Ultra-sensitive Inclinometer via Critical Coupling of a Gravitational Compound Pendulum for Nanoradian Tilt Measurement

Ultra-sensitive Inclinometer via Critical Coupling of a Gravitational Compound Pendulum for Nanoradian Tilt Measurement | 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 Ultra-sensitive Inclinometer via Critical Coupling of a Gravitational Compound Pendulum for Nanoradian Tilt Measurement Jianfei Long, Ying Wang, Linxiao Cong, Jiawen Xu, Mingshan Wu, and 7 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8304944/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 Accurate monitoring of the horizontal tilt is essential to suppress low-frequency noise in the measurement system of micro-thrust—a requirement for spacebased gravitational wave measurements. Unfortunately, the sensitivity of modern inclinometers is fundamentally limited by the noise floors of their physical and electronic components.To overcome these limitations is a new inclinometer design which consists of a gravitational compound pendulum and a displacement sensor that reach ultrahigh sensitivity. Our inclinometer implements a mechanical amplification mode of a quasi-zero stiffness system.By critically coupling the pendulum’s gravitational restoring moment with the stiffness of a flexure pivot, the system efficiently transforms minute tilt angles into measurable displacements. Theoretical modelling clarifies the mechanics of this angular amplification and guides our strategy for regulating the gravitational restoring moment.Experimental characterization demonstrates a resolution of 0.87 nrad over a 0–109 µrad range, the tunable amplification factor can be increased to exceeding 160 and the nonlinearity error as low as 1.18%. This compact and versatile design provides a strong motivation to deploy ultra-precision tilt measurement on advanced metrology and adaptive devices. Physical sciences/Physics/Techniques and instrumentation/Design, synthesis and processing Physical sciences/Engineering/Mechanical engineering Horizontal tilt measurement Gravitational compound pendulum Ultra sensitivity Micro-thrust measurement Critical coupling Nanoradian resolution Full Text Additional Declarations There is NO Competing Interest. 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-8304944","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":562433039,"identity":"f11e0e34-185a-456a-8abe-4b2d065848f7","order_by":0,"name":"Jianfei 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measurement, Critical coupling, Nanoradian resolution","lastPublishedDoi":"10.21203/rs.3.rs-8304944/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8304944/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Accurate monitoring of the horizontal tilt is essential to suppress low-frequency noise in the measurement system of micro-thrust—a requirement for spacebased gravitational wave measurements. Unfortunately, the sensitivity of modern inclinometers is fundamentally limited by the noise floors of their physical and electronic components.To overcome these limitations is a new inclinometer\r\ndesign which consists of a gravitational compound pendulum and a displacement sensor that reach ultrahigh sensitivity. Our inclinometer implements a mechanical amplification mode of a quasi-zero stiffness system.By critically coupling the pendulum’s gravitational restoring moment with the stiffness of a flexure pivot, the system efficiently transforms minute tilt angles into measurable\r\ndisplacements. Theoretical modelling clarifies the mechanics of this angular amplification and guides our strategy for regulating the gravitational restoring moment.Experimental characterization demonstrates a resolution of 0.87 nrad over a 0–109 µrad range, the tunable amplification factor can be increased to exceeding 160 and the nonlinearity error as low as 1.18%. 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