{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T00:41:11Z","timestamp":1760402471224,"version":"build-2065373602"},"reference-count":54,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,1,5]],"date-time":"2020-01-05T00:00:00Z","timestamp":1578182400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation (NSF) of China","award":["51275152 and 51875167"],"award-info":[{"award-number":["51275152 and 51875167"]}]},{"name":"National Natural Science Foundation of Hebei Province","award":["2018202114"],"award-info":[{"award-number":["2018202114"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper aims to investigate how to determine the basic parameters of the helical compression spring which supports a symmetrical cable-driven hybrid joint (CDHJ) towards the elbow joint of wheelchair-mounted robotic manipulator. The joint design of wheelchair-mounted robotic manipulator needs to consider lightweight but robust, workspace requirements, and variable stiffness elements, so we propose a CDHJ which becomes a variable stiffness joint due the spring under bending and compression provides nonlinear stiffness characteristics. Intuitively, different springs will make the workspace and stiffness of CDHJ different, so we focus on studying the spring effects on workspace and stiffness of CDHJ for its preliminary design. The key to workspace and stiffness analysis of CDHJ is the cable tension, the key to calculate the cable tension is the lateral bending and compression spring model. The spring model is based on Castigliano\u2019s theorem to obtain the relationship between spring force and displacement. The simulation results verify the correctness of the proposed spring model, and show that the spring, with properly chosen parameters, can increase the workspace of CDHJ whose stiffness also can be adjusted to meet the specified design requirements. Then, the modelling method can be extended to other cable-driven mechanism with a flexible compression spring.<\/jats:p>","DOI":"10.3390\/sym12010101","type":"journal-article","created":{"date-parts":[[2020,1,6]],"date-time":"2020-01-06T03:48:48Z","timestamp":1578282528000},"page":"101","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Spring Effects on Workspace and Stiffness of a Symmetrical Cable-Driven Hybrid Joint"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2280-8583","authenticated-orcid":false,"given":"Shan","family":"Zhang","sequence":"first","affiliation":[{"name":"College of Mechanical and Electrical Engineering, Zaozhuang University, Zaozhuang 277160, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zheng","family":"Sun","sequence":"additional","affiliation":[{"name":"College of Mechanical and Electrical Engineering, Zaozhuang University, Zaozhuang 277160, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jili","family":"Lu","sequence":"additional","affiliation":[{"name":"College of Mechanical and Electrical Engineering, Zaozhuang University, Zaozhuang 277160, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lei","family":"Li","sequence":"additional","affiliation":[{"name":"College of Mechanical and Electrical Engineering, Zaozhuang University, Zaozhuang 277160, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chunlei","family":"Yu","sequence":"additional","affiliation":[{"name":"College of Mechanical and Electrical Engineering, Zaozhuang University, Zaozhuang 277160, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dongxing","family":"Cao","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Hebei University of Technology, Tianjin 300130, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,1,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1179\/2045772313Y.0000000132","article-title":"Functional assessment and performance evaluation for assistive robotic manipulators: Literature review","volume":"36","author":"Chung","year":"2013","journal-title":"J. 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