{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T18:46:52Z","timestamp":1780512412805,"version":"3.54.1"},"reference-count":22,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,1,22]],"date-time":"2021-01-22T00:00:00Z","timestamp":1611273600000},"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":["No. 51505124"],"award-info":[{"award-number":["No. 51505124"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Science and Technology Research Project of Hebei Province","award":["ZD2020151"],"award-info":[{"award-number":["ZD2020151"]}]},{"name":"Foster Fund Projects of North China University of Science and Technology","award":["No. JP201505"],"award-info":[{"award-number":["No. JP201505"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This study proposes a parallel six-axis force\/torque sensor decoupling method based on an independent component analysis (ICA), and the experimental platform is built for experimental exploration. First of all, the structural model and mathematical model of the parallel six-axis force\/torque sensor are introduced, which is composed of single-dimensional force sensors with central symmetry. Secondly, the test prototype was developed and a test platform was built to perform online static loading test on the sensor, and the test results were analyzed. Finally, the ICA-based dynamic decoupling study of the sensor is carried out, the effectiveness and rationality of the proposed algorithm are proved. The research results of this paper have certain reference values for the further study of the decoupling of parallel six-axis force\/torque sensors.<\/jats:p>","DOI":"10.3390\/sym13020172","type":"journal-article","created":{"date-parts":[[2021,1,25]],"date-time":"2021-01-25T12:28:31Z","timestamp":1611577711000},"page":"172","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Research on Decoupling of Parallel Six-Axis Force\/Torque Sensor Based on an Independent Component Analysis"],"prefix":"10.3390","volume":"13","author":[{"given":"Zhijun","family":"Wang","sequence":"first","affiliation":[{"name":"College of Mechanical Engineering, North China University of Science and Technology, 21 Bohai Road, Tangshan 063210, China"},{"name":"Hebei Province Research Institute of Industrial Robot Industry Technology, Tangshan 063210, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8986-2429","authenticated-orcid":false,"given":"Lu","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, North China University of Science and Technology, 21 Bohai Road, Tangshan 063210, China"},{"name":"Hebei Province Research Institute of Industrial Robot Industry Technology, Tangshan 063210, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kai","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, North China University of Science and Technology, 21 Bohai Road, Tangshan 063210, China"},{"name":"Hebei Province Research Institute of Industrial Robot Industry Technology, Tangshan 063210, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jing","family":"He","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, Tangshan Industrial Vocational Technical College, Tangshan 063020, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhanxian","family":"Li","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, North China University of Science and Technology, 21 Bohai Road, Tangshan 063210, China"},{"name":"Hebei Province Research Institute of Industrial Robot Industry Technology, Tangshan 063210, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,22]]},"reference":[{"key":"ref_1","first-page":"1","article-title":"The design and analysis of a novel micro force sensor based on depletion type movable gate field effect transistor","volume":"99","author":"Gao","year":"2019","journal-title":"J. Microelectromech. Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1007\/s42102-019-00008-8","article-title":"Decoupling strength and grid resolution in peridynamic theory","volume":"1","author":"Stewart","year":"2019","journal-title":"J. Peridynamics Nonlocal Modeling"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1016\/j.ymssp.2018.03.015","article-title":"Research on static decoupling algorithm for piezoelectric six axis force\/torque sensor based on LSSVR fusion algorithm","volume":"110","author":"Li","year":"2018","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Zhao, Y., Zhang, C., Zhang, D., Shi, Z., and Zhao, T. (2016). Mathematical model and calibration experiment of a large measurement range flexible joints 6-UPUR six-axis force sensor. Sensors, 16.","DOI":"10.3390\/s16081271"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1007\/s11340-013-9824-4","article-title":"Advances in force and moments measurements by an innovative six-axis load cell","volume":"54","author":"Ballo","year":"2014","journal-title":"Exp. Mech."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"765","DOI":"10.1007\/s11740-014-0563-x","article-title":"Design and implementation of multi axial force sensing gripper fingers","volume":"8","author":"Hogrev","year":"2014","journal-title":"Prod. Eng. Res. Devel."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"418","DOI":"10.1016\/j.sna.2010.08.021","article-title":"Design, analysis and fabrication of a multidimensional acceleration sensor based on fully decoupled compliant parallel mechanism","volume":"163","author":"Gao","year":"2010","journal-title":"Sens. Actuators A Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2687","DOI":"10.1016\/j.ymssp.2009.05.014","article-title":"Research on force-sensing element\u2019s spatial arrangement of piezoelectric six-component force\/torque sensor","volume":"23","author":"Li","year":"2009","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_9","first-page":"177","article-title":"Performance and sealing material evaluation in 6-axis force-torque sensors for underwater robotics","volume":"48","author":"Palli","year":"2015","journal-title":"IFAC Pap."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/j.measurement.2015.01.005","article-title":"Design and optimization of a novel six-axis force\/torque sensor for space robot","volume":"65","author":"Sun","year":"2015","journal-title":"Measurement"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Hong, D., Li, C., and Jeong, J. (2012, January 17\u201319). A Crosstalk Compensation of a Multi-axis ForceTorque Sensor Based on the Least Squares Method Using LabVIEW. Proceedings of the Fourth International Conference on Computational & Information Sciences, Chongqing, China.","DOI":"10.1109\/ICCIS.2012.12"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1115\/1.2801238","article-title":"The Shape From Motion Approach to Rapid and Precise Force\/Torque Sensor Calibration","volume":"119","author":"Voyles","year":"1997","journal-title":"J. Dynam. Syst. Meas. Control"},{"key":"ref_13","unstructured":"Wang, J. (2007). Research on Miniature Six-Dimensional Force\/Torque Sensor and Its Automatic Calibration, Harbin Institute of Technology."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1164","DOI":"10.1016\/j.proeng.2014.12.699","article-title":"Design and calibration of a six-axis force\/torque sensor with large measurement range used for the space manipulator","volume":"99","author":"Chen","year":"2015","journal-title":"Procedia Eng."},{"key":"ref_15","unstructured":"Gao, F., Zhang, Y., Zhao, X.C., and Guo, W.Z. (2007, January 17\u201321). The Design and applications of F\/T sensor based on stewart platform. Proceedings of the 12th IFTOMM World Congress, Besancon, France."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"765","DOI":"10.1002\/rob.4620100512","article-title":"Kinematic decoupling in mechanisms and application to a passive hand controller design","volume":"10","author":"Hayward","year":"1993","journal-title":"J. Robot. Syst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2013","DOI":"10.1016\/j.measurement.2013.03.003","article-title":"Optimal design and experiment research of a fully pre-stressed six-axis force\/torque sensor","volume":"46","author":"Wang","year":"2013","journal-title":"Measurement"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1016\/j.measurement.2009.11.005","article-title":"Measurement method of six-axis load sharing based on the Stewart platform","volume":"43","author":"Jia","year":"2010","journal-title":"Measurement"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.sna.2008.11.030","article-title":"Theoretical analysis and experiment research of a statically indeterminate pre-stressed six-axis force sensor","volume":"150","author":"Yao","year":"2009","journal-title":"Sens. Actuators A Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1016\/j.mechmachtheory.2012.07.001","article-title":"Hyperstatic analysis of a fully pre-stressed six-axis force\/torque sensor","volume":"57","author":"Wang","year":"2012","journal-title":"Mech. Mach. Theory"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"406","DOI":"10.1016\/j.jsv.2008.07.025","article-title":"Diagonal dominance of damping and the decoupling approximation in linear vibratory systems","volume":"320","author":"Morzfeld","year":"2009","journal-title":"J. Sound Vib."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1265","DOI":"10.1109\/TNN.2006.875991","article-title":"Efficient Variant of Algorithm Fast ICA for Independent Component Analysis Attaining the Cram\u00c9r-Rao Lower Bound","volume":"17","author":"Koldovsky","year":"2006","journal-title":"IEEE Trans. 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