Geometrical modeling of the inertial unfolding of a multi-link pendulum in weightlessness

Authors

DOI:

https://doi.org/10.15587/1729-4061.2017.114269

Keywords:

multi-link pendulum, large-scale structure, deployment in cosmos, mirror in space, Lagrangian equation of the second kind

Abstract

We investigated a geometrical model of unfolding a rod frame of an orbital object as a process of oscillations of a multi-link pendulum under conditions of weightlessness and within an abstract plane. The initiation of oscillations is assumed to be driven by the pulse action on one of the nodal elements of the pendulum, implemented using a pulsed rocket engine. The transported (starting) position of a multilink pendulum shall be accepted in the “folded” form. A notation of the inertial frame unfolding is performed employing the Lagrange equation of the second kind, in which potential energy was not taken into consideration because of weightlessness.

It was established in the course of research:

– to unfold the structure, there is no need to synchronize the means of control over the magnitudes of angles in separate nodes;

– transverse oscillations of nodes (tremor) before the moment of full unfolding of a multi-link pendulum can be used as signal for the actuation of locks in order to fix the position of its adjacent links;

– based on a circuit for unfolding a single multi-link structure, it is possible to form multi-beam circuits with a shared non-movable attachment node (a triad as an example).

Reliability of the obtained approximate solution was tested using the created animated film about the unfolding process of the structure. An example of a four-link pendulum was studied in detail. The results might prove useful when designing the unfolding of large-size structures under conditions of weightlessness, for example, frames for solar mirrors

Author Biographies

Leonid Kutsenko, National University of Civil Protection of Ukraine Chernyshevska str., 94, Kharkiv, Ukraine, 61023

Doctor of Technical Sciences, Professor

Department of Engineering and Rescue Technology

Olga Shoman, National Technical University "Kharkiv Polytechnic Institute" Kyrpychova str., 2, Kharkiv, Ukraine, 61002

Doctor of Technical Sciences, Professor, Head of Department

Department of Geometrical Modeling and Computer Graphics 

Oleg Semkiv, National University of Civil Protection of Ukraine Chernyshevska str., 94, Kharkiv, Ukraine, 61023

Doctor of Technical Sciences, Vice-Rector

Department of Engineering and Rescue Technology

Leonid Zapolsky, The State Emergency Service of Ukraine Rybalska str., 18, Kyiv, Ukraine, 01011

PhD, Senior Researcher

Scientific and organizational department

Irina Adashevskay, National Technical University "Kharkiv Polytechnic Institute" Kyrpychova str., 2, Kharkiv, Ukraine, 61002

PhD, Associate Professor, Head of Department

Department of Geometrical Modeling and Computer Graphics 

Volodymyr Danylenko, Kharkiv National University of Automobile and Highways Yaroslava Mudroho str., 25, Kharkiv, Ukraine, 61002

Associate Professor

Department of Engineering and Computer Graphics 

Victoria Semenova-Kulish, Ukrainian State University of Railway Transportt Feierbakh sq., 7, Kharkiv, Ukraine, 61050

PhD, Associate Professor

Department of descriptive geometry and computer graphics

Dmitriy Borodin, Ukrainian State University of Railway Transportt Feierbakh sq., 7, Kharkiv, Ukraine, 61050

PhD, Associate Professor

Department of descriptive geometry and computer graphics

Jaroslav Legeta, Uzhhorod National University Narodna sq., 3, Uzhhorod, Ukraine, 88000

Senior Lecturer

Department of Technology of Mechanical Engineering

References

  1. Lovegrove, K., Stein, W. (2012). Concentrating Solar Power Technology. Principles, Developments and Applications. Cambridge: Woodhead Publishing Limited, 708.doi: 10.1533/9780857096173
  2. Krafft, A. E. (1979). The future of the space industry. Мoscow: Mechanical Engineering, 200.
  3. Barathwaj, G., Srinag, K. (2011). Wireless power transmission of space based solar power. Vol. 6. 2nd International Conference on Environmental Science and Technology, IPCBEE. IACSIT Press, Singapore, v2-227–v2-231.
  4. Szuminski, W. (2014). Dynamics of multiple pendula without gravity. Chaotic Modeling and Simulation, 1, 57–67. Available at: http://www.cmsim.eu/papers_pdf/january_2014_papers/7_CMSIM_Journal_2014_Szuminski_1_57-67.pdf
  5. Krylov, A. V., Churilin, S. A. (2011). Modeling of the disclosure of solar batteries of various configurations. Bulletin of the Moscow State Technical University. N. E. Bauman. Ser.: "Mechanical Engineering", 1, 106–111.
  6. Yudintsev, V. V. (2012). Modeling of the processes of disclosure of multi-element structures of space vehicles. Polelet, 5, 28–33.
  7. Borzykh, S. V., Bakulin, D. V., Shchiblev, Yu. N. (1999). Modeling of the process of opening large-sized solar batteries. Aviakosmicheskaya tekhnika i tekhnologiya, 1, 35–41.
  8. Bakulin, D. V., Borzykh, S. V., Ososov, N. S., Shchiblev, Yu. N. (2004). Modeling of the process of solar battery disclosure. Matem. Modeling, 16 (6), 88–92.
  9. Bushuyev, A. Yu., Farafonov, B. A. (2014). Mathematical modeling of the process of opening a large solar battery. Mathematical model and numerical methods, 2, 101–114.
  10. Anokhin, N. V. (2013). Reduction of a pendulum pendulum to a position of equilibrium by means of a single control torque. Izv. RAS. Theory and control systems, 5, 44–53.
  11. Anan'evskiy, I. M., Anokhin, N. V. (2014). Control of the spatial motion of a multi-link inverted pendulum with the help of a moment applied to the first link. Mathematics and Mechanics, 78 (6), 755–765.
  12. Schesnyak, S., Romanov, A. et. al. (2009). Designing and calculation of large-sized unfolding structures with the help of software complexes MSC.Software. CADmaster, 2-3, 28–36.
  13. Boykov, V. G. (2009). The program complex of the automated dynamic analysis of multi-component mechanical systems EULER. CAD and graphics, 9, 17–20.
  14. Zimin, V., Krylov, A., Meshkovskii, V., Sdobnikov, A., Fayzullin, F., Churilin, S. (2014). Features of the Calculation Deployment Large Transformable Structures of Different Configurations. Science and Education of the Bauman MSTU, 10, 179–191. doi: 10.7463/1014.0728802
  15. Simulation of the process of solar battery openings of Yamal-200 communications satellite. Available at: http://www.euler.ru/distr/praxis/space/yamal200.pdf
  16. Gmiterko, A., Grossman, M. (2010). N-link Inverted Pendulum Modeling. Recent Advances in Mechatronics, 151–156. doi: 10.1007/978-3-642-05022-0_26
  17. Martınez-Alfaro, H. Obtaining the dynamic equations, their simulation, and animation for N pendulums using Maple. Available at: http://www2.esm.vt.edu/~anayfeh/conf10/Abstracts/martinez-alfaro.pdf
  18. Kutsenko, L. N., Adashevska, I. Yu. (2008). Geometric modeling of the oscillation of multilink pendulums. Kharkiv: "NTMT", 176.
  19. Kutsenko, L. M. Iliustratsiy do heometrychnoho modeliuvannia inertsiynoho rozkryttia bahatolankovoho maiatnyka u nevahomosti. Available at: http://repositsc.nuczu.edu.ua/handle/123456789/4868

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Published

2017-11-07

How to Cite

Kutsenko, L., Shoman, O., Semkiv, O., Zapolsky, L., Adashevskay, I., Danylenko, V., Semenova-Kulish, V., Borodin, D., & Legeta, J. (2017). Geometrical modeling of the inertial unfolding of a multi-link pendulum in weightlessness. Eastern-European Journal of Enterprise Technologies, 6(7 (90), 42–50. https://doi.org/10.15587/1729-4061.2017.114269

Issue

Vol. 6 No. 7 (90) (2017): Applied mechanics

Section

Applied mechanics

License

Copyright (c) 2017 Leonid Kutsenko, Olga Shoman, Oleg Semkiv, Leonid Zapolsky, Irina Adashevskay, Volodymyr Danylenko, Victoria Semenova-Kulish, Dmitriy Borodin, Jaroslav Legeta

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