A simple and efficient method for isomorphism identification of planar kinematic chains

A simple and efficient method for isomorphism identification of planar kinematic chains | 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 Research Article A simple and efficient method for isomorphism identification of planar kinematic chains Luchuan Yu, Chenxu Cai, Jianhua Zhang, Qinhe Zhang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-470798/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 4 You are reading this latest preprint version Abstract Isomorphism identification plays an important role in structural design and innovative design. Based on the adjacency matrix and loop theory, a new method is proposed in this paper to identify the isomorphic kinematic chains. It enriches the application of loop-based theory for isomorphism identification. In the kinematic chain, links and joints are connected alternatively and every link corresponds to a fixed link degree. Due to the inherent characteristics, the labeled sequence of links can be random, which does not affect the result of isomorphism identification. By the programming software MATLAB, some examples with 6-, 8-, 10-, 11-, 12-link kinematic chains, and 15-vertex topological graphs are presented. Results show that the proposed method applies to topology graphs and kinematic chains with one or multiple joints. Compared with other methods, the proposed method is confirmed correctly. And there is no counterexample. It lays a solid foundation for structural synthesis in the future. Electrical Engineering Software Engineering isomorphism identification adjacency matrix pseudo-independence loop kinematic chain Full Text Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 04 Jun, 2021 Reviewers invited by journal 04 Jun, 2021 Editor assigned by journal 04 Jun, 2021 First submitted to journal 03 Jun, 2021 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. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-470798","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":31372517,"identity":"5e6bf9c0-eeeb-4590-ac18-d1a52e3c2eb3","order_by":0,"name":"Luchuan Yu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAzElEQVRIiWNgGAWjYFAC5gYGBjYGOfYGEMfAghgtjGAtxjwHwFokiNeS2APWwkCEFoMbiY0ff5QdTu9h7zHd8KNAgoG/vTuBkJZmaZ5zh3N7eI6l3ewBOkzizNkNhLS0MTO2Hc7dL5F87AYPUIuBRC5hLYw/2w6n80gktt38Q6wWBt62wwk8QFtuE2WL5JmHIL+kG4L8clvGQIKHoF/4jicfBIaYtTwPe4/ZzTd/bOT423vxa1E4gCbAg1c5CMg3EFQyCkbBKBgFIx4AAGDHSDjLLMO2AAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0002-3905-1513","institution":"Wenzhou University","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Luchuan","middleName":"","lastName":"Yu","suffix":""},{"id":31372518,"identity":"f6c0a8bc-47b2-4af7-82c4-ddf7c239e089","order_by":1,"name":"Chenxu Cai","email":"","orcid":"","institution":"Shandong University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Chenxu","middleName":"","lastName":"Cai","suffix":""},{"id":31372519,"identity":"691312f5-0d85-4fdf-8abf-1b300e0737e8","order_by":2,"name":"Jianhua Zhang","email":"","orcid":"","institution":"Shandong University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Jianhua","middleName":"","lastName":"Zhang","suffix":""},{"id":31372520,"identity":"9ec15533-7429-4438-9af5-1d6513807f39","order_by":3,"name":"Qinhe Zhang","email":"","orcid":"","institution":"Shandong University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Qinhe","middleName":"","lastName":"Zhang","suffix":""}],"badges":[],"createdAt":"2021-04-28 10:52:38","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-470798/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-470798/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":13641720,"identity":"9855ddc0-c864-4a90-a88b-615eff11743e","added_by":"auto","created_at":"2021-09-17 09:04:27","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":499590,"visible":true,"origin":"","legend":"","description":"","filename":"Maindocumentanonymous.pdf","url":"https://assets-eu.researchsquare.com/files/rs-470798/v1_covered.pdf"},{"id":10079795,"identity":"b64dfddd-f914-4046-a842-7cb221c07418","added_by":"auto","created_at":"2021-06-07 17:32:20","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":496087,"visible":true,"origin":"","legend":"","description":"","filename":"Maindocumentanonymous.pdf","url":"https://assets-eu.researchsquare.com/files/rs-470798/v1_covered.pdf"}],"financialInterests":"","formattedTitle":"A simple and efficient method for isomorphism identification of planar kinematic chains","fulltext":[{"header":"Full Text","content":"This preprint is available for \u003ca href='/article/rs-470798/latest.pdf' target='_blank'\u003edownload as a PDF\u003c/a\u003e."}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"soft-computing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"soco","sideBox":"Learn more about [Soft Computing](https://www.springer.com/journal/500)","snPcode":"500","submissionUrl":"https://submission.nature.com/new-submission/500/3","title":"Soft Computing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"isomorphism identification, adjacency matrix, pseudo-independence loop, kinematic chain","lastPublishedDoi":"10.21203/rs.3.rs-470798/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-470798/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIsomorphism identification plays an important role in structural design and innovative design. 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