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Deployable Structures pp 113–142Cite as

Infinitesimal and Finite Mechanisms

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Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 412))

Abstract

In the design of engineering structures, an important question is whether a structure is rigid. For conventional structures, rigidity is a fundamental requirement. However, there are cases where just the opposite is required. In order to answer the question of rigidity we have to know the static-kinematic properties of the structure. In the forthcoming, these properties will be investigated for bar-and-joint assemblies, that is, for structures composed of straight bars and frictionless pin joints. Firstly, we survey the basic terms to be used in the analysis.

Supported by OTKA Grant No. T031931 and FKFP Grant No. 0391/1997.

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References

  • Calladine, C.R. (1978). Buckminster Fuller’s “Tensegrity” structures and Clerk Maxwell’s rules for the construction of stiff frames. International Journal of Solids and Structures 14: 161–172.

    Article  MATH  Google Scholar 

  • Calladine, C.R. (1982). Modal stiffiiesses of a pretensioned cable net. International Journal of Solids and Structures 18: 829–846.

    Article  MATH  Google Scholar 

  • Coxeter, H.S.M. (1974). Projective Geometry. Toronto: University Press, 2nd edition.

    Google Scholar 

  • Crapo, H. and Whiteley, W. (1982). Statics of frameworks and motions of panel structures, a projective geometric introduction. Structural Topology 6: 43–82.

    MathSciNet  Google Scholar 

  • Föppl, A. (1942). Vorlesungen über technische Alechanik. Zweiter Band. München: Verlag von R. Oldenbourg, Neunte Auflage.

    Google Scholar 

  • Fuller, R.B. (1975). Synergetics. Explorations in the geometry of thinking. New York: MacMillan.

    Google Scholar 

  • Gluck, H. (1975). Almost all simply connected closed surfaces are rigid. Geometric Topology, Lecture Notes in Mathematics, no. 438. Berlin: Springer-Verlag.

    Google Scholar 

  • Hoff, N.J. and Fernandez-Sintes, J. (1980). Kinematically unstable space frameworks. In Nemat-Nasser, S., ed. Mechanics Today. Oxford: Pergamon, 95–111.

    Google Scholar 

  • Kuznetsov, E. (1991). Underconstrained Structural Systems. New York: Springer-Verlag.

    Book  Google Scholar 

  • Maxwell, J.C. (1864). On the calculation of the equilibrium and stiffness of frames. Philosophical Magazine Ser. 4, 27:294–299. (The Scientific Papers of James Clerk Maxwell. Cambridge: University Press, 1890, Vol. 1:598–604.)

    Google Scholar 

  • Müller-Breslau, H. (1913). Die neueren Methoden der Festigkeitslehre und der Statik der Baukonstruktionen. Leipzig: A. Kremer Verlag, Vierte Auflage.

    MATH  Google Scholar 

  • Pellegrino, S. (1988). On the rigidity of triangulated hyperbolic paraboloids. Proceedings of the Royal Society of London A 418: 425–452.

    Article  MATH  MathSciNet  Google Scholar 

  • Rankine, W.J.M. (1863). On the application of barycentric perspective to the transformation of structures. Philosophical Magazine Ser. 4, 26:387–388. (Paper XXXV in Miscellaneous Scientific Papers. London: Griffin, 1881.)

    Google Scholar 

  • Roth, B. and Whiteley, W. (1981). Tensegrity frameworks. Transactions of the American Mathematical Society 265: 419–446.

    Article  MATH  MathSciNet  Google Scholar 

  • Southwell, R.V. (1920). Primary stress determination in space frames. Engineering 109: 165–168.

    Google Scholar 

  • Szabo, J. and Roller, B. (1978). Anwendung der Matrizenrechnung auf Stabwerke. Budapest: Akadéminii Kiad6.

    Google Scholar 

  • Szabô, J. and Rbzsa, P. (1971). Die Matrizengleichung von Stabkonstruktionen (im Falle kleiner Verschiebungen). Acta Technica Academiae Scienciarum Hungariae 71: 133–148.

    Google Scholar 

  • Tannai, T. (1980). Simultaneous static and kinematic indeterminacy of space trusses with cyclic symmetry. International Journal of Solids and Structures 16: 347–359.

    Article  Google Scholar 

  • Tarnai, T. (1989). Duality between plane trusses and grillages. International Journal of Solids and Structures 25: 1395–1409.

    Article  MATH  MathSciNet  Google Scholar 

  • Tannai, T. and Gaspar, Zs. (1983). Improved packing of equal circles on a sphere and rigidity of its graph. Mathematical Proceedings of the Cambridge Philosophical Society 93: 191–218.

    Article  MathSciNet  Google Scholar 

  • Timoshenko, S.P. and Young, D.H. (1965). Theory of Structures. New York: McGraw-Hill, 2nd edition.

    Google Scholar 

  • Tornyos, A. (1985). Dynamic analysis of space frameworks with cyclic symmetry. International Journal of Space Structures 1: 111–115.

    Google Scholar 

  • Wester, T. (1987). The plate-lattice dualism. International Colloquium on Space Structures for Sports Buildings. Beijing, China.

    Google Scholar 

  • Whiteley, W. (1987). Rigidity and polarity. Geometriae Dedicata 22: 329–362.

    Article  MATH  MathSciNet  Google Scholar 

  • Wunderlich, W. (1982). Projective invariance of shaky structures. Acta Mechanica 42: 171–181.

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Budapest University of Technology and Economics, Budapest, Hungary

    Tibor Tarnai

Authors
  1. Tibor Tarnai
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Editor information

Editors and Affiliations

  1. Department of Engineering, University of Cambridge, Trumpington Street, CB2 1PZ, Cambridge, UK

    S. Pellegrino

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© 2001 Springer-Verlag Wien

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Tarnai, T. (2001). Infinitesimal and Finite Mechanisms. In: Pellegrino, S. (eds) Deployable Structures. International Centre for Mechanical Sciences, vol 412. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2584-7_7

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  • DOI: https://doi.org/10.1007/978-3-7091-2584-7_7

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-83685-9

  • Online ISBN: 978-3-7091-2584-7

  • eBook Packages: Springer Book Archive

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