A concept of the metamodel based on the dynamics analysis results of the eccentric crank-rocker mechanism

A concept of the metamodel based on the dynamics analysis results of the eccentric crank-rocker mechanism | 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 concept of the metamodel based on the dynamics analysis results of the eccentric crank-rocker mechanism Andrzej Urbaś, Jacek Stadnicki This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6306079/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 paper presents the concept of using the metamodel of the dynamics of the crank-rocker mechanism with eccentricity for its synthesis. The formalism of joint coordinates, homogeneous transformation matrices, and Lagrange equations are used to derive the mathematical model of the mechanism, which considers the flexibility of the drive and con-rod. Using the mathematical model of the mechanism, the function of which is to compact the raw material using a rocker, the simulation of many dimensional variants of the mechanism is performed. Next, based on the results, a metamodel of the mechanism is proposed, with the design criterion being the maximal value of the rocker kinetic energy, which is adopted as a measure of the efficiency of raw material compaction. The metamodel is used in practice to determine the lengths of links of the mechanism that met the adopted design criteria. A comparison of options of the analysis of mechanism models with and without the flexibility of the drive or/and con-rod is also presented. crank-rocker mechanism dynamics eccentricity flexibility metamodel 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. 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-6306079","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":462300880,"identity":"7852a5cc-48ea-480e-9b66-16c88239b251","order_by":0,"name":"Andrzej Urbaś","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAwklEQVRIiWNgGAWjYHACNiC2YTCQAFI8QMxHpJY0hBY2IrUcJkEL/4zcZw9+/DmfuF26gfHB2zaGPIJaJG6kmxv2tt1O3DnnALPh3DaGYsIOu5HGJsHbcDtxw40ENmneNobENkI65IFaJP/8OQfSwv6bKC0GQC3SPGwHwLYwE6XF8MwzdmPZtmTjnXMONkvOOSdB2C9yx9PYHr75Yye7Xbr54Ic3ZTZ5/IS0IAHGBiAhkUCCDiggQ8soGAWjYBQMdwAAaVM9ZwYLDeAAAAAASUVORK5CYII=","orcid":"","institution":"University of Bielsko-Biala","correspondingAuthor":true,"prefix":"","firstName":"Andrzej","middleName":"","lastName":"Urbaś","suffix":""},{"id":462300881,"identity":"89811858-a3d0-45fa-8585-97b62a35f3d9","order_by":1,"name":"Jacek Stadnicki","email":"","orcid":"","institution":"University of Bielsko-Biala","correspondingAuthor":false,"prefix":"","firstName":"Jacek","middleName":"","lastName":"Stadnicki","suffix":""}],"badges":[],"createdAt":"2025-03-25 17:53:06","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6306079/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6306079/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":84603332,"identity":"c2e8d874-e532-4880-b7f3-1322a304c101","added_by":"auto","created_at":"2025-06-14 10:23:37","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":694811,"visible":true,"origin":"","legend":"","description":"","filename":"MSD20259.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6306079/v1_covered_590a76cf-ecdf-4d4c-acc0-611ad7ce2c5c.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A concept of the metamodel based on the dynamics analysis results of the eccentric crank-rocker mechanism","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":" crank-rocker mechanism, dynamics, eccentricity, flexibility, metamodel","lastPublishedDoi":"10.21203/rs.3.rs-6306079/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6306079/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This paper presents the concept of using the metamodel of the dynamics of the crank-rocker mechanism with eccentricity for its synthesis. The formalism of joint coordinates, homogeneous transformation matrices, and Lagrange equations are used to derive the mathematical model of the mechanism, which considers the flexibility of the drive and con-rod. Using the mathematical model of the mechanism, the function of which is to compact the raw material using a rocker, the simulation of many dimensional variants of the mechanism is performed. Next, based on the results, a metamodel of the mechanism is proposed, with the design criterion being the maximal value of the rocker kinetic energy, which is adopted as a measure of the efficiency of raw material compaction. The metamodel is used in practice to determine the lengths of links of the mechanism that met the adopted design criteria. 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