Almuramady, N., Al-Mayali, M., Esmail, E., Muhammed, M., Jassim, Z., Obaid, A. (2025). An innovative graph-based approach for the topological structure of planetary gear mechanisms. , 18(4), 403-415. doi: 10.30772/qjes.2023.141737.1008
Nabeel Almuramady; M. F. Al-Mayali; Essam L. Esmail; Muhammed A. Muhammed; Zahraa Aqeel A. Jassim; Alaa F. Obaid. "An innovative graph-based approach for the topological structure of planetary gear mechanisms". , 18, 4, 2025, 403-415. doi: 10.30772/qjes.2023.141737.1008
Almuramady, N., Al-Mayali, M., Esmail, E., Muhammed, M., Jassim, Z., Obaid, A. (2025). 'An innovative graph-based approach for the topological structure of planetary gear mechanisms', , 18(4), pp. 403-415. doi: 10.30772/qjes.2023.141737.1008
Almuramady, N., Al-Mayali, M., Esmail, E., Muhammed, M., Jassim, Z., Obaid, A. An innovative graph-based approach for the topological structure of planetary gear mechanisms. , 2025; 18(4): 403-415. doi: 10.30772/qjes.2023.141737.1008

An innovative graph-based approach for the topological structure of planetary gear mechanisms

Al-Qadisiyah Journal for Engineering Sciences
Volume 18, Issue 4, December 2025, Pages 403-415    PDF (8.23 M)
Document Type: Research Paper
DOI: 10.30772/qjes.2023.141737.1008
Authors
Nabeel Almuramady* 1; M. F. Al-Mayali1; Essam L. Esmail1; Muhammed A. Muhammed* 1; Zahraa Aqeel A. Jassim2; Alaa F. Obaid3
1Department of Mechanical Engineering, College of Engineering, The University of Al-Qadisiyah Al Diwaniyah, Iraq.
2Scientific Affairs, University of Al-Qadisiyah, Al-Diwaniyah, Iraq.
3Department of Chemical Engineering, College of Engineering, University of Al-Muthanna, Samawah, Iraq.
Abstract
Planetary gear mechanisms (PGMs) are commonly employed in mechanical applications. Graph theory is a useful tool for synthesizing PGM structures to develop new transmission systems. The synthesis of 1- and 2-degree-of-freedom (DOF) planetary gear trains received a lot of attention. Nevertheless, the synthesis results are inconsistent because previous graph representations were insufficient for the synthesis processes. This paper proposes a graph model that improves upon earlier models, introducing the concept of type-2 pseudo-isomorphic graphs. The vertex levels are used to construct PGM-spanning trees and define geared graphs. This approach avoids pseudo-isomorphic graphs and maintains a one-to-one correspondence between PGM elements and the graph. The 6-link 2-DOF PGM synthesis demonstrated the current graph representation, yielding 24 non-isomorphic mechanisms of 11 or more than previously reported. Possible explanations for the inconsistency of synthesis results with earlier studies are investigated, and the advantages of the modified graph over existing approaches are discussed in detail.
Keywords
Graph theory; Isomorphism; Planetary gear mechanism; Structure synthesis; Transmission
References
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