{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,15]],"date-time":"2026-06-15T12:48:57Z","timestamp":1781527737631,"version":"3.54.1"},"reference-count":29,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2023,8,18]],"date-time":"2023-08-18T00:00:00Z","timestamp":1692316800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["51505124"],"award-info":[{"award-number":["51505124"]}]},{"name":"National Natural Science Foundation of China","award":["ZD2020151"],"award-info":[{"award-number":["ZD2020151"]}]},{"name":"National Natural Science Foundation of China","award":["21130208D"],"award-info":[{"award-number":["21130208D"]}]},{"name":"Science and Technology Project of Hebei Education Department","award":["51505124"],"award-info":[{"award-number":["51505124"]}]},{"name":"Science and Technology Project of Hebei Education Department","award":["ZD2020151"],"award-info":[{"award-number":["ZD2020151"]}]},{"name":"Science and Technology Project of Hebei Education Department","award":["21130208D"],"award-info":[{"award-number":["21130208D"]}]},{"name":"Tangshan Science and Technology Innovation Team Training Plan Project","award":["51505124"],"award-info":[{"award-number":["51505124"]}]},{"name":"Tangshan Science and Technology Innovation Team Training Plan Project","award":["ZD2020151"],"award-info":[{"award-number":["ZD2020151"]}]},{"name":"Tangshan Science and Technology Innovation Team Training Plan Project","award":["21130208D"],"award-info":[{"award-number":["21130208D"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper proposed a circular flexible spherical joint to reduce the processing difficulty and manufacturing cost, and design a six-dimensional force sensor based on it. This paper analyzes the influence of the structural parameters of the flexible spherical joints on the accuracy of the six-dimensional force sensor by comparing the force mapping matrix of flexible spherical and ideal spherical joints. As the force mapping matrix is related to the stiffness matrix, the stiffness matrix of a six-dimensional force sensor based on a circular flexible spherical joint and the force mapping matrix of the generalized external force acting on the sensor was derived. Finally, a set of optimal parameters was selected to create a prototype and was verified through finite elements and experiments. The results show that the six-dimensional force sensor with a circular flexible spherical joint has good accuracy and provides some guidance for the design and analysis of the sensor.<\/jats:p>","DOI":"10.3390\/s23167247","type":"journal-article","created":{"date-parts":[[2023,8,18]],"date-time":"2023-08-18T10:28:48Z","timestamp":1692354528000},"page":"7247","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Accuracy Analysis and Experimental Study of a Six-Dimensional Force Sensor with Circular Flexible Spherical Joints"],"prefix":"10.3390","volume":"23","author":[{"given":"Zhijun","family":"Wang","sequence":"first","affiliation":[{"name":"College of Mechanical Engineering, North China University of Science and Technology, Tangshan 063210, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaotao","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, North China University of Science and Technology, Tangshan 063210, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-0559-0377","authenticated-orcid":false,"given":"Mengxiang","family":"Li","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, North China University of Science and Technology, Tangshan 063210, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"111863","DOI":"10.1016\/j.measurement.2022.111863","article-title":"Performance analysis of over-constrained orthogonal parallel six-axis force sensor","volume":"202","author":"Niu","year":"2022","journal-title":"Measurement"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1381","DOI":"10.1109\/TMECH.2016.2640194","article-title":"A Novel 6-Axis Force\/Torque Sensor for Robotic Applications","volume":"1","author":"Kim","year":"2017","journal-title":"IEEE\/ASME Trans. 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