On Limits of Friction to Maintain a State of Rest of a Tripod

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The article presents the results of a constructive study of the ability of dry friction to hold a tripod at rest under the influence of external forces. Until now, there has been no constructive discussion or specific examples of friction distribution in supports in the scientific literature.

The identified features will ensure a rest stage for the body of a vibration robot resting on a rough plane with three points.

作者简介

M. Dosaev

Institute of Mechanics of LMSU

编辑信件的主要联系方式.
Email: dosayev@imec.msu.ru
俄罗斯联邦, Moscow

V. Samsonov

Institute of Mechanics of LMSU

Email: dosayev@imec.msu.ru
俄罗斯联邦, Moscow

M. Garbuz

Institute of Mechanics of LMSU

Email: dosayev@imec.msu.ru
俄罗斯联邦, Moscow

参考

  1. Dosaev M., Samsonov V., Hwang S. Construction of control algorithm in the problem of the planar motion of a friction-powered robot with a flywheel and an eccentric weight // Appl. Math. Model., 2021, vol. 89 (2), pp. 1517–1527.
  2. Garbuz M., Dosaev M., Samsonov V. Organizing the rotation of the body of a vibration robot around the vertical // J. of Comput.&Syst. Sci. Int., 2023, vol. 1, pp. 164–176.
  3. Jellett J.H. A Treatise on the Theory of Friction. Dublin: Hodges, Foster, 1872. 220 p.
  4. Schiller N. Note on the equilibrium of a rigid body under the action of friction on some flat part of its surface // Proc. of the Dep. of Phys. Sci. of the Soc. of Natural Sci. Lovers, 1892, no. V (1), pp. 1–5.
  5. Zhukovsky N.E. Equilibrium Condition of a Rigid Body Supported by a Certain Platform on a Fixed Plane and Capable of Moving along This Plane with Friction. Moscow: Volchaninov Publ., 1897. 23 p.
  6. Routh E.J. A Treatise on Analytical Statics, with Numerous Examples. Vol. 1. Cambridge: Univ. Press, 1909. 391 p.
  7. Chernous’ko F.L. Equilibrium conditions of a body on a rough plane // Izv. AN SSSR. MTT, 1988, no. 6, pp. 6–17.
  8. Smyshlyaev A.S., Chernous’ko F.L. Equilibrium conditions for a rod on a rough plane // JAMM, 2002, vol. 66, iss. 2, pp. 165–170.
  9. Rosenblat G.M. On the equilibrium of Zhukovsky’s bench // Dokl. RAN, 2017, vol. 472, no. 6, pp. 659–665.
  10. Ivanov A.P. On the extremal property of bond reactions // JAMM, 2012, vol. 76, iss. 2, pp. 142–153.
  11. Levi-Civita T. Sulla stabilit delle lavagne a cavalletto // Periodico di Mathematische, 1924, s. IV, vol. IV, pp. 59–73.
  12. Sumbatov A.S. On the equilibrium of the stand of a physical pendulum on a horizontal plane with dry friction // Int. J. of Non-Lin. Mech., 2020, vol. 126, p. 1–5.https://doi.org/10.1016/j.ijnonlinmec.2020.103571
  13. Rosenblat G.M. Mechanics in Problems and Solutions. Moscow: Editorial URSS, 2004. 160 p.

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