Chaos intensity: Using Lyapunov exponent and uniformity to judge the intensity of mechanism chaos based on a planar slider–crank mechanism with multi-clearance joints

Chaos intensity: Using Lyapunov exponent and uniformity to judge the intensity of mechanism chaos based on a planar slider–crank mechanism with multi-clearance joints | 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 Method Article Chaos intensity: Using Lyapunov exponent and uniformity to judge the intensity of mechanism chaos based on a planar slider–crank mechanism with multi-clearance joints Hui Li, Mao Run, Pucha Song, Yongping Gu, Yang Shu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3892502/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 Mechanism chaos, a real nonlinear dynamic phenomenon arises from a mechanism with nonlinear characteristics, whose chaotic behavior can directly affect the performance of machinery. For general mechanism, it will cause undesired impact and vibration, furthermore, reducing the life span of the machine, and then it should be suppressed or controlled. For some special applications, however, it is beneficial to improve the performance of the mechanism, and then it should be excited or enhanced. In addition, there is a coupling of several nonlinear factors existing in the mechanism. In all these circumstances, it is necessary to establish a method to judge chaos intensity (MJCI). However, there has not been widely accepted and effective MJCI until now. To satisfy the need, this paper focuses on the establishment of MJCI. To verify the correctness of this method, Logistic mapping, Duffing chaotic oscillator, and Lorenz system are used. Finally, the MJCI is used to analyze the chaos intensity of a planar slider–crank mechanism with a single or two clearance joints, the results show that with the change of clearance sizes or driving speeds, the chaos intensity can be suppressed or excited, and the practicability of MJCI in mechanism is proved. Chaos intensity Chaos suppression Chaos excitation Clearance joints Uniformity Lyapunov exponent 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. 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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-3892502","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Method Article","associatedPublications":[],"authors":[{"id":269042178,"identity":"9b1745e0-9901-4c15-b98d-33259e7cff11","order_by":0,"name":"Hui Li","email":"","orcid":"","institution":"Chengdu University","correspondingAuthor":false,"prefix":"","firstName":"Hui","middleName":"","lastName":"Li","suffix":""},{"id":269042179,"identity":"52a3450c-a2cb-4381-a5af-daf8292ad702","order_by":1,"name":"Mao Run","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA0klEQVRIiWNgGAWjYBACNvb+jw8S//2zY2NvPkCcFj6eA8YGH9gOJPPzHEsgToucRIKZ5Ay2A4wzZ/gYEOkwhoRkYx6eO8wGN3g+3njDYCen20BQy4GDj3kknvEZ3O7dbDmHIdnY7AAhLYyNzcY8BszMBnfObpPmYTiQuI2gFmZmNmmeBGbGDTdynhGpBQgkZxw4DPR+DhuRWnh4mA0+NqSBAtnYco4BEX6Rn/+G8UFigw0oKh/eeFNhJ0dQCwqQ4CEyapC1kKpjFIyCUTAKRgQAAFmmQRGXVeCFAAAAAElFTkSuQmCC","orcid":"","institution":"Chengdu University","correspondingAuthor":true,"prefix":"","firstName":"Mao","middleName":"","lastName":"Run","suffix":""},{"id":269042180,"identity":"bb57487e-4ea9-4ee5-af21-522e20a44075","order_by":2,"name":"Pucha Song","email":"","orcid":"","institution":"Chengdu University","correspondingAuthor":false,"prefix":"","firstName":"Pucha","middleName":"","lastName":"Song","suffix":""},{"id":269042181,"identity":"e5989020-3fa4-4793-83e4-a76918aa7f58","order_by":3,"name":"Yongping Gu","email":"","orcid":"","institution":"Chengdu University","correspondingAuthor":false,"prefix":"","firstName":"Yongping","middleName":"","lastName":"Gu","suffix":""},{"id":269042182,"identity":"f6bb5dfb-c47d-41ff-945b-ef01fcb4feb8","order_by":4,"name":"Yang Shu","email":"","orcid":"","institution":"Chengdu University","correspondingAuthor":false,"prefix":"","firstName":"Yang","middleName":"","lastName":"Shu","suffix":""}],"badges":[],"createdAt":"2024-01-24 01:29:15","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3892502/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3892502/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":52343033,"identity":"dac2e30f-ff52-438b-a608-14d093aa6941","added_by":"auto","created_at":"2024-03-09 14:08:05","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1466167,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3892502/v1_covered_5a761635-a216-402d-9ab8-039586b677c7.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Chaos intensity: Using Lyapunov exponent and uniformity to judge the intensity of mechanism chaos based on a planar slider–crank mechanism with multi-clearance joints","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":"Chaos intensity, Chaos suppression, Chaos excitation, Clearance joints, Uniformity, Lyapunov exponent","lastPublishedDoi":"10.21203/rs.3.rs-3892502/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3892502/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eMechanism chaos, a real nonlinear dynamic phenomenon arises from a mechanism with nonlinear characteristics, whose chaotic behavior can directly affect the performance of machinery. For general mechanism, it will cause undesired impact and vibration, furthermore, reducing the life span of the machine, and then it should be suppressed or controlled. For some special applications, however, it is beneficial to improve the performance of the mechanism, and then it should be excited or enhanced. In addition, there is a coupling of several nonlinear factors existing in the mechanism. In all these circumstances, it is necessary to establish a method to judge chaos intensity (MJCI). However, there has not been widely accepted and effective MJCI until now. To satisfy the need, this paper focuses on the establishment of MJCI. To verify the correctness of this method, Logistic mapping, Duffing chaotic oscillator, and Lorenz system are used. 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