Topological Synthesis and Enumerative Generation of One-DOF Epicyclic Gear Trains up to Twelve Links

Topological Synthesis and Enumerative Generation of One-DOF Epicyclic Gear Trains up to Twelve Links | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Topological Synthesis and Enumerative Generation of One-DOF Epicyclic Gear Trains up to Twelve Links JIYAUL MUSTAFA, Abdullah Aamir Hayat, Shahnawaz Ahmad, Tanveer Ahmed This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8700940/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This study presents a novel approach for the topological synthesis and isomorphism detection of Epicyclic Gear Trains (EGTs) using the Wiener Number Technique. The proposed method integrates graph theory with computational modeling to systematically generate and classify EGTs having one degree of freedom. A MATLAB-based algorithm was developed to evaluate Wiener numbers derived from connectivity matrices of conventional graphs of EGTs. Comparing Wiener numbers enables accurate identification of isomorphic and non-isomorphic structures, thereby eliminating duplicate configurations in the synthesis process. The technique was tested on EGTs with four, five, and six links with one and two DOFs. The results show that the proposed method effectively distinguishes structurally distinct mechanisms, correlating well with existing literature. Furthermore, the algorithm facilitates the generation of higher-order EGTs (up to 12 links) via systematic graph expansion rules, thereby enhancing the accuracy and efficiency of mechanism design. This research contributes a robust computational tool for the structural synthesis and classification of gear mechanisms, advancing the automation of EGT modeling for modern mechanical systems. Physical sciences/Engineering Physical sciences/Mathematics and computing Epicyclic Gear Trains Topological Synthesis Isomorphism Detection Graph Theory Wiener Number Technique Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8700940","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":583422254,"identity":"909ac793-2a8e-49d1-bd35-02615449ada1","order_by":0,"name":"JIYAUL MUSTAFA","email":"","orcid":"","institution":"Bennett University","correspondingAuthor":false,"prefix":"","firstName":"JIYAUL","middleName":"","lastName":"MUSTAFA","suffix":""},{"id":583422255,"identity":"ac25bed1-f50b-440e-8dfc-199d5c6ba84c","order_by":1,"name":"Abdullah Aamir Hayat","email":"","orcid":"","institution":"United Arab Emirates University","correspondingAuthor":false,"prefix":"","firstName":"Abdullah","middleName":"Aamir","lastName":"Hayat","suffix":""},{"id":583422256,"identity":"1a448d14-5641-4226-a833-eef9cc4afda2","order_by":2,"name":"Shahnawaz Ahmad","email":"","orcid":"","institution":"Bennett University","correspondingAuthor":false,"prefix":"","firstName":"Shahnawaz","middleName":"","lastName":"Ahmad","suffix":""},{"id":583422257,"identity":"4cb8e96c-f2bb-4da7-bd63-e216e3a55fb2","order_by":3,"name":"Tanveer Ahmed","email":"data:image/png;base64,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","orcid":"","institution":"Symbiosis International University","correspondingAuthor":true,"prefix":"","firstName":"Tanveer","middleName":"","lastName":"Ahmed","suffix":""}],"badges":[],"createdAt":"2026-01-26 13:53:21","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8700940/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8700940/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104217839,"identity":"ba21ac8e-672e-4b52-a992-d7dcaa794f5a","added_by":"auto","created_at":"2026-03-09 09:27:17","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":737825,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8700940/v1_covered_3f08eb72-527f-4ed3-aa23-cb9196e5f437.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Topological Synthesis and Enumerative Generation of One-DOF Epicyclic Gear Trains up to Twelve Links","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Epicyclic Gear Trains, Topological Synthesis, Isomorphism Detection, Graph Theory, Wiener Number Technique","lastPublishedDoi":"10.21203/rs.3.rs-8700940/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8700940/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This study presents a novel approach for the topological synthesis and isomorphism detection of Epicyclic Gear Trains (EGTs) using the Wiener Number Technique. 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