{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T18:05:33Z","timestamp":1774029933401,"version":"3.50.1"},"reference-count":25,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2019,6,14]],"date-time":"2019-06-14T00:00:00Z","timestamp":1560470400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Zhejiang Provincial Natural Science Foundation of China","award":["LZ16E050001"],"award-info":[{"award-number":["LZ16E050001"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["U1709206"],"award-info":[{"award-number":["U1709206"]}],"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":["51275465"],"award-info":[{"award-number":["51275465"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Due to the flexible and compact structures, spherical joints are widely used in parallel manipulators and industrial robots. Real-time detection of the clearance between the ball and the socket in spherical joints is beneficial to compensate motion errors of mechanical systems and improve their transmission accuracy. This work proposes an improved capacitive sensor for detecting the micro-clearance of spherical joints. First, the structure of the capacitive sensor is proposed. Then, the mathematical model for the differential capacitance of the sensor and the eccentric micro-displacement of the ball is deduced. Finally, the capacitance values of the capacitive sensor are simulated with Ansoft Maxwell. The simulated values of the differential capacitances at different eccentric displacements agree well with the theoretical ones, indicating the feasibility of the proposed detection method. In addition, the simulated results show that the proposed capacitive sensor could effectively reduce the capacitive fringe effect, improving the measurement accuracy.<\/jats:p>","DOI":"10.3390\/s19122694","type":"journal-article","created":{"date-parts":[[2019,6,14]],"date-time":"2019-06-14T11:19:58Z","timestamp":1560511198000},"page":"2694","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["An Improved Capacitive Sensor for Detecting the Micro-Clearance of Spherical Joints"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0084-0910","authenticated-orcid":false,"given":"Wen","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenjun","family":"Qiu","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1540-1793","authenticated-orcid":false,"given":"He","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haimei","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guang","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3768-2714","authenticated-orcid":false,"given":"Zhanfeng","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Keqing","family":"Lu","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kui","family":"Xiang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Zhejiang University, Hangzhou 310027, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bingfeng","family":"Ju","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Zhejiang University, Hangzhou 310027, China"},{"name":"State Key Lab of Fluid Power &amp; Mechatronic Systems, Zhejiang University, Hangzhou 310027, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,6,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.precisioneng.2005.01.001","article-title":"Measurement and characterization of precision spherical joints","volume":"30","author":"Robertson","year":"2006","journal-title":"Precis. Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.mechmachtheory.2017.12.002","article-title":"A comprehensive survey of the analytical, numerical and experimental methodologies for dynamics of multibody mechanical systems with clearance or imperfect joints","volume":"122","author":"Tian","year":"2018","journal-title":"Mech. Mach. Theory"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1007\/s40430-018-1015-x","article-title":"Clearance-induced vibration responses of mechanical systems: Computational and experimental investigations","volume":"40","author":"Erkaya","year":"2018","journal-title":"J. Braz. Soc. Mech. Sci. Eng."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1115\/1.2198877","article-title":"Dynamics of multibody systems with spherical clearance joints","volume":"1","author":"Flores","year":"2006","journal-title":"J. Comput. Nonlinear Dyn."},{"key":"ref_5","first-page":"82","article-title":"Effects of Joint Clearance on the Motion Accuracy of Robotic Manipulators","volume":"64","author":"Erkaya","year":"2018","journal-title":"J. Mech. Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1016\/j.mechmachtheory.2017.11.014","article-title":"Experimental investigation of flexible connection and clearance joint effects on the vibration responses of mechanisms","volume":"121","author":"Erkaya","year":"2018","journal-title":"Mech. Mach. Theory"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1007\/s11071-009-9583-z","article-title":"Spatial rigid-multibody systems with lubricated spherical clearance joints: Modeling and simulation","volume":"60","author":"Flores","year":"2010","journal-title":"Nonlinear Dyn."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2625","DOI":"10.1007\/s11071-018-4513-6","article-title":"Chaotic characteristic analysis of spatial parallel mechanism with clearance in spherical joint","volume":"94","author":"Chen","year":"2018","journal-title":"Nonlinear Dyn."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1007","DOI":"10.1007\/s11071-016-2942-7","article-title":"Reducing the undesirable effects of joint clearance on the behavior of the planar 3-RRR parallel manipulators","volume":"86","author":"Daniali","year":"2016","journal-title":"Nonlinear Dyn."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1007\/s11071-013-0782-2","article-title":"Dynamic analysis of planar rigid-body mechanical systems with two-clearance revolute joints","volume":"73","author":"Muvengei","year":"2013","journal-title":"Nonlinear Dyn."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"9595","DOI":"10.1109\/TIE.2017.2726982","article-title":"Advances in capacitive, eddy current, and magnetic displacement sensors and corresponding interfaces","volume":"64","author":"George","year":"2017","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"045102","DOI":"10.1088\/1361-6501\/aa912e","article-title":"Online monitoring of dynamic tip clearance of turbine blades in high temperature environments","volume":"29","author":"Han","year":"2018","journal-title":"Meas. Sci. Technol."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/S0924-4247(04)00482-0","article-title":"Tubomachinery blade vibration amplitude measurement through tip timing with capacitance tip clearance probes","volume":"118","author":"Lawson","year":"2005","journal-title":"Sens. Actuators A Phys."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"085010","DOI":"10.1088\/1361-6501\/aace30","article-title":"A displacement sensing method based on alternating current magnetic flux measurement","volume":"29","author":"Zhang","year":"2018","journal-title":"Meas. Sci. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1108","DOI":"10.1109\/JSEN.2010.2043429","article-title":"Advances in magnetic field sensors","volume":"10","author":"Ripka","year":"2010","journal-title":"IEEE Sens. J."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Podhra\u0161ki, M., and Trontelj, J. (2016). A differential monolithically integrated inductive linear displacement measurement microsystem. Sensors, 16.","DOI":"10.3390\/s16030384"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1109\/JMEMS.2015.2499301","article-title":"Resonant inductive coupling-based piston position sensing mechanism for large vertical displacement micromirrors","volume":"25","author":"Tseng","year":"2016","journal-title":"J. Microelectromec. Syst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"3346","DOI":"10.1109\/JSEN.2012.2204321","article-title":"Design strategies for eddy-current displacement sensor systems: Review and recommendations","volume":"12","author":"Nabavi","year":"2012","journal-title":"IEEE Sens. J."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1088\/0957-0233\/18\/1\/038","article-title":"An active sensor for monitoring bearing wear by means of an eddy current displacement sensor","volume":"18","author":"Yamaguchi","year":"2007","journal-title":"Meas. Sci. Technol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2027","DOI":"10.1088\/0957-0233\/17\/7\/049","article-title":"A cylindrical capacitive sensor (CCS) for both radial and axial motion measurements","volume":"17","author":"Ahn","year":"2006","journal-title":"Meas. Sci. Technol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"64012","DOI":"10.1088\/1361-6501\/aab705","article-title":"Measurement method of rotation angle and clearance in intelligent spherical hinge","volume":"29","author":"Hu","year":"2018","journal-title":"Meas. Sci. Technol."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Wang, W., Yang, H., Zhang, M., Chen, Z.F., Shi, G., Lu, K.Q., Xiang, K., and Ju, B.F. (2018). A novel method for the micro-clearance measurement of a precision spherical joint based on a spherical differential capacitive sensor. Sensors, 18.","DOI":"10.3390\/s18103366"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1458","DOI":"10.1166\/sl.2011.1651","article-title":"Impact of fringe effect on measuring accuracy of planar capacitive sensors","volume":"9","author":"Wang","year":"2011","journal-title":"Sens. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Wang, W., Yang, H., Zhang, M., Chen, Z.F., Shi, G., Lu, K.Q., Xiang, K., and Ju, B.F. (2019). A novel approach for detecting rotational angles of a precision spherical joint based on a capacitive sensor. Micromachines, 10.","DOI":"10.3390\/mi10050280"},{"key":"ref_25","unstructured":"Merlet, J.-P. (2002). Parallel Robots, Springer."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/12\/2694\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:58:36Z","timestamp":1760187516000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/12\/2694"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,6,14]]},"references-count":25,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2019,6]]}},"alternative-id":["s19122694"],"URL":"https:\/\/doi.org\/10.3390\/s19122694","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,6,14]]}}}