A compact variable stiffness joint for compliant robotics enabled by torsion-spring mean-diameter variation

A compact variable stiffness joint for compliant robotics enabled by torsion-spring mean-diameter variation | 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 A compact variable stiffness joint for compliant robotics enabled by torsion-spring mean-diameter variation Xiangxu Qu, Zhengkai Feng, Kang Ju, Cui Liu, Lan Chen, Ruiqi Xu, and 4 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9120862/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 10 You are reading this latest preprint version Abstract For robotic applications that require compliance and safety in rehabilitation training, physical human–robot collaboration, and unstructured environments, this study proposes a variable-stiffness joint design method, termed TSDV, based on the mean-coil-diameter variation mechanism of a torsion spring. First, the variation of the mean coil diameter of a cylindrical torsion spring with joint deflection angle is analysed. On this basis, a structural scheme for stiffness modulation is proposed by constraining the inward contraction of the spring inner diameter. The joint mainly consists of a torsion spring, an internal slotted sleeve, and a ball-guiding sleeve, and features a compact architecture, a wide stiffness regulation range, coaxial alignment with the robot joint axis, and both passive and active stiffness modulation modes. Subsequently, a nonlinear stiffness model of the variable-stiffness joint system is established using an energy-based method, and the validity of the theoretical model is verified through numerical simulations and finite-element analysis. The results show that both the output torque and the joint stiffness exhibit tunable nonlinear characteristics with respect to the deflection angle and regulation parameters. Finally, experiments are conducted on a TSDV prototype. The experimental results demonstrate that, under motor actuation, the proposed joint can achieve both passive and active stiffness regulation. When the deflection angle reaches 1.2 rad, the output torque range increases from 0–3.8 Nm to 0–9.2 Nm. Moreover, when the slotted sleeve fully suppresses the variation of the torsion spring inner diameter, the joint exhibits a locking function and transitions into a rigid joint. These findings indicate that the proposed variable-stiffness joint offers a compact structure, a large stiffness regulation range, and high control resolution, and thus provides a new approach for safe interaction and compliant actuation in robotic systems. Physical sciences/Engineering Physical sciences/Physics Variable stiffness joint torsion spring compliant actuation human-robot interaction Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 07 Apr, 2026 Reviews received at journal 07 Apr, 2026 Reviews received at journal 31 Mar, 2026 Reviewers agreed at journal 30 Mar, 2026 Reviewers agreed at journal 20 Mar, 2026 Reviewers invited by journal 18 Mar, 2026 Editor assigned by journal 18 Mar, 2026 Editor invited by journal 18 Mar, 2026 Submission checks completed at journal 16 Mar, 2026 First submitted to journal 16 Mar, 2026 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-9120862","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":608078214,"identity":"24d75028-9955-4540-8540-1b8c0f6a7e09","order_by":0,"name":"Xiangxu Qu","email":"","orcid":"","institution":"Qingdao Binhai University","correspondingAuthor":false,"prefix":"","firstName":"Xiangxu","middleName":"","lastName":"Qu","suffix":""},{"id":608078215,"identity":"fe305b8d-cac3-4000-9276-4cc30fe16222","order_by":1,"name":"Zhengkai 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variation\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Variable stiffness joint, torsion spring, compliant actuation, human-robot interaction","lastPublishedDoi":"10.21203/rs.3.rs-9120862/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9120862/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eFor robotic applications that require compliance and safety in rehabilitation training, physical human\u0026ndash;robot collaboration, and unstructured environments, this study proposes a variable-stiffness joint design method, termed TSDV, based on the mean-coil-diameter variation mechanism of a torsion spring. First, the variation of the mean coil diameter of a cylindrical torsion spring with joint deflection angle is analysed. On this basis, a structural scheme for stiffness modulation is proposed by constraining the inward contraction of the spring inner diameter. The joint mainly consists of a torsion spring, an internal slotted sleeve, and a ball-guiding sleeve, and features a compact architecture, a wide stiffness regulation range, coaxial alignment with the robot joint axis, and both passive and active stiffness modulation modes. Subsequently, a nonlinear stiffness model of the variable-stiffness joint system is established using an energy-based method, and the validity of the theoretical model is verified through numerical simulations and finite-element analysis. The results show that both the output torque and the joint stiffness exhibit tunable nonlinear characteristics with respect to the deflection angle and regulation parameters. Finally, experiments are conducted on a TSDV prototype. The experimental results demonstrate that, under motor actuation, the proposed joint can achieve both passive and active stiffness regulation. When the deflection angle reaches 1.2 rad, the output torque range increases from 0\u0026ndash;3.8 Nm to 0\u0026ndash;9.2 Nm. Moreover, when the slotted sleeve fully suppresses the variation of the torsion spring inner diameter, the joint exhibits a locking function and transitions into a rigid joint. These findings indicate that the proposed variable-stiffness joint offers a compact structure, a large stiffness regulation range, and high control resolution, and thus provides a new approach for safe interaction and compliant actuation in robotic systems.\u003c/p\u003e","manuscriptTitle":"A compact variable stiffness joint for compliant robotics enabled by torsion-spring mean-diameter variation","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-20 06:34:33","doi":"10.21203/rs.3.rs-9120862/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-04-07T07:26:21+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-04-07T05:57:22+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-04-01T00:45:51+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"149339592875926996977644157749634199753","date":"2026-03-30T05:03:20+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"28476291882441232457384623112009905567","date":"2026-03-20T08:11:20+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-03-18T06:43:22+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-03-18T06:39:59+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2026-03-18T06:37:41+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-03-16T15:53:31+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2026-03-16T13:35:02+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"34392df0-38e5-436b-80c6-f9cbae5e071f","owner":[],"postedDate":"March 20th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":64830533,"name":"Physical sciences/Engineering"},{"id":64830534,"name":"Physical sciences/Physics"}],"tags":[],"updatedAt":"2026-04-24T11:54:38+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-20 06:34:33","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9120862","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9120862","identity":"rs-9120862","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}