Infinitesimal and Finite Mechanisms

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


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.


Internal Force Compatibility Equation Kinematic Property Plane Truss Internal Displacement 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 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.CrossRefMATHGoogle Scholar
  2. Calladine, C.R. (1982). Modal stiffiiesses of a pretensioned cable net. International Journal of Solids and Structures 18: 829–846.CrossRefMATHGoogle Scholar
  3. Coxeter, H.S.M. (1974). Projective Geometry. Toronto: University Press, 2nd edition.Google Scholar
  4. Crapo, H. and Whiteley, W. (1982). Statics of frameworks and motions of panel structures, a projective geometric introduction. Structural Topology 6: 43–82.MathSciNetGoogle Scholar
  5. Föppl, A. (1942). Vorlesungen über technische Alechanik. Zweiter Band. München: Verlag von R. Oldenbourg, Neunte Auflage.Google Scholar
  6. Fuller, R.B. (1975). Synergetics. Explorations in the geometry of thinking. New York: MacMillan.Google Scholar
  7. Gluck, H. (1975). Almost all simply connected closed surfaces are rigid. Geometric Topology, Lecture Notes in Mathematics, no. 438. Berlin: Springer-Verlag.Google Scholar
  8. 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
  9. Kuznetsov, E. (1991). Underconstrained Structural Systems. New York: Springer-Verlag.CrossRefGoogle Scholar
  10. 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
  11. Müller-Breslau, H. (1913). Die neueren Methoden der Festigkeitslehre und der Statik der Baukonstruktionen. Leipzig: A. Kremer Verlag, Vierte Auflage.MATHGoogle Scholar
  12. Pellegrino, S. (1988). On the rigidity of triangulated hyperbolic paraboloids. Proceedings of the Royal Society of London A 418: 425–452.CrossRefMATHMathSciNetGoogle Scholar
  13. 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
  14. Roth, B. and Whiteley, W. (1981). Tensegrity frameworks. Transactions of the American Mathematical Society 265: 419–446.CrossRefMATHMathSciNetGoogle Scholar
  15. Southwell, R.V. (1920). Primary stress determination in space frames. Engineering 109: 165–168.Google Scholar
  16. Szabo, J. and Roller, B. (1978). Anwendung der Matrizenrechnung auf Stabwerke. Budapest: Akadéminii Kiad6.Google Scholar
  17. Szabô, J. and Rbzsa, P. (1971). Die Matrizengleichung von Stabkonstruktionen (im Falle kleiner Verschiebungen). Acta Technica Academiae Scienciarum Hungariae 71: 133–148.Google Scholar
  18. Tannai, T. (1980). Simultaneous static and kinematic indeterminacy of space trusses with cyclic symmetry. International Journal of Solids and Structures 16: 347–359.CrossRefGoogle Scholar
  19. Tarnai, T. (1989). Duality between plane trusses and grillages. International Journal of Solids and Structures 25: 1395–1409.CrossRefMATHMathSciNetGoogle Scholar
  20. 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.CrossRefMathSciNetGoogle Scholar
  21. Timoshenko, S.P. and Young, D.H. (1965). Theory of Structures. New York: McGraw-Hill, 2nd edition.Google Scholar
  22. Tornyos, A. (1985). Dynamic analysis of space frameworks with cyclic symmetry. International Journal of Space Structures 1: 111–115.Google Scholar
  23. Wester, T. (1987). The plate-lattice dualism. International Colloquium on Space Structures for Sports Buildings. Beijing, China.Google Scholar
  24. Whiteley, W. (1987). Rigidity and polarity. Geometriae Dedicata 22: 329–362.CrossRefMATHMathSciNetGoogle Scholar
  25. Wunderlich, W. (1982). Projective invariance of shaky structures. Acta Mechanica 42: 171–181.CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Wien 2001

Authors and Affiliations

  • Tibor Tarnai
    • 1
  1. 1.Budapest University of Technology and EconomicsBudapestHungary

Personalised recommendations