{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,26]],"date-time":"2025-11-26T16:27:24Z","timestamp":1764174444490,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2018,1,30]],"date-time":"2018-01-30T00:00:00Z","timestamp":1517270400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper a new concept of a liquid-surface-based three-axis inclination sensor for evaluation of angular error motion of a precision linear slide, which is often used in the field of precision engineering such as ultra-precision machine tools, coordinate measuring machines (CMMs) and so on, is proposed. In the liquid-surface-based three-axis inclination sensor, a reference float mounting a line scale grating having periodic line grating structures is made to float over a liquid surface, while its three-axis angular motion is measured by using an optical sensor head based on the three-axis laser autocollimation capable of measuring three-axis angular motion of the scale grating. As the first step of research, in this paper, theoretical analysis on the angular motion of the reference float about each axis has been carried out based on simplified kinematic models to evaluate the possibility of realizing the proposed concept of a three-axis inclination sensor. In addition, based on the theoretical analyses results, a prototype three-axis inclination sensor has been designed and developed. Through some basic experiments with the prototype, the possibility of simultaneous three-axis inclination measurement by the proposed concept has been verified.<\/jats:p>","DOI":"10.3390\/s18020398","type":"journal-article","created":{"date-parts":[[2018,1,30]],"date-time":"2018-01-30T08:03:34Z","timestamp":1517299414000},"page":"398","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["A Liquid-Surface-Based Three-Axis Inclination Sensor for Measurement of Stage Tilt Motions"],"prefix":"10.3390","volume":"18","author":[{"given":"Yuki","family":"Shimizu","sequence":"first","affiliation":[{"name":"Department of Finemechanics, Tohoku University, Sendai 980-8579, Japan"}]},{"given":"Satoshi","family":"Kataoka","sequence":"additional","affiliation":[{"name":"Department of Finemechanics, Tohoku University, Sendai 980-8579, Japan"}]},{"given":"Tatsuya","family":"Ishikawa","sequence":"additional","affiliation":[{"name":"Department of Finemechanics, Tohoku University, Sendai 980-8579, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1641-051X","authenticated-orcid":false,"given":"Yuan-Liu","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Finemechanics, Tohoku University, Sendai 980-8579, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7067-5084","authenticated-orcid":false,"given":"Xiuguo","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Finemechanics, Tohoku University, Sendai 980-8579, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8125-9708","authenticated-orcid":false,"given":"Hiraku","family":"Matsukuma","sequence":"additional","affiliation":[{"name":"Department of Finemechanics, Tohoku University, Sendai 980-8579, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9336-2729","authenticated-orcid":false,"given":"Wei","family":"Gao","sequence":"additional","affiliation":[{"name":"Department of Finemechanics, Tohoku University, Sendai 980-8579, Japan"}]}],"member":"1968","published-online":{"date-parts":[[2018,1,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"660","DOI":"10.1016\/j.cirp.2008.09.008","article-title":"Geometric error measurement and compensation of machines\u2014An update","volume":"57","author":"Schwenke","year":"2008","journal-title":"CIRP Ann. 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