{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T14:18:16Z","timestamp":1772115496418,"version":"3.50.1"},"reference-count":34,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,5,11]],"date-time":"2021-05-11T00:00:00Z","timestamp":1620691200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100014583","name":"SFI Offshore Mechatronics","doi-asserted-by":"publisher","award":["237896"],"award-info":[{"award-number":["237896"]}],"id":[{"id":"10.13039\/100014583","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005416","name":"Norges Forskningsr\u00e5d","doi-asserted-by":"publisher","award":["261647\/O20"],"award-info":[{"award-number":["261647\/O20"]}],"id":[{"id":"10.13039\/501100005416","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotics"],"abstract":"<jats:p>A closed-form dynamic model of the planar multi-link flexible manipulator is presented. The assumed modes method is used with the Lagrangian formulation to obtain the dynamic equations of motion. Explicit equations of motion are derived for a three-link case assuming two modes of vibration for each link. The eigenvalue problem associated with the mass boundary conditions, which changes with the robot configuration and payload, is discussed. The time-domain simulation results and frequency-domain analysis of the dynamic model are presented to show the validity of the theoretical derivation.<\/jats:p>","DOI":"10.3390\/robotics10020070","type":"journal-article","created":{"date-parts":[[2021,5,11]],"date-time":"2021-05-11T22:53:40Z","timestamp":1620773620000},"page":"70","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["Dynamic Modeling of Planar Multi-Link Flexible Manipulators"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1731-3786","authenticated-orcid":false,"given":"Dipendra","family":"Subedi","sequence":"first","affiliation":[{"name":"Department of Engineering Sciences, University of Agder, 4879 Grimstad, Norway"}]},{"given":"Ilya","family":"Tyapin","sequence":"additional","affiliation":[{"name":"Department of Engineering Sciences, University of Agder, 4879 Grimstad, Norway"}]},{"given":"Geir","family":"Hovland","sequence":"additional","affiliation":[{"name":"Department of Engineering Sciences, University of Agder, 4879 Grimstad, Norway"}]}],"member":"1968","published-online":{"date-parts":[[2021,5,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"141","DOI":"10.4173\/mic.2020.3.2","article-title":"Review on Modeling and Control of Flexible Link Manipulators","volume":"41","author":"Subedi","year":"2020","journal-title":"Model. 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