Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Schulz M. and Pellegrino S. 2000Equilibrium paths of mechanical systems with unilateral constraints II. Deployable reflectorProc. R. Soc. Lond. A.4562243–2262http://doi.org/10.1098/rspa.2000.0611SectionRestricted accessResearch articleEquilibrium paths of mechanical systems with unilateral constraints II. Deployable reflector M. Schulz M. Schulz Department FV/SLT2, Robert Bosch GmbH, PO Box 30 02 40, 70442 Stuttgart,, Germany () Google Scholar Find this author on PubMed Search for more papers by this author and S. Pellegrino S. Pellegrino Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK () Google Scholar Find this author on PubMed Search for more papers by this author M. Schulz M. Schulz Department FV/SLT2, Robert Bosch GmbH, PO Box 30 02 40, 70442 Stuttgart,, Germany () Google Scholar Find this author on PubMed Search for more papers by this author and S. Pellegrino S. Pellegrino Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK () Google Scholar Find this author on PubMed Search for more papers by this author Published:08 September 2000https://doi.org/10.1098/rspa.2000.0611AbstractThe paper presents a simulation of the deployment/retraction of a solid surface deployable reflector recently developed at Cambridge University. The simulation takes proper account of the contacts that can develop between panels of adjacent wings of the reflector, by implementing the theory for tracing the equilibrium path of a mechanical system with unilateral constraints that has been proposed in the companion paper. Six–fold symmetry is assumed, as experiments on a physical model of the reflector show that asymmetries do not play a significant role. During deployment, at a certain point the model shows a sudden increase in the rate of motion, although the (slow) rate of turning of the electric motors driving the model remains uniform. It is shown that the reason for this behaviour, which had not been previously explained, is the existence of a corner limit point on the equilibrium path of this structure. A corner limit point is a kind of limit point that can be encountered only in systems with unilateral constraints; the equilibrium path is non–smooth and the first–order equilibrium equations non–singular. A second limit point, of the standard type, exists on the equilibrium path. It should cause the model to jump to a configuration close to fully folded, but cannot be achieved in practice. A characteristic conical shape of the physical model is observed at the end of the retraction and is predicted by the simulation as well. Previous ArticleNext Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited by Hu N and Burgueño R (2015) Buckling-induced smart applications: recent advances and trends, Smart Materials and Structures, 10.1088/0964-1726/24/6/063001, 24:6, (063001), Online publication date: 1-Jun-2015. Schulz M and Pellegrino S (2000) Equilibrium paths of mechanical systems with unilateral constraints I. Theory, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 456:2001, (2223-2242), Online publication date: 8-Sep-2000. This Issue08 September 2000Volume 456Issue 2001 Article InformationDOI:https://doi.org/10.1098/rspa.2000.0611Published by:Royal SocietyPrint ISSN:1364-5021Online ISSN:1471-2946History: Published online08/09/2000Published in print08/09/2000 License: Citations and impact Keywordsunilateral constraintlimit pointsolid surface deployable antennasnap throughmultibody systems
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