Higher-Order Kinematics Modeling of 3-RRS Parallel Mechanism Based on CGA

Higher-Order Kinematics Modeling of 3-RRS Parallel Mechanism Based on CGA | 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 Original Article Higher-Order Kinematics Modeling of 3-RRS Parallel Mechanism Based on CGA Chang Wang, Tieshi Zhao, Erwei Li, Yanzhi Zhao, Hui Bian, Mingchao Geng This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-101801/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 Higher-order kinematics of mechanisms has been applied in servo motor control, human-robot interaction and machinery life design fields, etc. The representations of acceleration and jerk by screws have been fully developed by researchers with the methods of the differential of the matrix representation of SE (3) group. Clifford algebra, which is tighter and with higher computational efficiency than the matrix method, is another representation of the motions of rigid bodies. It has been used in position kinematics, grub task motion planning, and robot vision for its convenience of geometric representations and calculations. As far as we know, the work of higher-order kinematics of mechanisms based on Clifford algebra is rare. First, after recalling the based theory of motion representation in conformal geometric algebra (CGA), the mathematical relationships between flag and motor are built. Second, a method for the higher-order kinematics modeling of serial chain mechanisms is proposed. Finally, the higher-order kinematics of the 3-RRS parallel mechanism is built to prove the correctness of the algorithm. This work further enriches the application of CGA for the higher-order kinematics modeling of parallel mechanisms. Mechanical Engineering CGA Flag Rigid body framing Higher-order kinematics 3-RRS parallel mechanism Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 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-101801","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Original Article","associatedPublications":[],"authors":[{"id":4300586,"identity":"2607b928-734f-44f9-8067-f6a27500ebc0","order_by":0,"name":"Chang Wang","email":"","orcid":"","institution":"Yanshan University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Chang","middleName":"","lastName":"Wang","suffix":""},{"id":4300587,"identity":"a53361ae-0667-46cc-9f71-bd85d4295912","order_by":1,"name":"Tieshi 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a PDF\u003c/a\u003e.\u003c/p\u003e"}],"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":false,"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":"CGA, Flag, Rigid body framing, Higher-order kinematics, 3-RRS parallel mechanism","lastPublishedDoi":"10.21203/rs.3.rs-101801/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-101801/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eHigher-order kinematics of mechanisms has been applied in servo motor control, human-robot interaction and machinery life design fields, etc. The representations of acceleration and jerk by screws have been fully developed by researchers with the methods of the differential of the matrix representation of \u003cem\u003eSE\u003c/em\u003e(3) group. Clifford algebra, which is tighter and with higher computational efficiency than the matrix method, is another representation of the motions of rigid bodies. It has been used in position kinematics, grub task motion planning, and robot vision for its convenience of geometric representations and calculations. As far as we know, the work of higher-order kinematics of mechanisms based on Clifford algebra is rare. First, after recalling the based theory of motion representation in conformal geometric algebra (CGA), the mathematical relationships between flag and motor are built. Second, a method for the higher-order kinematics modeling of serial chain mechanisms is proposed. Finally, the higher-order kinematics of the 3-RRS parallel mechanism is built to prove the correctness of the algorithm. This work further enriches the application of CGA for the higher-order kinematics modeling of parallel mechanisms.\u003c/p\u003e","manuscriptTitle":"Higher-Order Kinematics Modeling of 3-RRS Parallel Mechanism Based on CGA","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2020-11-06 15:41:49","doi":"10.21203/rs.3.rs-101801/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"2ac69c8a-1db0-4f51-bbd5-95eb8b7d798e","owner":[],"postedDate":"November 6th, 2020","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":996473,"name":"Mechanical Engineering"}],"tags":[],"updatedAt":"2021-05-01T21:57:37+00:00","versionOfRecord":[],"versionCreatedAt":"2020-11-06 15:41:49","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-101801","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-101801","identity":"rs-101801","version":["v1"]},"buildId":"7rjqhiLT3MXkJMwkYKINL","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}