Skip to main content
SpringerLink
Log in

Mathematical Model of Speeds Change Device on the Basis of Switched Differential Mechanisms

  • Published:
International Applied Mechanics Aims and scope

The geometry and kinematics of a dynamic system with several degrees of freedom and controllable friction clutches are considered. The necessary kinematic transmission ratio between the input and output links is obtained using the friction clutches. The model uses a smooth approximation of the discontinuous function of the moment of friction. This allows continuous numerical integration of the equations of motion without changing their structure, i.e., preserving their number. The switching from one speed of rotation of the output link to another is controlled by specifying time functions that implement the pressure of the clutch discs. An example of a numerical study of such a mechanism consisting of three differentials and four clutches is considered. Dynamic processes for this system are analyzed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. D. R. Bukhgol’ts, A Course of Theoretical Mechanics [In Russian], Vol. 2, Nauka, Moscow (1979).

    Google Scholar 

  2. Yu. N. Kirdyshev, Multiple Power Path Differential Transmissions [In Russian], Mashinostr., Leningrad (1969).

    Google Scholar 

  3. S. N. Kozhevnikov, The Dynamics of Machines with Elastic Linkage [In Russian], Izd. AN USSR, Kiev (1961).

    Google Scholar 

  4. A. F. Filippov, Differential Equations with a Discontinuous Right-Hand Side [In Russian], Nauka, Moscow (1985).

    Google Scholar 

  5. E. Ya. Antonyuk and A.T. Zabuga, “Dynamics of a two-link vehicle in an l-shaped corridor revisited,” Int. Appl. Mech., 50, No. 2, 222–230 (2014).

    Article  ADS  MathSciNet  Google Scholar 

  6. E. Ya. Antonyuk and A.T. Zabuga, “Motion of an articulated vehicle with two-dimensional sections subject to lateral obstacles,” Int. Appl. Mech., 52, No. 4, 404–412 (2016).

    Article  ADS  MathSciNet  Google Scholar 

  7. I. I. Hussein and A.M. Bloch, “Optimal control of underactuated nonholonomic mechanical systems,” IEEE Trans. Automat. Control, 53, No. 3, 668–682 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  8. A. S. Khoroshun, “Stability of the horizontal flight of an aircraft,” Int. Appl. Mech., 52, No. 1, 96–104 (2016).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. V. B. Larin and A. A. Tunik, “On problem of synthesis of control system for quadrocopter,” Int. Appl. Mech., 53, No. 3, 342–348 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  10. A. A. Martynyuk and N. V. Nikitina, “On the quanlitative analysis of one model of transport vehicle,” Int. Appl. Mech., 54, No. 2, 231–238 (2018).

    Article  ADS  Google Scholar 

  11. N. V. Nikitina, “Analyzing the mechanisms of loss of orbital stability in mathematical models of three-dimensional systems,” Int. Appl. Mech., 53, No. 6, 716–726 (2017).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. L. A. Pars, A Treatise on Analytical Dynamics, Heinemann, London (1964).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterova St., Kyiv, 03057, Ukraine

    E. Ya. Antonyuk & A. T. Zabuga

Authors
  1. E. Ya. Antonyuk
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. T. Zabuga
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. T. Zabuga.

Additional information

Translated from Prikladnaya Mekhanika, Vol. 55, No. 2, pp. 126–132, March–April, 2019.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Antonyuk, E.Y., Zabuga, A.T. Mathematical Model of Speeds Change Device on the Basis of Switched Differential Mechanisms. Int Appl Mech 55, 222–228 (2019). https://doi.org/10.1007/s10778-019-00952-4

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10778-019-00952-4

Keywords

Search

Navigation