{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T07:36:02Z","timestamp":1772004962179,"version":"3.50.1"},"reference-count":31,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,4,3]],"date-time":"2023-04-03T00:00:00Z","timestamp":1680480000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key Research and Development Program of China","award":["2022YFB4703000"],"award-info":[{"award-number":["2022YFB4703000"]}]},{"name":"National Key Research and Development Program of China","award":["2022CXGC010503"],"award-info":[{"award-number":["2022CXGC010503"]}]},{"name":"National Key Research and Development Program of China","award":["238226"],"award-info":[{"award-number":["238226"]}]},{"name":"Key Research and Development Program of Shandong Province","award":["2022YFB4703000"],"award-info":[{"award-number":["2022YFB4703000"]}]},{"name":"Key Research and Development Program of Shandong Province","award":["2022CXGC010503"],"award-info":[{"award-number":["2022CXGC010503"]}]},{"name":"Key Research and Development Program of Shandong Province","award":["238226"],"award-info":[{"award-number":["238226"]}]},{"name":"Shandong Provincial Postdoctoral Innovative Talents Funded Scheme","award":["2022YFB4703000"],"award-info":[{"award-number":["2022YFB4703000"]}]},{"name":"Shandong Provincial Postdoctoral Innovative Talents Funded Scheme","award":["2022CXGC010503"],"award-info":[{"award-number":["2022CXGC010503"]}]},{"name":"Shandong Provincial Postdoctoral Innovative Talents Funded Scheme","award":["238226"],"award-info":[{"award-number":["238226"]}]},{"name":"Fundamental Research Funds for the Central Universities and Young Scholars Program of Shandong University","award":["2022YFB4703000"],"award-info":[{"award-number":["2022YFB4703000"]}]},{"name":"Fundamental Research Funds for the Central Universities and Young Scholars Program of Shandong University","award":["2022CXGC010503"],"award-info":[{"award-number":["2022CXGC010503"]}]},{"name":"Fundamental Research Funds for the Central Universities and Young Scholars Program of Shandong University","award":["238226"],"award-info":[{"award-number":["238226"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Concentric tube robots (CTRs) are a promising prospect for minimally invasive surgery due to their inherent compliance and ability to navigate in constrained environments. Existing mechanics-based kinematic models typically neglect friction, clearance, and torsion between each pair of contacting tubes, leading to large positioning errors in medical applications. In this paper, an improved kinematic modeling method is developed. The effect of clearance on tip position during concentric tube assembly is compensated by the database method. The new kinematic model is mechanic-based, and the impact of friction moment and torsion on tubes is considered. Integrating the infinitesimal torsion of the concentric tube robots eliminates the errors caused by the interaction force between the tubes. A prototype is built, and several experiments with kinematic models are designed. The results indicate that the error of tube rotations is less than 2 mm. The maximum error of the feeding experiment does not exceed 0.4 mm. The error of the new modeling method is lower than that of the previous kinematic model. This paper has substantial implications for the high-precision and real-time control of concentric tube robots.<\/jats:p>","DOI":"10.3390\/s23073709","type":"journal-article","created":{"date-parts":[[2023,4,4]],"date-time":"2023-04-04T02:03:00Z","timestamp":1680573780000},"page":"3709","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Modeling of and Experimenting with Concentric Tube Robots: Considering Clearance, Friction and Torsion"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-7362-6772","authenticated-orcid":false,"given":"Tianxiang","family":"Liu","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering, Shandong University, Jinan 250061, China"},{"name":"Key Laboratory of High-Efficiency and Clean Mechanical Manufacture of MOE, Shandong University, Jinan 250061, China"},{"name":"Engineering Research Center of Intelligent Unmanned System, Ministry of Education, Jinan 250061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9843-1818","authenticated-orcid":false,"given":"Gang","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Shandong University, Jinan 250061, China"},{"name":"Key Laboratory of High-Efficiency and Clean Mechanical Manufacture of MOE, Shandong University, Jinan 250061, China"},{"name":"Engineering Research Center of Intelligent Unmanned System, Ministry of Education, Jinan 250061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peng","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Shandong University, Jinan 250061, China"},{"name":"Key Laboratory of High-Efficiency and Clean Mechanical Manufacture of MOE, Shandong University, Jinan 250061, China"},{"name":"Engineering Research Center of Intelligent Unmanned System, Ministry of Education, Jinan 250061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tianyu","family":"Cheng","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Shandong University, Jinan 250061, China"},{"name":"Key Laboratory of High-Efficiency and Clean Mechanical Manufacture of MOE, Shandong University, Jinan 250061, China"},{"name":"Engineering Research Center of Intelligent Unmanned System, Ministry of Education, Jinan 250061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zijie","family":"Luo","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Shandong University, Jinan 250061, China"},{"name":"Key Laboratory of High-Efficiency and Clean Mechanical Manufacture of MOE, Shandong University, Jinan 250061, China"},{"name":"Engineering Research Center of Intelligent Unmanned System, Ministry of Education, Jinan 250061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shengsong","family":"Wang","sequence":"additional","affiliation":[{"name":"Shandong Center for Food and Drug Evaluation & Inspection, Jinan 250014, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9781-9677","authenticated-orcid":false,"given":"Fuxin","family":"Du","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Shandong University, Jinan 250061, China"},{"name":"Key Laboratory of High-Efficiency and Clean Mechanical Manufacture of MOE, Shandong University, Jinan 250061, China"},{"name":"Engineering Research Center of Intelligent Unmanned System, Ministry of Education, Jinan 250061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"844","DOI":"10.1016\/j.ejcts.2004.02.001","article-title":"First experiences with the da Vinci\u2122 operating robot in thoracic surgery","volume":"25","author":"Bodner","year":"2004","journal-title":"Eur. 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