Analyzing the Stability Problem of Chairs from the Perspective of Force Equilibrium

Analyzing the Stability Problem of Chairs from the Perspective of Force Equilibrium | 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 Article Analyzing the Stability Problem of Chairs from the Perspective of Force Equilibrium Hui ZHANG This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7263120/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 chair stability model is an important mathematical tool for analyzing the stability of chair placement. Its core lies in accurately judging the risk of chair tipping and quantitatively evaluating the placement stability.This study innovatively constructs a physical-mathematical coupling model based on the theory of rigid body static equilibrium. By defining the height function of chair legs off the ground and the contact force distribution function, and combining with the mathematical zero-point theorem, it is strictly proved that on a ground satisfying continuity conditions, there must exist a specific rotation angle that can achieve simultaneous four-leg grounding.The model deeply analyzes the simplification mechanism of symmetric structures on moment equilibrium equations, and numerical simulations verify the accuracy and reliability of the theoretical derivation. The research results provide important theoretical basis and methodological guidance for fields such as furniture structural optimization design and robot foot configuration improvement. Physical sciences/Engineering Physical sciences/Mathematics and computing Zero-point theorem Contact force distribution Stability problem 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-7263120","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":494345380,"identity":"cbdad4fb-09fc-4746-8447-bf2914491e07","order_by":0,"name":"Hui ZHANG","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAy0lEQVRIiWNgGAWjYBAC+/MN6R8+8Njw8LM3EKvnxoFnjDNk0mQkew4Qq+VA4jNmDpvDNgY3EojUwdhwOO0xQw4zD8PNxxtvMNTYRBPUwszclm5ccIaNh3F2WrEFw7G03AZCWtgYziRIz+zh4WGWzjGTANpJWAsPQ/4Had5/EjxskmeI1CLBkJAmzcNjwMMjwUOkFgOJA8mGM3gSgDqAfkkgxi8G/A2JDz7w/Le3P354440PNTaEtaDamECKcogWUnWMglEwCkbByAAAKZE9QtMqpYgAAAAASUVORK5CYII=","orcid":"","institution":"China West Normal University","correspondingAuthor":true,"prefix":"","firstName":"Hui","middleName":"","lastName":"ZHANG","suffix":""}],"badges":[],"createdAt":"2025-07-31 14:08:35","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7263120/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7263120/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":88233113,"identity":"3d279894-9a8b-4521-8a28-3b0109f67e87","added_by":"auto","created_at":"2025-08-04 09:48:13","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":463750,"visible":true,"origin":"","legend":"","description":"","filename":"AnalyzingtheStabilityProblemofChairsfromthe.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7263120/v1_covered_98f734b5-a776-4e79-bab5-074aa65804f2.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Analyzing the Stability Problem of Chairs from the Perspective of Force Equilibrium","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"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":"Zero-point theorem, Contact force distribution, Stability problem","lastPublishedDoi":"10.21203/rs.3.rs-7263120/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7263120/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"The chair stability model is an important mathematical tool for analyzing the stability of chair placement. 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