Dynamic Modeling of a 3-PRS Parallel Mechanism Based on the Hierarchical Aggregation Modeling Method

Dynamic Modeling of a 3-PRS Parallel Mechanism Based on the Hierarchical Aggregation Modeling Method | 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 Dynamic Modeling of a 3-PRS Parallel Mechanism Based on the Hierarchical Aggregation Modeling Method Qiao Chen, Bo Wang, Wu Yangong This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9379764/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 The 3-PRS (3-prismatic-revolute-spherical) mechanism is widely used in high-end machining equipment. However, its dynamic modeling has long been restricted by strong coupling among multiple subsystems and complex constraint processing, limiting further improvement of equipment accuracy.To solve this problem, this paper proposes a `hierarchical aggregation modeling method' based on the Udwadia‑Kalaba (U‑K) approach and applies it to establish the dynamic model of the 3-PRS mechanism. The mechanism is first decomposed into three limbs; dynamic equations of each unconstrained subsystem are established via the Lagrange method, greatly reducing modeling difficulty. Second-order differential constraint equations are then derived from geometric constraints of the moving platform. Finally, subsystems and constraints are integrated using U-K equations to obtain the complete constrained dynamic model. The method features clear principle, high solving efficiency and standardized process.Owing to its hierarchical aggregation property, system dynamic equations can be efficiently fused with actual and virtual constraints. An integrated trajectory tracking control framework is further constructed to realize collaborative optimization of dynamic modeling and trajectory control. Simulation results show that constraint errors can be controlled at the micron level, fully verifying the accuracy and reliability of the model. Dynamic Modeling 3PRS Parallel Mechanism Udwadia-Kalaba Method Trajectory Tracking Control 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. 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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-9379764","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":626026073,"identity":"bef86a37-b784-4396-adca-b6e4a75bac16","order_by":0,"name":"Qiao Chen","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA5klEQVRIiWNgGAWjYDACCRBRISHHz97AwMDYQLSWMzbGkj0HoFrYiNHC2JaWuGFGApFa+Gc3H3vwhu0w4wbJN4YPfu5gyOOXJ+A6iTvH0g3n8BxmNpfOMTbsPcNQLNlGwBYDiRwzaR6Jw2yWs3PMJHjbGBI3HCOoJf+bNI/BYR6Dm2fMf/4FatlPWEsOmzRPQpqEwQ0eM2awLYS8L3EjzUxyzgEbA8metGJp2TaJxBnHEvBr4Z+R/Ezi7T+J+n72wxs/vm2zSexvPkDAGhDgAZMcBgzQmCVaC/sDIpWPglEwCkbBSAMAZutCkrnAKcoAAAAASUVORK5CYII=","orcid":"","institution":"China Electronics Technology Group Corporation","correspondingAuthor":true,"prefix":"","firstName":"Qiao","middleName":"","lastName":"Chen","suffix":""},{"id":626026074,"identity":"2404a815-29b5-43f7-8ada-5f9c1ed75b3e","order_by":1,"name":"Bo Wang","email":"","orcid":"","institution":"Harbin Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Bo","middleName":"","lastName":"Wang","suffix":""},{"id":626026075,"identity":"6d11dc2b-57a1-4475-a6d4-d7dcfbba337d","order_by":2,"name":"Wu Yangong","email":"","orcid":"","institution":"Harbin Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Wu","middleName":"","lastName":"Yangong","suffix":""}],"badges":[],"createdAt":"2026-04-10 12:54:13","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9379764/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9379764/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":109026977,"identity":"53c135a2-868f-4a55-93b9-e3d7a6b821e6","added_by":"auto","created_at":"2026-05-11 21:39:36","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1244965,"visible":true,"origin":"","legend":"","description":"","filename":"3PRS.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9379764/v1_covered_c1cc659d-cae5-4c28-a1f5-af11db171907.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Dynamic Modeling of a 3-PRS Parallel Mechanism Based on the Hierarchical Aggregation Modeling Method","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":"Dynamic Modeling, 3PRS Parallel Mechanism, Udwadia-Kalaba Method, Trajectory Tracking Control","lastPublishedDoi":"10.21203/rs.3.rs-9379764/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9379764/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe 3-PRS (3-prismatic-revolute-spherical) mechanism is widely used in high-end machining equipment. However, its dynamic modeling has long been restricted by strong coupling among multiple subsystems and complex constraint processing, limiting further improvement of equipment accuracy.To solve this problem, this paper proposes a `hierarchical aggregation modeling method' based on the Udwadia‑Kalaba (U‑K) approach and applies it to establish the dynamic model of the 3-PRS mechanism. The mechanism is first decomposed into three limbs; dynamic equations of each unconstrained subsystem are established via the Lagrange method, greatly reducing modeling difficulty. Second-order differential constraint equations are then derived from geometric constraints of the moving platform. Finally, subsystems and constraints are integrated using U-K equations to obtain the complete constrained dynamic model. The method features clear principle, high solving efficiency and standardized process.Owing to its hierarchical aggregation property, system dynamic equations can be efficiently fused with actual and virtual constraints. An integrated trajectory tracking control framework is further constructed to realize collaborative optimization of dynamic modeling and trajectory control. 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