Regular and Chaotic Dynamics

, Volume 13, Issue 4, pp 257–266 | Cite as

The dynamics of Charles Taylor’s remarkable one-wheeled vehicle

  • E. S. Lew
  • B. Orazov
  • O. M. O’ReillyEmail author
Nonholonomic Mechanics


In the 1950s and 1960s, Charles F. Taylor designed and tested various prototype one-wheeled vehicles. These machines were stabilized and steered using gyroscopes. In this paper, a simple model of a one-wheeled vehicle is presented and analyzed. This analysis explains the ability of these machines to exhibit stable steady motions.

Key words

one-wheeled vehicle nonholonomic system 

MSC 2000 numbers

70B15 70E55 70E50 70F25 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Taylor, C.F., Vehicle, U.S. Patent number 3145797 issued on August 25, 1964.Google Scholar
  2. 2.
    Appell, P., Sur l’intégration des équations du mouvement d’un corps pesant de révolution roulant par une arête circulaire sur un plan horizontal, Rendiconti del Circolo Mathematico di Palermo, 1900, vol. 14, pp. 1–6.zbMATHGoogle Scholar
  3. 3.
    Chaplygin, S.A., On a Motion of a Heavy Body of Revolution on a Horizontal Plane, Regul. Chaotic Dyn., 2002, vol. 7, no. 2, pp. 119–130, translated from the 1897 Russian original.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Cushman, R., Hermans, J., and Kemppainen, D., The Rolling Disc, in: Nonlinear Dynamical Systems and Chaos (Groningen, 1995), vol. 19 of Progr. Nonlinear Differential Equations Appl., Basel: Birkhäuser, 1996, pp. 21–60.Google Scholar
  5. 5.
    Karapetyan, A.V. and Kuleshov, A.S., Steady Motions of Nonholonomic Systems, Regul. Chaotic Dyn., 2002, vol. 7, no. 1, pp. 81–117.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Kessler, P. and O’Reilly, O.M., The Ringing of Euler’s Disk, Regul. Chaotic Dyn., 2002, vol. 7, no. 1, pp. 49–60.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    O’Reilly, O.M., The Dynamics of Rolling Disks and Sliding Disks, Nonlinear Dynamics, 1996, vol. 10, pp. 287–305.CrossRefMathSciNetGoogle Scholar
  8. 8.
    Routh, E.J., The Advanced Part of a Treatise on the Dynamics of a System of Rigid Bodies, 6th ed., London: Macmillan, 1905.Google Scholar
  9. 9.
    Orazov, B., The Dynamics of Charles Taylor’s One-Wheeled Vehicle, Master’s thesis, Department of Mechanical Engineering, University of California at Berkeley, 2007.Google Scholar
  10. 10.
    O’Reilly, O.M. and Tongue, B.H., Some Comments on Vehicle Instability due to Brake Lockup. Journal of Sound and Vibration, 1996, vol. 194, pp. 760–765.CrossRefGoogle Scholar

Copyright information

© MAIK Nauka 2008

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of California at BerkeleyBerkeleyUSA

Personalised recommendations