{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T19:04:21Z","timestamp":1773083061522,"version":"3.50.1"},"reference-count":27,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2011,8,4]],"date-time":"2011-08-04T00:00:00Z","timestamp":1312416000000},"content-version":"vor","delay-in-days":215,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2011,1]]},"abstract":"<jats:p>Both the forward and backward kinematics of the Gough\u2010Stewart mechanism exhibit nonlinear\nbehavior. It is critically important to take account of this nonlinearity in some applications such\nas path control in parallel kinematics machine tools. The nonlinearity of inverse kinematics is\nstraightforward and has been first studied in this paper. However the nonlinearity of forward\nkinematics is more challenging to be considered as there is no analytic solution to the forward\nkinematic solution of the mechanism. A statistical approach including the Bates and Watts\nmeasures of nonlinearity has been employed to investigate the nonlinearity of the forward\nkinematics. The concept of standard sphere has been used to check the significance of the\nnonlinearity of the mechanism. It is demonstrated that the length of the region, defined as the\nlinear approximation of the lifted line, has a significant impact on the nonlinearity of the\nmechanism.<\/jats:p>","DOI":"10.1155\/2011\/393072","type":"journal-article","created":{"date-parts":[[2011,8,4]],"date-time":"2011-08-04T19:01:34Z","timestamp":1312484494000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["A Statistical Approach to the Forward Kinematics Nonlinearity Analysis of Gough\u2010Stewart Mechanism"],"prefix":"10.1155","volume":"2011","author":[{"given":"Davoud","family":"Karimi","sequence":"first","affiliation":[]},{"given":"Mohammad Javad","family":"Nategh","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2011,8,4]]},"reference":[{"key":"e_1_2_6_1_2","unstructured":"GoughV. E.andWhitehallS. G. 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The research on direct kinematic problem of a special class of the stewart-gough manipulators Proceedings of the IEEE International Conference on Mechatronics and Automation (ICMA \u203208) 2008 971\u2013976 2-s2.0-64949126294 https:\/\/doi.org\/10.1109\/ICMA.2008.4798890.","DOI":"10.1109\/ICMA.2008.4798890"},{"key":"e_1_2_6_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0094\u2010114X(99)00009\u20109"},{"key":"e_1_2_6_18_2","unstructured":"ZhengK.-J. GaoJ.-S. andZhaoY.-S. Path control algorithms of a novel 5-DOF parallel machine tool Proceedings of the IEEE International Conference on Mechatronics and Automation Niagara Falls 2005 Canada 1381\u20131385."},{"key":"e_1_2_6_19_2","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1111\/j.2517-6161.1960.tb00353.x","article-title":"Confidence regions in non-linear estimation","volume":"22","author":"Beale E. M. L.","year":"1960","journal-title":"Journal of the Royal Statistical Society. 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