{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:22:53Z","timestamp":1760145773308,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2024,8,22]],"date-time":"2024-08-22T00:00:00Z","timestamp":1724284800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12302132","2021J05114","2023J05249"],"award-info":[{"award-number":["12302132","2021J05114","2023J05249"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003392","name":"Natural Science Foundation of Fujian Province","doi-asserted-by":"publisher","award":["12302132","2021J05114","2023J05249"],"award-info":[{"award-number":["12302132","2021J05114","2023J05249"]}],"id":[{"id":"10.13039\/501100003392","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Force measurement is crucial in numerous engineering applications, while traditional force sensors often face problems such as elevated expenses or significant measurement errors. To tackle this issue, we propose an innovative force sensor employing three nested flexible rings fabricated through 3D additive manufacturing, which detects external forces through the displacement variations of flexible rings. An analytical model on the basis of the minimal energy method is developed to elucidate the force-displacement correlation with nonlinearity. Both FEM simulations and experiments verify the sensor\u2019s effectiveness. This sensor has the advantages of low expenses and easy manufacture, indicating promising prospects in a range of applications, including robotics, the automotive industry, and iatrical equipment.<\/jats:p>","DOI":"10.3390\/s24165441","type":"journal-article","created":{"date-parts":[[2024,8,23]],"date-time":"2024-08-23T12:58:07Z","timestamp":1724417887000},"page":"5441","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Design and Validation of Single-Axis 3D-Printed Force Sensor Based on Three Nested Flexible Rings"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4753-3109","authenticated-orcid":false,"given":"Pengfei","family":"Yang","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou 350108, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shiwei","family":"Xin","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou 350108, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuqing","family":"Mao","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou 350108, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fei","family":"Dang","sequence":"additional","affiliation":[{"name":"College of Physics and Electronic Information Engineering, Minjiang University, Fuzhou 350108, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Feng","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou 350108, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"9423","DOI":"10.1109\/JSEN.2021.3054381","article-title":"Gyro-Free inertial measurement unit with unfettered accelerometer array distribution and for the object with position change in center of gravity","volume":"21","author":"Yang","year":"2021","journal-title":"IEEE Sens. 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