A new Isomorphism Identification Method for Kinematic Chain Based on Exchange and Compare of Lower-Triangle Matrix with Whole Information

A new Isomorphism Identification Method for Kinematic Chain Based on Exchange and Compare of Lower-Triangle Matrix with Whole Information | 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 new Isomorphism Identification Method for Kinematic Chain Based on Exchange and Compare of Lower-Triangle Matrix with Whole Information LIANGBO SUN, Xiaocui Liu, Xin Liu, Xixi Hong, Deping Zhang, Houchang Pei This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2861663/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 Isomorphism identification is an important step and costs major counting labor (more than 90%) in kinematic chain (KC) structure synthesis, many isomorphism identification methods have been proposed by researchers in past decades. The identification principle is simple and easy to be understood, the result has no objection, and the programming is simple and efficient, these are main criterions for isomorphism identification method. A new Matrix with Whole Information (MWI) has been proposed to describe the structure information of KC, and the principles of determining multiple joints and polygonal links are also proposed. Based on the principle that the Lower Triangular Matrix with Whole Information (LTMWI) can uniquely express the structure of KC, a new isomorphism identification method, based on the exchange and compare of LTMWI is proposed. This method is based on the law of exchange of links’ numbers and key points’ numbers, and two KCs are expressed by LTMWI, in which one LTMWI is selected as the datum matrix, the key points are arranged in different groups and non-zero elements of key points are moved forward, the definite and indefinite key points are obtained, under the assumption that all key points in the same positions have the mapping relationships one-to-one between exchange matrix and datum matrix, a finite number of exchange matrices are generated and compared with datum matrix, then isomorphism can be drawn. This method has the advantages such as simple principle, easy to program and only analysis and comparisons are needed in the identification process. The isomorphism identification results and the mapping relationships of links and even revolute pairs can all be obtained. The isomorphic analysis results of several KCs have shown the above characteristics of this method. Isomorphism identification Matrix with whole information (MWI) Lower triangular matrix with whole information (LTMWI) Multiple-joint Polygonal link. Full Text 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. 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-2861663","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":199746147,"identity":"ab207b93-2540-4673-8d9f-0e9dfd96a3da","order_by":0,"name":"LIANGBO 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The identification principle is simple and easy to be understood, the result has no objection, and the programming is simple and efficient, these are main criterions for isomorphism identification method. A new Matrix with Whole Information (MWI) has been proposed to describe the structure information of KC, and the principles of determining multiple joints and polygonal links are also proposed. Based on the principle that the Lower Triangular Matrix with Whole Information (LTMWI) can uniquely express the structure of KC, a new isomorphism identification method, based on the exchange and compare of LTMWI is proposed. This method is based on the law of exchange of links’ numbers and key points’ numbers, and two KCs are expressed by LTMWI, in which one LTMWI is selected as the datum matrix, the key points are arranged in different groups and non-zero elements of key points are moved forward, the definite and indefinite key points are obtained, under the assumption that all key points in the same positions have the mapping relationships one-to-one between exchange matrix and datum matrix, a finite number of exchange matrices are generated and compared with datum matrix, then isomorphism can be drawn. This method has the advantages such as simple principle, easy to program and only analysis and comparisons are needed in the identification process. The isomorphism identification results and the mapping relationships of links and even revolute pairs can all be obtained. 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