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Thereafter, by combining an electromagnetic model for the VCMs with the equivalent magnetic network method, an electromagnetic\u2013mechanical coupling optimization method with multiple constraints was proposed for the stage to achieve a millimeter-range motion with a maximized natural frequency. The mechanical and electromagnetic performances were then verified by finite element analysis software. The optimized prototype was tested with a stroke of \u00b13.41 and \u00b13.08\u00a0mm for X axis and Y axis, respectively, a closed-loop resolution of 100\u00a0nm for X axis and 150\u00a0nm for Y axis, and a resonant frequency of 11.75\u00a0Hz for both axes. The tracking of a 0.1\u00a0Hz spiral of Archimedes achieved a maximum tracking error of 2.9%.<\/jats:p>","DOI":"10.1063\/5.0173722","type":"journal-article","created":{"date-parts":[[2023,12,20]],"date-time":"2023-12-20T13:48:42Z","timestamp":1703080122000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":5,"title":["Design, optimization, and characterization of an XY nanopositioning stage with multi-level spatial flexure hinges for high-precision large-stroke motion guidance"],"prefix":"10.1063","volume":"94","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-3797-2896","authenticated-orcid":false,"given":"Zhichao","family":"Shi","sequence":"first","affiliation":[{"name":"Sino-French Engineer School, Nanjing University of Science and Technology 1 , Nanjing, Jiangsu Province 210094, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaoquan","family":"Li","sequence":"additional","affiliation":[{"name":"Kuka Robotics Guangdong China Co., Ltd. 2 , Foshan, Guangdong Province 528311, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6989-9953","authenticated-orcid":false,"given":"Zhiwei","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Nanjing University of Science and Technology 3 , Nanjing, Jiangsu Province 210094, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2023,12,20]]},"reference":[{"key":"2023122013483331700_c1","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1007\/s41871-021-00114-6","article-title":"Development and implementation of a rotating nanoimprint lithography tool for orthogonal imprinting on edges of curved surfaces","volume":"4","author":"Supreeti","year":"2021","journal-title":"Nanomanuf. 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