{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,6]],"date-time":"2026-06-06T15:07:26Z","timestamp":1780758446594,"version":"3.54.1"},"reference-count":47,"publisher":"SAGE Publications","issue":"10","license":[{"start":{"date-parts":[[2010,4,1]],"date-time":"2010-04-01T00:00:00Z","timestamp":1270080000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The International Journal of Robotics Research"],"published-print":{"date-parts":[[2010,9]]},"abstract":"<jats:p>Robots consisting of several concentric, preshaped, elastic tubes can work dexterously in narrow, constrained, and\/or winding spaces, as are commonly found in minimally invasive surgery. Previous models of these \u201cactive cannulas\u201d assume piecewise constant precurvature of component tubes and neglect torsion in curved sections of the device. In this paper we develop a new coordinate-free energy formulation that accounts for general preshaping of an arbitrary number of component tubes, and which explicitly includes both bending and torsion throughout the device. We show that previously reported models are special cases of our formulation, and then explore in detail the implications of torsional flexibility for the special case of two tubes. Experiments demonstrate that this framework is more descriptive of physical prototype behavior than previous models1 it reduces model prediction error by 82% over the calibrated bending-only model, and 17% over the calibrated transmissional torsion model in a set of experiments.<\/jats:p>","DOI":"10.1177\/0278364910367543","type":"journal-article","created":{"date-parts":[[2010,4,1]],"date-time":"2010-04-01T20:46:05Z","timestamp":1270154765000},"page":"1263-1280","source":"Crossref","is-referenced-by-count":187,"title":["Equilibrium Conformations of Concentric-tube Continuum Robots"],"prefix":"10.1177","volume":"29","author":[{"given":"D. Caleb","family":"Rucker","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, Vanderbilt University, 2301 Vanderbilt Place, PMB 351592 Nashville, TN 37235-1592, USA,"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"suffix":"III","given":"Robert J.","family":"Webster","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Vanderbilt University, 2301 Vanderbilt Place, PMB 351592 Nashville, TN 37235-1592, USA,"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gregory S.","family":"Chirikjian","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, John Hopkins University, 3400 North Charles Street, Baltimore, MD 21218, USA,"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Noah J.","family":"Cowan","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, John Hopkins University, 3400 North Charles Street, Baltimore, MD 21218, USA,"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2010,4,1]]},"reference":[{"key":"atypb1","volume-title":"IEEE\/RSJ International Conference on Intelligent Robots and Systems","author":"Alterovitz, R."},{"key":"atypb2","volume-title":"Nonlinear Ordinary Equations in Transport Processes","author":"Ames, W.F.","year":"1968"},{"key":"atypb3","volume-title":"Nonlinear Problems of Elasticity","author":"Antman, S.S.","year":"2005","edition":"2"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.1987.4767965"},{"key":"atypb5","first-page":"34","volume":"27","author":"Bergou, M.","year":"2008","journal-title":"SIGGRAPH (ACM Transactions on Graphics)"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.2307\/2319846"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2008.2002311"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1115\/1.2826721"},{"key":"atypb9","volume-title":"Stochastic Models, Information Theory, and Lie Groups, Volume 2","author":"Chirikjian, G.S.","year":"2011"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1109\/70.478427"},{"key":"atypb11","volume-title":"Engineering applications of noncommutative harmonic analysis","author":"Chirikjian, G.S.","year":"2001"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1109\/4233.826855"},{"issue":"572","key":"atypb13","first-page":"593","volume":"6","author":"Daum, W.","year":"2003","journal-title":"Patent"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1109\/TBME.2005.847548"},{"key":"atypb15","volume-title":"IEEE International Conference on Robtics and Automation","author":"Dupont, P.E."},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1109\/TBME.2004.827346"},{"key":"atypb17","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1007\/s11548-006-0053-5","volume":"1","author":"Furusho, J.","year":"2006","journal-title":"Journal of Computer Assisted Radiology and Surgery"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2007.898972"},{"key":"atypb19","volume-title":"Design, Analysis and Experimentation: the Fundamentals of Continuum Robotic Manipulators. 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