{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,14]],"date-time":"2026-09-14T12:52:43Z","timestamp":1789390363533,"version":"build-2803163510"},"reference-count":36,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,1,25]],"date-time":"2025-01-25T00:00:00Z","timestamp":1737763200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Bioengineering"],"abstract":"<jats:p>This study introduced a novel force-driven automated staging design method for clear aligners, aimed at enhancing treatment planning efficiency and outcomes. The method simplified the alignment process into a force-driven mechanics model that calculates forces and moments exerted on teeth while adhering to Newton\u2019s third law, determining their displacement and rotation at each position. An optimal path was generated by iteratively moving teeth from their initial to target positions and subsequently divided into stages based on a predefined step size. The algorithm was implemented in C++ and incorporated into the WebGL-based SmarteeCheck3.0 software for visualization. In a maxillary extraction case, the automated staging method (0.25 mm step size) generated 51 stages in merely 5 s, while manual staging (&gt;0.25 mm step size) necessitated 30 min to achieve 55 stages. In a molar distalization case, the automated method demonstrated similar efficiency advantages, generating 30 stages for the maxilla and 34 for the mandible, compared to 41 stages each in manual staging. The automated staging approach yielded shorter and more precise tooth movement paths that adhered to aligner biomechanics and physical principles, surpassing the limitations of manual staging. For cases requiring entire arch displacement, the method incorporated sequential movements with anchorage control to maintain force equilibrium. This innovative method substantially improved design efficiency and accuracy, ultimately elevating the efficacy of clear aligner therapy, although further biomechanical analyses and experimental validations are needed to refine the model parameters.<\/jats:p>","DOI":"10.3390\/bioengineering12020111","type":"journal-article","created":{"date-parts":[[2025,1,27]],"date-time":"2025-01-27T03:54:27Z","timestamp":1737950067000},"page":"111","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Force-Driven Model for Automated Clear Aligner Staging Design Based on Stepwise Tooth Displacement and Rotation in 3D Space"],"prefix":"10.3390","volume":"12","author":[{"given":"Sensen","family":"Yang","sequence":"first","affiliation":[{"name":"Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200072, China"},{"name":"Smartee Biomechanics Research Laboratory, Shanghai Smartee Denti-Technology, Shanghai 201210, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0967-4111","authenticated-orcid":false,"given":"Yumin","family":"Cheng","sequence":"additional","affiliation":[{"name":"Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200072, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Mart\u00ednez-Lozano, D., Castellanos-Andr\u00e9s, D., and L\u00f3pez-Jim\u00e9nez, A.J. 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