{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:24:03Z","timestamp":1760059443322,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T00:00:00Z","timestamp":1750118400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Nature Science Foundation of China","doi-asserted-by":"publisher","award":["52305052","CSTB2023NSCQ-MSX0813","KJQN202403120","KJZD-M202403101","KJZD-K202203104","KJZD-K202303103","KJZD-K202403104","KJZD-K202203404"],"award-info":[{"award-number":["52305052","CSTB2023NSCQ-MSX0813","KJQN202403120","KJZD-M202403101","KJZD-K202203104","KJZD-K202303103","KJZD-K202403104","KJZD-K202203404"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Chongqing Natural Science Foundation","award":["52305052","CSTB2023NSCQ-MSX0813","KJQN202403120","KJZD-M202403101","KJZD-K202203104","KJZD-K202303103","KJZD-K202403104","KJZD-K202203404"],"award-info":[{"award-number":["52305052","CSTB2023NSCQ-MSX0813","KJQN202403120","KJZD-M202403101","KJZD-K202203104","KJZD-K202303103","KJZD-K202403104","KJZD-K202203404"]}]},{"name":"Scientific and Technological Research Program of Chongqing Municipal Education Commission","award":["52305052","CSTB2023NSCQ-MSX0813","KJQN202403120","KJZD-M202403101","KJZD-K202203104","KJZD-K202303103","KJZD-K202403104","KJZD-K202203404"],"award-info":[{"award-number":["52305052","CSTB2023NSCQ-MSX0813","KJQN202403120","KJZD-M202403101","KJZD-K202203104","KJZD-K202303103","KJZD-K202403104","KJZD-K202203404"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>The torsional stiffness of rehabilitation robot joints is a critical performance determinant, significantly affecting motion accuracy, stability, and user comfort. This paper introduces an innovative traction drive mechanism that transmits torque through friction forces, overcoming mechanical impact issues of traditional gear transmissions, though accurately modeling surface roughness effects remains challenging. Based on fractal theory, this study presents a comprehensive torsional stiffness analysis for advanced traction drive joints. Surface topography is characterized using the Weierstrass\u2013Mandelbrot function, and a contact mechanics model accounting for elastic\u2013plastic deformation of micro-asperities is developed to derive the tangential stiffness of individual contact pairs. Static force analysis determines load distribution, and overall joint torsional stiffness is calculated through the integration of individual contact contributions. Parametric analyses reveal that contact stiffness increases with normal load, contact length, and radius, while decreasing with the tangential load and roughness parameter. Stiffness exhibits a non-monotonic relationship with fractal dimension, reaching a maximum at intermediate values. Overall system stiffness demonstrates similar parameter dependencies, with a slight decrease under increasing output load when sufficient preload is applied. This fractal-based model enables more accurate stiffness prediction and offers valuable theoretical guidance for design optimization and performance improvement in rehabilitation robot joints.<\/jats:p>","DOI":"10.3390\/ma18122866","type":"journal-article","created":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T10:45:26Z","timestamp":1750157126000},"page":"2866","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Modeling and Analysis of Torsional Stiffness in Rehabilitation Robot Joints Using Fractal Theory"],"prefix":"10.3390","volume":"18","author":[{"given":"Shuaidong","family":"Zou","sequence":"first","affiliation":[{"name":"College of Smart Health, Chongqing Polytechnic University of Electronic Technology, Chongqing 401331, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenjie","family":"Yan","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Mechanical Transmission for Advanced Equipment, Chongqing University, Chongqing 400044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guanghui","family":"Xie","sequence":"additional","affiliation":[{"name":"College of Smart Health, Chongqing Polytechnic University of Electronic Technology, Chongqing 401331, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Renqiang","family":"Yang","sequence":"additional","affiliation":[{"name":"College of Smart Health, Chongqing Polytechnic University of Electronic Technology, Chongqing 401331, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huachao","family":"Xu","sequence":"additional","affiliation":[{"name":"College of Smart Health, Chongqing Polytechnic University of Electronic Technology, Chongqing 401331, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fanwei","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Engineering, University of Auckland, Auckland 0632, New Zealand"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"780","DOI":"10.1109\/TMRB.2023.3310086","article-title":"Mechanism design and control of shoulder rehabilitation robots: A Review","volume":"5","author":"Shah","year":"2023","journal-title":"IEEE Trans. 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