of planetary gear-cam mechanisms using graph theory. , 2026; 19(1): 11-19. doi: 10.30772/qjes.2023.142157.1015

Structural synthesis and classification of planetary gear-cam mechanisms using graph theory

Al-Qadisiyah Journal for Engineering Sciences
Article 2, Volume 19, Issue 1, March 2026, Pages 11-19    PDF (8.25 M)
Document Type: Review Paper
DOI: 10.30772/qjes.2023.142157.1015
Authors
Farah Mohammed Saoud; Sajad Hussein Abdali; Essam Esmail*
Department of Mechanical Engineering, College of Engineering, University of Al-Qadisiyah, Al-Diwaniyah, Iraq.
Abstract
This paper presents a comprehensive study on the structural synthesis and classification of planetary gear mechanisms (PGCMs), which combine the advantages of planetary gear trains (PGTs) and cam mechanisms to produce precise, intermittent, or variable-speed motions. These mechanisms are particularly suitable for high-performance industrial applications, such as indexing tables, path generation systems, and rigid body guidance. The work begins by detailing the kinematic and structural characteristics of PGCMs and identifying possible configurations based on degrees of freedom, link types, and joint arrangements. Using graph theory, rooted graph representations are developed to systematically enumerate two-degree-of-freedom PGCMs, up to seven links. A spanning-tree-based synthesis method is used to generate candidate structures, followed by genetic compatibility analysis to identify viable PGCM configurations. The proposed method produces a set of functionally and structurally distinct PGCMs, including a novel five-link mechanism that achieves precise path generation with minimal complexity. This study not only enhances the theoretical framework for PGCM design, but also provides a practical basis for its application in modern mechanical systems.
Keywords
Mechanism enumeration; Planetary gear-cam mechanism; Classification; Spanning tree; Generate and classify PGCMs
References
  1. .Rothbart, Cam Design Handbook. McGraw Hill LLC, 2003. [Online]. Available: https://books.google.ws/books?id=7l8mA8x LdoC
  2. L. Tsai, Mechanism Design: Enumeration of Kinematic Structures According to Function, ser. Mechanical and Aerospace Engineering Series. CRC Press,
    2000. [Online]. Available: https://books.google.iq/books?id=X0AHKxwWTsYC
  3. R.-C. SOONG, “A new cam-geared mechanism for exact path generation,” Journal of Advanced Mechanical Design, Systems, and Manufacturing, vol. 9,
    no. 2, pp. JAMDSM0020–JAMDSM0020, 2015.
  4. R.-C. Soong, A CAM-GEARED MECHANISM FOR RIGID BODY GUIDANCE. Transactions of the Canadian Society for Mechanical Engineering, 2017,
    vol. 41, no. 1. [Online]. Available: https://doi.org/10.1139/tcsme-2017-1010
  5. D. Lahr and D. Hong, “Operation and kinematic analysis of a cam-based infinitely variable transmission,” Journal of Mechanical Design, vol. 131, no. 8, p.
    081009, 07 2009. [Online]. Available: https://doi.org/10.1115/1.3179004
  6. T. Yang, S. Yan, W. Ma, and Z. Han, “Joint dynamic analysis of space manipulator with planetary gear train transmission,” Robotica, vol. 34, no. 5, p.
    1042–1058, 2016. [Online]. Available: https://doi.org/10.1017/S0263574714002045
  7. M. Cammalleri and A. Castellano, “Analysis of hybrid vehicle transmissions with any number of modes and planetary gearing: kinematics, power flows,
    mechanical power losses,” Mechanism and Machine Theory, vol. 162, p. 104350, 2021. [Online]. Available: https://doi.org/10.1016/j.mechmachtheory.2021.
    104350
  8. Y. Yu, C. Lin, and P. Xu, “Pattern classification and gear design of spatial noncircular gear continuously variable transmission,” Applied Sciences, vol. 12,
    no. 5, 2022. [Online]. Available: https://www.mdpi.com/2076-3417/12/5/2715
  9. A. Marciniec, M. Sobolak, and P. Połowniak, “Graphical method for the analysis of planetary gear trains,” Alexandria Engineering Journal, vol. 61, no. 5, pp.
    4067–4079, 2022. [Online]. Available: https://doi.org/10.1016/j.aej.2021.09.036
  10. S. H. Abdali and E. L. Esmail, “The structural synthesis of non-fractionated, three-degree-of-freedom planetary gear mechanisms,” Journal of Applied and
    Computational Mechanics, vol. 10, no. 1, pp. 205–223, 2024. [Online]. Available: https://doi.org/10.22055/jacm.2023.44563.4240
  11. A. Mironov and D. Mironovs, “Condition monitoring of helicopter main gearbox planetary stage,” in Reliability and Statistics in Transportation and
    Communication, I. Kabashkin, I. Yatskiv (Jackiva), and O. Prentkovskis, Eds. Cham: Springer International Publishing, 2019, pp. 421–430.
  12. D. F. Lahr, “Development of a novel cam-based infinitely variable transmission,” Master’s thesis, Virginia Polytechnic Institute and State University, 2009.
    [Online]. Available: http://hdl.handle.net/10919/35759
  13. A. Al-Hamood, H. Jamalia, A. Imran, O. Abdullah, A. Senatore, and H. Kaleli, “Modeling and theoretical analysis of a novel ratcheting-type
    cam-based infinitely variable transmission system,” Comptes Rendus. M ´ecanique, vol. 347, no. 12, pp. 891–902, 2019. [Online]. Available:
    https://doi.org/10.1016/j.crme.2019.10.005
  14. A. Al-Hamood, H. U. Jamali, O. I. Abdullah, and J. Schlattmann, “The performance of one-way clutch in a cam-based infinitely variable
    transmission,” IOP Conference Series: Materials Science and Engineering, vol. 671, no. 1, p. 012008, jan 2020. [Online]. Available:
    https://dx.doi.org/10.1088/1757-899X/671/1/012008
  15. J. Drewniak, J. Kope ´c, and S. Zawi ´slak, Kinematical Analysis of Variants of Wind Turbine Drive by Means of Graphs. Cham: Springer International
    Publishing, 2017, pp. 81–95. [Online]. Available: https://doi.org/10.1007/978-3-319-39020-8 6
  16. N. Sclater and N. Chironis, Mechanisms and Mechanical Devices Sourcebook, Fourth Edition. McGraw-Hill Education, 2007. [Online]. Available:
    https://books.google.iq/books?id=v3JMQW-n1Q0C
  17. R.-C. SOONG, “A new cam-geared mechanism for exact path generation,” Journal of Advanced Mechanical Design, Systems, and Manufacturing, vol. 9,
    no. 2, pp. JAMDSM0020–JAMDSM0020, 2015. [Online]. Available: https://doi.org/10.1299/jamdsm.2015jamdsm0020
  18. R.-C. Soong, “A cam-geared mechanism for rigid body guidance,” Transactions of the Canadian Society for Mechanical Engineering, vol. 41, no. 1, pp.
    143–157, 2017. [Online]. Available: https://doi.org/10.1139/tcsme-2017-1010
  19. A. Marciniec, M. Sobolak, and P. Połowniak, “Graphical method for the analysis of planetary gear trains,” Alexandria Engineering Journal, vol. 61, no. 5, pp.
    4067–4079, 2022. [Online]. Available: https://doi.org/10.1016/j.aej.2021.09.036
  20. E. L. Esmail, “A matrix-based method for detection of degenerate structures in planetary gear trains,” Mechanism and Machine Theory, vol. 175, p. 104925,
    2022. [Online]. Available: https://doi.org/10.1016/j.mechmachtheory.2022.104925
  21. J. Ye, X. Zhao, Y. Wang, X. Sun, J. Chen, and X. Xia, “A novel planar motion generation method based on the synthesis of planetary gear train with noncircular
    gears,” Journal of Mechanical Science and Technology, vol. 33, no. 10, pp. 4939–4949, 2019. [Online]. Available: https://doi.org/10.1007/s12206-019-0933-6
  22. W.-H. Hsieh, “An experimental study on cam-controlled planetary gear trains,” Mechanism and Machine Theory, vol. 42, no. 5, pp. 513–525, 2007. [Online].
    Available: https://doi.org/10.1016/j.mechmachtheory.2006.10.006
  23. W. H. Hsieh, “Kinematic synthesis of cam-controlled planetary gear trains,” Mechanism and Machine Theory, vol. 44, no. 5, pp. 873–895, 2009. [Online].
    Available: https://doi.org/10.1016/j.mechmachtheory.2008.07.001
  24. W.-H. Hsieh and S.-J. Chen, “Innovative design of cam-controlled planetary gear trains,” International Journal of Engineering and Technology Innovation,
    vol. 1, no. 1, p. 1–11, Oct. 2011. [Online]. Available: https://ojs.imeti.org/index.php/IJETI/article/view/3
  25. W. Hsieh, “Kinetostatic and mechanical efficiency studies on cam-controlled planetary gear trains (part ii): Design and experiment,” Indian Journal of
    Engineering and Materials Sciences, vol. 20, no. 3, p. 199–204, 2013. [Online]. Available: http://nopr.niscpr.res.in/handle/123456789/19061
  26. E. L. Esmail and F. M. Saoud, “Creative design of planetary gear-cam mechanisms,” Results in Engineering, vol. 19, p. 101350, 2023. [Online]. Available:
    https://doi.org/10.1016/j.rineng.2023.101350
  27. W.-H. Hsieh and I.-C. Li, “Modelling and control of cam-controlled planetary gear trains,” International Journal of Modelling, Identification and Control,
    vol. 12, no. 3, pp. 272–279, 2011.
  28. W. Yang, H. Ding, and A. Kecskem´ethy, “Automatic structural synthesis of non-fractionated 2-dof planetary gear trains,” Mechanism and Machine Theory,
    vol. 155, p. 104125, 2021. [Online]. Available: https://doi.org/10.1016/j.mechmachtheory.2020.104125
  29. H. A. Nafeh and E. Lauibi Esmail, “Genetically compatible graphs for planetary gear train synthesis,” Al-Qadisiyah Journal for Engineering Sciences, vol. 15,
    no. 1, pp. 9–17, 2022. [Online]. Available: https://doi.org/10.30772/qjes.v15i1.807
  30. H. A. Nafeh, E. L. Esmail, and S. H. Abdali, “Automatic structural synthesis of planetary geared mechanisms using graph theory,” Journal of Applied and
    Computational Mechanics, vol. 9, no. 2, pp. 384–403, 2023. [Online]. Available: https://doi.org/10.22055/jacm.2022.41255.3721
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