Structural Synthesis of Epicyclic Gear Trains by Deep Learning and Generative AI for Adaptive Automation

Jiyaul Mustafa; Shahnawaz Ahmad; Mohammed Wasid; Mohd. Aquib Ansari; Shaharyar Alam Ansari

doi:10.57159/jcmm.5.1.25247

Authors

Jiyaul Mustafa Department of Mechanical Engineering, Bennett University, Greater Noida, Uttar Pradesh, India 201310
Shahnawaz Ahmad School of Computer Science Engineering & Technology, Bennett University, Greater Noida, Uttar Pradesh, India 201310
Mohammed Wasid Department of Computer Science and Engineering, The LNM Institute of Information Technology, Jaipur, Rajasthan, India 302031
Mohd. Aquib Ansari School of Computing Science & Engineering, Galgotias University, Greater Noida, Uttar Pradesh, India 203201
Shaharyar Alam Ansari School of Computer Science Engineering & Technology, Bennett University, Greater Noida, Uttar Pradesh, India 201310

DOI:

https://doi.org/10.57159/jcmm.5.1.25247

Keywords:

Deep Learning, Generative AI, Epicyclic Gear Trains, Isomorphism Detection, Adaptive Automation

Abstract

Structural synthesis of Epicyclic Gear Trains (EGTs) is a computationally demanding activity, particularly when identifying isomorphism between complex topologies and producing new gear designs to support high-performance automation systems. Graph-theoretic and algebraic methods are traditional and involve manual intervention and duplicate solutions. To address this shortcoming, this paper proposes a DL-based Generative AI framework for the automated synthesis and classification of EGTs. A Generative Adversarial Network (GAN) is trained on existing EGT topologies, learning their structures, creating new feasible structural mechanisms, and identifying duplication through degree sequence estimation and graph matching. The strategy is combined with the calculation of the connectivity matrix and the representation of the structural graph to ensure manufacturability and kinematic feasibility. The effectiveness of the proposed AI model is validated by the analysis of different EGTs, with 4--5 links, single DOF. Findings demonstrate that the GAN-based synthesis reliably distinguishes structurally distinct gear trains, eliminates pseudo-isomorphic designs, and saves a significant amount of design time. The technique justifies adaptive automation by designing intelligent mechanisms that require minimal human intervention. The paper demonstrates that AI-based synthesis can be highly effective in next-generation smart factories, robotic actuation, transmission systems, and reconfigurable automation platforms.

References

F. Freudenstein, “The basic concepts of Pólya’s theory of enumeration, with application to the structural classification of mechanisms,” Journal of Mechanisms, vol. 2, no. 3, pp. 275–290, 1967.

L. Dobrjanskyj and F. Freudenstein, “Some applications of graph theory to the structural analysis of mechanisms,” ASME Journal of Engineering for Industry, vol. 89, no. 1, pp. 153–158, 1967.

Z. Levai, “Structure and analysis of planetary gear trains,” Journal of Mechanisms, vol. 3, pp. 131–148, 1968.

F. Buchsbaum and F. Freudenstein, “Synthesis of kinematic structure of geared kinematic chains and other mechanisms,” Journal of Mechanisms, vol. 5, pp. 357–392, 1970.

F. Freudenstein, “An application of Boolean algebra to the motion of epicyclic drives,” ASME Journal of Engineering for Industry, vol. 93, no. 1, pp. 176–182, 1971.

J. Wojnarowski and R. Lidwin, “Application of signal flow graphs—The kinematic analysis of planetary gear trains,” Mechanism and Machine Theory, vol. 10, pp. 17–31, 1975.

J. J. Uicker Jr. and A. Raicu, “A method for the identification and recognition of equivalence of kinematic chains,” Mechanism and Machine Theory, vol. 10, no. 5, pp. 375–383, 1975.

T. S. Mrutyunjaya and M. R. Raghavan, “Structural analysis of kinematic chains and mechanisms based on matrix representation,” ASME Journal of Mechanical Design, vol. 101, no. 3, pp. 488–494, 1979.

R. R. Allen, “Multiport models for the kinematic and dynamic analysis of gear power transmissions,” ASME Journal of Mechanical Design, vol. 101, no. 2, pp. 258–267, 1979.

C. P. Day, H. A. Akeel, and L. J. Gutkowski, “Kinematic design and analysis of coupled planetary bevel-gear trains,” ASME Journal of Mechanisms, Transmissions, and Automation in Design, vol. 105, no. 3, pp. 441–444, 1983.

D. Gibson and S. Kramer, “Symbolic notation and kinematic equations of motion of the twenty-two basic spur planetary gear trains,” Journal of Mechanisms, Transmissions, and Automation in Design, vol. 106, no. 3, pp. 333–340, 1984.

R. Ravishankar and T. S. Mruthyunjaya, “Computerized synthesis of the structure of geared kinematic chains,” Mechanism and Machine Theory, vol. 20, no. 5, pp. 367–387, 1985.

J. Mustafa and A. Hasan, “Some application of graph theory to isomorphic analysis of epicyclic geared mechanisms,” Journal of the Institution of Engineers (India) Series C, vol. 102, no. 4, pp. 1051–1057, 2021.

J. Mustafa and A. Hasan, “Generation of one-DOF epicyclic gear trains with up to eight links,” Materials Today: Proceedings, vol. 15, no. 1, pp. 1123–1130, 2021, doi: 10.1016/j.matpr.2021.05.275.

J. Mustafa and A. Hasan, “Comparative study between modified path matrix approach, modified gradient method and Bocher’s technique to detect isomorphism in EGTs,” Materials Today: Proceedings, vol. 27, no. 3, pp. 1941–1948, 2021, doi: 10.1016/j.matpr.2021.04.123.

J. Mustafa, A. Hasan, and R. A. Khan, “An application of modified path matrix approach for detection of isomorphism among epicyclic gear trains,” Journal of the Institution of Engineers (India) Series C, vol. 101, no. 3, pp. 463–472, 2020.

J. Chu and Y. Zou, “Topological graph descriptions and structural automatic synthesis of planar multiple joint and geared-linkage kinematic chains,” Mechanics Science, vol. 36, pp. 12–19, 2016.

W. Yang, H. Ding, B. Zi, and D. Zhang, “New graph representation for planetary gear trains,” ASME Journal of Mechanical Design, vol. 140, no. 1, Art. no. 012303, 2017.

M. F. Gao and J. B. Hu, “Kinematic analysis of planetary gear trains based on topology,” ASME Journal of Mechanical Design, vol. 140, no. 1, pp. 1–12, 2017.

V. V. Kamesh, K. M. Rao, and A. B. S. Rao, “An innovative approach to detect isomorphism in planar and geared kinematic chains using graph theory,” ASME Journal of Mechanical Design, vol. 139, no. 12, pp. 12–22, 2017.

J. Mustafa, A. Hasan, and R. A. Khan, “An innovative approach for detection of isomorphism of epicyclic gear trains,” Materials Today: Proceedings, vol. 25, no. 1, pp. 862–867, 2020.

F. V. Morlin, A. P. Carboni, and D. Martins, “Synthesis of Assur groups via group and matroid theory,” Mechanism and Machine Theory, vol. 184, Art. no. 105279, 2023.

R. Alizade, S. Soltanov, and A. Hamidov, “Structural synthesis of lower-class robot manipulators with general constraint one,” Robotics, vol. 10, no. 1, Art. no. 14, 2021.

W. Yang, H. Ding, and A. Kecskemety, “Structural synthesis towards intelligent design of plane mechanisms: current status and future research trend,” Mechanism and Machine Theory, vol. 171, Art. no. 104715, 2022.

G. Bouritsas, F. Frasca, S. Zafeiriou, and M. M. Bronstein, “Improving graph neural network expressivity via subgraph isomorphism counting,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 45, no. 1, pp. 657–668, 2022.

L. Sun, X. Liu, X. Liu, X. Hong, H. Pei, and D. Zhang, “An isomorphism identification method of kinematic chain based on optimal arrangement and comparison of branch-chain matrix derived from dendrogram graph,” Advances in Mechanical Engineering, vol. 14, no. 12, Art. no. 16878132221131193, 2022.

L. Sun, R. Cui, Z. Ye, Y. Zhou, Y. Xu, and C. Wu, “Similarity recognition and isomorphism identification of planar kinematic chains,” Mechanism and Machine Theory, vol. 145, Art. no. 103678, 2020.

M. Wasid, A. Y. A. Amar, S. Ahmad, and J. Mustafa, “Enhancing reliability and security in online social networks: intelligent learning models for cybercrime detection,” Life Cycle Reliability and Safety Engineering, pp. 1–17, 2025.

U. C. Okonkwo, C. E. Okafor, S. Ahmad, C. C. Ohagwu, M. E. Aronu, I. P. Okokpujie, C. I. Idumah, N. N. Chukwu, C. E. Chukwunyelu, and J. Mustafa, “Research advancements in machine learning-assisted design of reinforced composite radiation shields,” Life Cycle Reliability and Safety Engineering, pp. 1–35, 2025.

N. K. Maurya, R. K. Singh, D. Gupta, R. Mishra, and J. Mustafa, “Evaluation of the mechanical properties of AlSi10Mg composites reinforced with TiB₂ particles (wt%) fabricated via selective laser melting process,” Life Cycle Reliability and Safety Engineering, pp. 1–9, 2025.

J. Mustafa, S. Ahmad, and S. Hussain, “Machine learning-based data processing for predictive modeling in mechanical systems,” Life Cycle Reliability and Safety Engineering, pp. 1–10, 2025.

V. V. Asrith, S. Mann, S. Garg, and J. Mustafa, “Numerical and mathematical modelling of connecting rod of internal combustion engine,” Life Cycle Reliability and Safety Engineering, pp. 1–9, 2025.

S. Sharma, J. Mustafa, and S. Bhati, “Experimental study of gyroscopic effects on rotating disc,” Journal of the Institution of Engineers (India) Series C, vol. 105, pp. 573–585, 2024.

L. W. Tsai, Mechanism Design: Enumeration of Kinematic Structures According to Function. Boca Raton, FL, USA: CRC Press, 2001.

L. W. Tsai, Robot Analysis: The Mechanics of Serial and Parallel Manipulators. New York, NY, USA: Wiley, 1999.