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Geometric Constraints in the Problem of Motion of a Caster Board

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Abstract

In this paper, we study kinematics of the motion of a two-wheeled caster board. Using the theory of finite rotations, we propose an elementary derivation of the formula connecting the angles of slope of the decks of the caster board with the angles of rotation of the wheels.

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References

  1. Yu. P. Golubev, “A method for controlling the motion of a robot snakeboarder,” Prikl. Mat. Mekh., 70, No. 3, 355–370 (2006).

    MathSciNet  Google Scholar 

  2. M. Hubbard, “Lateral dynamics and stability of the skateboard,” J. Appl. Mech., 46, 931–936 (1979).

    Article  Google Scholar 

  3. M. Hubbard, “Human control of the skateboard,” J. Biomech., 13, 745–754 (1980).

    Article  Google Scholar 

  4. Yu. G. M. Ispolov and B. A. Smolnikov, “Skateboard dynamics,” Comput. Methods Appl. Mech. Eng., 131, 327–333 (1996).

    Article  Google Scholar 

  5. A. V. Kremnev and A. S. Kuleshov, Nonlinear Dynamics and Stability of the Motion of the Simplest Model of the Skateboard [in Russian], Moscow (2007).

  6. A. V. Kremnev and A. S. Kuleshov, Mathematical Model of the Skateboard with Three Degrees of Freedom [in Russian], Moscow (2008).

  7. A. S. Kuleshov, “Mathematical model of the snakeboard,” Mat. Model., 18, No. 5, 37–48 (2006).

    MathSciNet  MATH  Google Scholar 

  8. A. S. Kuleshov, “Further development of the mathematical model of a snakeboard,” Regul. Chaot. Dynam., 12, 321–334 (2007).

    Article  MathSciNet  Google Scholar 

  9. A. D. Lewis, J. P. Ostrowski, R. M. Murray, and J. W. Burdick, “Nonholonomic mechanics and locomotion: the snakeboard example,” in: Proc. IEEE Int. Conf. on Robotics and Automation (1994), pp. 2391–2400.

  10. A. I. Lur’e, Analytic Mechanics [in Russian], GIFML, Moscow (1961).

    Google Scholar 

  11. T. Wang, B. Su, Sh. Kuang, J. Wang, “On kinematic mechanism of a two-wheel skateboard: The essboard,” J. Mech. Robot., 5, 034503-1–034503-7 (2013).

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Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, Moscow, Russia

    M. M. Gadzhiev, A. S. Kuleshov & A. I. Bukanov

Authors
  1. M. M. Gadzhiev
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  2. A. S. Kuleshov
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  3. A. I. Bukanov
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Corresponding author

Correspondence to M. M. Gadzhiev.

Additional information

Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 148, Proceedings of the International Conference “Geometric Methods in Control Theory and Mathematical Physics: Differential Equations, Integrability, and Qualitative Theory” (Ryazan, September 15–18, 2016), 2018.

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Gadzhiev, M.M., Kuleshov, A.S. & Bukanov, A.I. Geometric Constraints in the Problem of Motion of a Caster Board. J Math Sci 248, 392–396 (2020). https://doi.org/10.1007/s10958-020-04879-x

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  • DOI: https://doi.org/10.1007/s10958-020-04879-x

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