Modeling and Analysis of Unilateral Rigid Impacts in a Universal Joint with Clearance

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Bajaj This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7014961/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 16 Mar, 2026 Read the published version in Nonlinear Dynamics → Version 1 posted 11 You are reading this latest preprint version Abstract This study presents the modeling and dynamic analysis of a universal joint (U-Joint) with radial clearance, focusing on the mod-eling of rigid unilateral frictional contacts at the cross-piece and yoke interfaces. Previous literature on the modeling and dynamic analysis of U-Joints neglect the crosspiece inertial characteristics and friction between yoke and cross-piece contact interface in the presence of mechanical clearances. While in studies without clearance the inertial and frictional dynamics can be neglected, they become essential for accurately capturing and understanding the non-smooth dynamics introduced by radial clearance between yoke and crosspiece. The impacts between yoke and crosspiece contact points are assumed to be rigid and characterized using a set-valued impact law based on Signorini’s condition combined with quasi-static LuGre friction law, capturing the complex contact interactions. The numerical simulations demonstrate the significant influence of clearance on the dynamic response of U-Joints, revealing phenomena such as symmetrical double walled impact-induced oscillations, quasi-periodic oscillations, grazing bifurcations, and chaos. Set-Valued Theory Non-Smooth Dynamics Contact Dynamics Universal Joint Multibody Modeling Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 16 Mar, 2026 Read the published version in Nonlinear Dynamics → Version 1 posted Editorial decision: Revision requested 17 Aug, 2025 Reviews received at journal 15 Aug, 2025 Reviews received at journal 06 Aug, 2025 Reviews received at journal 29 Jul, 2025 Reviewers agreed at journal 16 Jul, 2025 Reviewers agreed at journal 15 Jul, 2025 Reviewers agreed at journal 14 Jul, 2025 Reviewers invited by journal 14 Jul, 2025 Editor assigned by journal 04 Jul, 2025 Submission checks completed at journal 01 Jul, 2025 First submitted to journal 30 Jun, 2025 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. 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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-7014961","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":485712037,"identity":"83061e4d-a8fc-47d2-bb5d-e1a35c8b17dd","order_by":0,"name":"Junaid Ali","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAw0lEQVRIiWNgGAWjYDACdsaGAx8MbEBMAxDB2EBQCzNj48EZBWkkaWFgPszz4TAJWvibmRsOzjA4n2dw+/A2iQ8MNrIbDhDQInEY7JfbxQbn0sokZzCkGRPUwgDUArTlduKGMzxm0jwMhxMJapEHajnMY3AOouUPw3/CWgwgWg5AtDAwHCCsxRDisORiyTNsxZY9BsnGMwlpkTve/vjDhz92eXxnmDfe+FFhJ9tHSAsMJEDdSaRyJC2jYBSMglEwCrAAAC8USlTBQwCDAAAAAElFTkSuQmCC","orcid":"","institution":"Purdue University","correspondingAuthor":true,"prefix":"","firstName":"Junaid","middleName":"","lastName":"Ali","suffix":""},{"id":485712038,"identity":"c71c053c-b054-4bec-b75f-3ec12ca29cda","order_by":1,"name":"Gregory Shaver","email":"","orcid":"","institution":"Purdue University","correspondingAuthor":false,"prefix":"","firstName":"Gregory","middleName":"","lastName":"Shaver","suffix":""},{"id":485712039,"identity":"2af9d5fd-b11b-46e3-a691-36a41ec006f1","order_by":2,"name":"Anil K. 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