{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,13]],"date-time":"2024-07-13T13:15:45Z","timestamp":1720876545010},"reference-count":15,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2018,6,25]],"date-time":"2018-06-25T00:00:00Z","timestamp":1529884800000},"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":["51575141"],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005046","name":"Natural Science Foundation of Heilongjiang Province","doi-asserted-by":"publisher","award":["QC2016065"],"id":[{"id":"10.13039\/501100005046","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"This paper proposes a decoupled six degrees of freedom (DOF) displacement measurement methodology, which is accomplished by utilizing six pairs of permanent magnets and six Hall sensors. Firstly, the coordinate transformation was mathematically derived, which represented the relationships between the main coordinate system of the motion system and each body coordinate system of the Hall sensors. With the aid of an ellipsoid function and the least squares method, only the output voltages of the six Hall sensors were required to decouple the six-DOF displacement and inclination of the motion platform with high accuracy. Finally, the experimental measurements demonstrate the effectiveness of the six DOF displacement measurement methodology, based on which the maximum errors of displacements can reach 0.23 mm and the maximum errors of inclinations can reach 0.07\u00b0.<\/jats:p>","DOI":"10.3390\/s18072030","type":"journal-article","created":{"date-parts":[[2018,6,25]],"date-time":"2018-06-25T15:03:25Z","timestamp":1529939005000},"page":"2030","source":"Crossref","is-referenced-by-count":4,"title":["Six Degrees of Freedom Displacement Measurement System for Wafer Stage Composed of Hall Sensors"],"prefix":"10.3390","volume":"18","author":[{"given":"Bo","family":"Zhao","sequence":"first","affiliation":[{"name":"School of Electrical Engineering and Automation, Harbin Institute of Technology, D-403 Science Park, 2 Yikuang Street, Harbin 150080, China"}]},{"given":"Weijia","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering and Automation, Harbin Institute of Technology, D-403 Science Park, 2 Yikuang Street, Harbin 150080, China"}]},{"given":"Jiawei","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering and Automation, Harbin Institute of Technology, D-403 Science Park, 2 Yikuang Street, Harbin 150080, China"}]},{"given":"Ming","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering and Automation, Harbin Institute of Technology, D-403 Science Park, 2 Yikuang Street, Harbin 150080, China"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-2218-4280","authenticated-orcid":false,"given":"Xue","family":"Qi","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering and Automation, Harbin Institute of Technology, D-403 Science Park, 2 Yikuang Street, Harbin 150080, China"}]},{"given":"Jiaxin","family":"Li","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering and Automation, Harbin Institute of Technology, D-403 Science Park, 2 Yikuang Street, Harbin 150080, China"}]},{"given":"Feng","family":"Li","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering and Automation, Harbin Institute of Technology, D-403 Science Park, 2 Yikuang Street, Harbin 150080, China"}]},{"given":"Jiubin","family":"Tan","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering and Automation, Harbin Institute of Technology, D-403 Science Park, 2 Yikuang Street, Harbin 150080, China"}]}],"member":"1968","published-online":{"date-parts":[[2018,6,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Chen, Z., Liu, Y., Fu, Z., Song, S., and Tan, J. (2016). Calibration of the hall measurement system for a 6-dof precision stage using self-adaptive hybrid tlbo. Sensors, 16.","DOI":"10.3390\/s16060872"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Sen, M., Balabozov, I., Yatchev, I., and Ivanov, R. (2017, January 1\u20133). Modelling of current sensor based on hall effect. Proceedings of the 2017 15th International Conference on Electrical Machines, Drives and Power Systems (ELMA), Sofia, Bulgaria.","DOI":"10.1109\/ELMA.2017.7955485"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Pan, S., Commins, P.A., and Du, H. (2015, January 27\u201330). Tubular linear motor position detection by hall-effect sensors. Proceedings of the 2015 Australasian Universities Power Engineering Conference (AUPEC), Wollongong, Australia.","DOI":"10.1109\/AUPEC.2015.7324830"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Sriratana, W., and Murayama, R. (2013, January 28\u201331). 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Actuators A Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1016\/j.sna.2017.02.007","article-title":"Calibration scheme for a new type of 3d hall sensor","volume":"257","author":"Wouters","year":"2017","journal-title":"Sens. Actuators A Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"7355","DOI":"10.1109\/JSEN.2017.2755467","article-title":"A soft four degree-of-freedom load cell based on the hall effect","volume":"17","author":"Nie","year":"2017","journal-title":"IEEE Sens. J."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"22530","DOI":"10.3390\/s150922530","article-title":"Design and realization of a three degrees of freedom displacement measurement system composed of hall sensors based on magnetic field fitting by an elliptic function","volume":"15","author":"Zhao","year":"2015","journal-title":"Sensors"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"771","DOI":"10.1016\/j.precisioneng.2013.03.005","article-title":"A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage","volume":"37","author":"Li","year":"2013","journal-title":"Precis. Eng."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Lee, C., and Lee, S.-K. (2013). 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Res."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/7\/2030\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T09:58:50Z","timestamp":1718099930000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/7\/2030"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,6,25]]},"references-count":15,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2018,7]]}},"alternative-id":["s18072030"],"URL":"https:\/\/doi.org\/10.3390\/s18072030","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,6,25]]}}}