Kinematics of single-degree-of-freedom closed-loop systems with C2 Hermite Spline interpolation

Kinematics of single-degree-of-freedom closed-loop systems with C2 Hermite Spline interpolation | 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 Kinematics of single-degree-of-freedom closed-loop systems with C 2 Hermite Spline interpolation Nicolas Capette, Vaclav Houdek, Olivier Verlinden, Bryan Olivier This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6873327/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 a procedure for computing the kinematics of closed-loop multibody subsystems when their kinematics cannot be analytically expressed in terms of the system’s degrees of freedom (DOF). The approach expresses the kinematics by a separate interpolation in translation and rotation. Firstly, the kinematics of the system is formulated through constraint equations in Cartesian coordinates. Then, the Newton-Raphson algorithm is used to solve the constraint equations and determine positions and orientations, followed by computing the solution at velocity and acceleration levels. Furthermore, an incremental interpolation method using fifth-order Hermite splines, between the reference configurations, ensures C2 continuity. The proposed interpolation approach is compared with rotation interpolation based on Tait-Bryant angles and applied to two benchmark systems: a double wishbone suspension and a slider-crank mech- anism. The results showed that interpolation with Bryant angles provide better accuracy for the slider-crank mechanism, reducing velocity and acceleration oscillations. Mechanical Engineering Robotics Computational Mathematics Closed-loop systems Multibody Dynamics Kinematics Interpolation Full Text Additional Declarations The authors declare no competing interests. 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-6873327","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":469913043,"identity":"0adb23b1-c6b1-47a3-b6a1-de38a8a65cbd","order_by":0,"name":"Nicolas 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