{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,8]],"date-time":"2026-09-08T17:23:13Z","timestamp":1788888193775,"version":"build-2803163510"},"reference-count":17,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2024,2,24]],"date-time":"2024-02-24T00:00:00Z","timestamp":1708732800000},"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":["51805124"],"award-info":[{"award-number":["51805124"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["LZY22E050001"],"award-info":[{"award-number":["LZY22E050001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Zhejiang Provincial Natural Science Foundation of China","award":["51805124"],"award-info":[{"award-number":["51805124"]}]},{"name":"Zhejiang Provincial Natural Science Foundation of China","award":["LZY22E050001"],"award-info":[{"award-number":["LZY22E050001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Multi-degree-of-freedom piezoelectric motors have the advantages of high torque and resolution, simple structure, and direct drive, which are widely used in robot wrist joints, deep-sea mechanisms, medical equipment, and space mechanisms. To solve the problems of high force\/torque coupling degree and ball low stator and rotor bonding strength of the traditional traveling wave type three-degree-of-freedom piezoelectric spherical motor, a new structure of ball-hinged piezoelectric spherical motor is proposed. Through coordinate transformation and force analysis, the driven mathematical model of the spherical motor is given. The model shows that the three degrees of freedom of the motor are coupled with each other. According to the mathematical model of the spherical motor, the mechanical properties of the motor are analyzed by the computer simulation. The results show that the stalling torque coefficient kt has a linear relationship with the friction coefficient \u03b5 and the stator preload Fc, has a nonlinear relationship with the stator radius R and the rotor radius r, and increases with the increase of R and decreases with the increase of r. The no-load speed of motor \u03c9n is not related to the friction coefficient \u03b5 and the stator preload Fc, and increases with the increase of R and decreases with the increase of r. The anisotropic characteristics of torque and speed of a spherical motor are further analyzed, which lays a theoretical foundation for the drive control of a spherical motor.<\/jats:p>","DOI":"10.3390\/s24051470","type":"journal-article","created":{"date-parts":[[2024,2,26]],"date-time":"2024-02-26T03:34:04Z","timestamp":1708918444000},"page":"1470","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Model and Property Analysis for a Ball-Hinged Three-Degree-of-Freedom Piezoelectric Spherical Motor"],"prefix":"10.3390","volume":"24","author":[{"given":"Zhenyu","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering, Hangzhou Dianzi University Information Engineering College, Hangzhou 311305, China"},{"name":"School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jun","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wanbing","family":"Liu","sequence":"additional","affiliation":[{"name":"Hengda Fuji Elevator Co., Ltd., Huzhou 313009, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guanshuai","family":"Jia","sequence":"additional","affiliation":[{"name":"College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2880-9752","authenticated-orcid":false,"given":"Ban","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310018, China"},{"name":"College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2307","DOI":"10.1109\/TMAG.2013.2238616","article-title":"A performance study on a permanent magnet spherical motor","volume":"49","author":"Park","year":"2013","journal-title":"IEEE Trans. Magn."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1016\/j.ultras.2017.01.005","article-title":"A ring-type multi-DOF ultrasonic motor with four feet driving consistently","volume":"76","author":"Shi","year":"2017","journal-title":"Ultrasonics"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1045","DOI":"10.1049\/elp2.12096","article-title":"Friction Torque Field Distribution of a Permanent-Magnet Spherical Motor Based on Multi-Physical Field Coupling Analysis","volume":"15","author":"Li","year":"2021","journal-title":"IET Electr. Power Appl."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1080\/01691864.2012.754077","article-title":"Spherical ultrasonic motor drive system for camera orientation in pipe inspection","volume":"27","author":"Hoshina","year":"2013","journal-title":"Adv. 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Jpn."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/5\/1470\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:04:15Z","timestamp":1760105055000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/5\/1470"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2,24]]},"references-count":17,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2024,3]]}},"alternative-id":["s24051470"],"URL":"https:\/\/doi.org\/10.3390\/s24051470","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,2,24]]}}}