Geometrical modeling of the unfolding of spatial rod structures, similar to the four-link pendulum, in weightlessness

Authors

DOI:

https://doi.org/10.15587/1729-4061.2018.141855

Keywords:

rod structure, process of unfolding in space, manipulator to grip bodies, Lagrange equation of the second kind

Abstract

We have continued studying geometrical models of unfolding, under conditions of weightlessness, the orbital rod structures whose elements are connected similar to a four-link pendulum [21‒24]. The links of the structure move due to the action of pulses from pyrotechnic jet engines at the endpoints of the links. The description of the motion of the derived inertial unfolding of a rod structure is based on the Lagrange equation of the second kind, and, given the conditions of weightlessness, constructed using solely the kinetic energy of the system.

The relevance of the subject is defined by the need to improve and study the new technological schemes for unfolding the frames of space infrastructures. These include the frames of parabolic antennas, whose elements are a family of similar confocal parabolas obtained when one of them rotates, at a certain angular step, around a common axis. In addition, it is of interest to consider the new technologies for performing mounting operations in orbit using the structures of mechanical grippers (the type of a "robot's arm"), located outside spacecraft.

Based on the inertial unfolding of four-link rod structures, we developed schemes of action of manipulators to grip cylindrical bodies whose axes are in parallel or perpendicular relative to the surface of a spacecraft. We have defined parameters and initial conditions for starting the motion of a four-link rod structure in order to obtain the required arrangement of links. It is shown that the implementation of variants of the inertial unfolding requires that the endpoints of links should be exposed to the action of a set of pyrotechnic devices whose pulses' magnitudes are determined by the coordinates of vector U¢={0.1, 1.9, 1.3, 2.5} in conventional units and the time it stops should be determined. We have constructed plots of change over time in the functions of the angles' values as the generalized coordinates, as well as the first and second derivatives from these functions. The result is the evaluation of strength characteristics of the system at the time of braking (stopping) the process of unfolding.

The results are intended for the geometrical modeling of variants of unfolding four-link rod structures under conditions of weightlessness. For example, frames for orbital infrastructures, as well as mechanical manipulators to grip space objects

Author Biographies

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

Doctor of Technical Sciences, Professor

Department of Engineering and Rescue Technology

Volodymyr Vanin, National Technical University of Ukraine «Igor Sikorsky Kyiv Polytechnic Institute» Peremohy ave., 37, Kyiv, Ukraine, 03056

Doctor of Technical Sciences, Professor

Department of Descriptive Geometry, Engineering and Computer Graphics

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

Doctor of Technical Sciences, Vice-Rector

Department of prevention activities and monitoring

Leonid Zapolskiy, Ukrainian Research Institute of Civil Defense Rybalska str., 18, Kyiv, Ukraine, 01011

PhD, Senior Researcher

Department of Scientific and organizational

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

Viacheslav Martynov, Kyiv National University of Сonstruction and Architecture Povitroflotskyi ave., 31, Kyiv, Ukraine, 03037

Doctor of Technical Sciences, Associate Professor

Department of Architectural Constructions

Galina Morozova, Ukrainian State University of Railway Transport Feierbakha sq., 7, Kharkiv, Ukraine, 61050

PhD, Senior Researcher

Department of descriptive geometry and computer graphics

Volodymyr Danylenko, National Technical University "Kharkiv Polytechnic Institute" Kyrpychova str., 2, Kharkiv, Ukraine, 61002

Associate Professor

Department of Geometrical Modeling and Computer Graphics

Boris Krivoshey, National University of Civil Defense of Ukraine Chernyshevska str., 94, Kharkiv, Ukraine, 61023

PhD, Senior Researcher

Department of Engineering and rescue machinery

Oleksandr Kovalov, National University of Civil Defense of Ukraine Chernyshevska str., 94, Kharkiv, Ukraine, 61023

PhD

Department of Engineering and rescue machinery

References

  1. Alpatov, A. P. (2013). Dynamika perspektyvnykh kosmichnykh aparativ. Visnyk NAN Ukrainy, 7, 6–13
  2. 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: https://doi.org/10.7463/1014.0728802
  3. Yan, X., Fu-ling, G., Yao, Z., Mengliang, Z. (2012). Kinematic analysis of the deployable truss structures for space applications. Journal of Aerospace Technology and Management, 4 (4), 453–462. doi: https://doi.org/10.5028/jatm.2012.04044112
  4. Deployable Perimeter Truss with Blade Reel Deployment Mechanism. Available at: https://www.techbriefs.com/component/content/article/tb/techbriefs/mechanics-and-machinery/24098
  5. Buyanova, L. V., Zhuravlev, E. I. (2015). Metodika proektirovaniya pirotekhnicheskih ustroystv sistem otdeleniya. Inzhenerniy vestnik, 07, 56–62.
  6. 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
  7. Lopes, A. M., Tenreiro Machado, J. A. (2016). Dynamics of the N-link pendulum: a fractional perspective. International Journal of Control, 90 (6), 1192–1200. doi: https://doi.org/10.1080/00207179.2015.1126677
  8. Udwadia, F. E., Koganti, P. B. (2015). Dynamics and control of a multi-body planar pendulum. Nonlinear Dynamics, 81 (1-2), 845–866. doi: https://doi.org/10.1007/s11071-015-2034-0
  9. 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
  10. Yudincev, V. V. (2012). Modelirovanie processov raskrytiya mnogoelementnyh konstrukciy kosmicheskih apparatov. Polet, 5, 28–33.
  11. Bakulin, D. V., Borzyh, S. V., Ososov, N. S., Shchiblev, Yu. N. (2004). Modelirovanie processa raskrytiya solnechnyh batarey. Matematicheskoe modelirovanie, 16 (6), 88–92.
  12. Gmiterko, A., Grossman, M. (2010). N-link Inverted Pendulum Modeling. Recent Advances in Mechatronics, 151–156. doi: https://doi.org/10.1007/978-3-642-05022-0_26
  13. Anohin, N. V. (2013). Privedenie mnogozvennogo sterzhnevoy konstrukcii v polozhenie ravnovesiya s pomoshch'yu odnogo upravlyayushchego momenta. Izv. RAN. Teoriya i sistemy upravleniя, 5, 44–53.
  14. Anan'evskiy, I. M., Anohin, N. V. (2014). Upravlenie prostranstvennym dvizheniem mnogozvennogo perevernutogo mayatnika s pomoshch'yu momenta, prilozhennogo k pervomu zvenu. Prikladnaya matematika i mekhanіka, 78 (6), 755–765.
  15. Bushuev, A. Yu., Farafonov, B. A. (2014). Matematicheskoe modelirovanie processa raskrytiya solnechnoy batarei bol'shoy ploshchadi. Matematicheskoe modelirovanie i chislennye metody, 2, 101–114.
  16. Bushuev, A. Yu. (2017). Proektirovanie trosovoy sistemy raskrytiya mnogozvennoy konstrukcii solnechnoy batarei v usloviyah neopredelennosti. Inzhenerniy zhurnal: nauka i innovacii, 1, 1–11.
  17. Bushuev, A. Yu. (2017). Matematicheskaya model' dubliruyushchey sistemy raskrytiya solnechnoy batarei bol'shoy ploshchadi. Inzhenerniy zhurnal: nauka i innovacii, 2, 1–11.
  18. Bushuev, A. Yu., Farafonov, B. A. (2015). Optimizaciya parametrov trosovoy sistemy raskrytiya mnogozvennoy konstrukcii solnechnoy batarei. Inzhenerniy zhurnal: nauka i innovacii, 7.
  19. Krylov, A. V., Churilin, S. A. (2012). Modelirovanie razvertyvaniya mnogozvennyh zamknutyh kosmicheskih konstrukciy. Vestnik MGTU im. N. E. Baumana. Ser.: Mashinostroenie, 80–91.
  20. Krylov, A. V., Churilin, S. A. Modelirovanie raskrytiya solnechnyh batarey razlichnyh konfiguraciy. Vestnik MGTU im. N. E. Baumana. Ser.: Mashinostroenie, 1, 106–111.
  21. Kutsenko, L. M., Zapolskyi, L. L. (2017). Heometrychne modeliuvannia rozghortannia u nevahomosti bahatolankovoi konstruktsiyi z inertsiynym rozkryttiam. Visnyk Khersonskoho natsionalnoho tekhnichnoho universytetu, 2 (3 (62)), 284–291.
  22. Kutsenko, L., Shoman, O., Semkiv, O., Zapolsky, L., Adashevskay, I., Danylenko, V. et. al. (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.doi: https://doi.org/10.15587/1729-4061.2017.114269
  23. Kutsenko, L. M., Piksasov, M. M., Zapolskyi, L. L. Iliustratsiyi do heometrychnoho modeliuvannia inertsiynoho rozkryttia bahatolankovoho maiatnyka u nevahomosti. Available at: http://repositsc.nuczu.edu.ua/handle/123456789/4868
  24. Kutsenko, L., Semkiv, O., Zapolskiy, L., Shoman, O., Ismailova, N., Vasyliev, S. et. al. (2018). Geometrical modeling of the shape of a multilink rod structure in weightlessness under the influence of pulses on the end points of its links. Eastern-European Journal of Enterprise Technologies, 2 (7 (92)), 44–58. doi: https://doi.org/10.15587/1729-4061.2018.126693
  25. Kutsenko L. M., Piksasov M. M., Zapolskyi L. L. Iliustratsiyi do statti heometrychne modeliuvannia protsesu rozkryttia sterzhnevykh konstruktsiyi u nevahomosti. Available at: http://repositsc.nuczu.edu.ua/handle/123456789/6335
  26. Kutsenko, L. M., Piksasov, M. M., Zapolskyi, L. L. Heometrychne modeliuvannia rozkryttia u nevahomosti deiakykh prostorovykh sterzhnevykh konstruktsiy. Available at: http://repositsc.nuczu.edu.ua/handle/123456789/7051

Downloads

Published

2018-09-12

How to Cite

Kutsenko, L., Vanin, V., Semkiv, O., Zapolskiy, L., Shoman, O., Martynov, V., Morozova, G., Danylenko, V., Krivoshey, B., & Kovalov, O. (2018). Geometrical modeling of the unfolding of spatial rod structures, similar to the four-link pendulum, in weightlessness. Eastern-European Journal of Enterprise Technologies, 5(7 (95), 70–80. https://doi.org/10.15587/1729-4061.2018.141855

Issue

Vol. 5 No. 7 (95) (2018): Applied mechanics

Section

Applied mechanics

License

Copyright (c) 2018 Leonid Kutsenko, Volodymyr Vanin, Oleg Semkiv, Leonid Zapolskiy, Olga Shoman, Viacheslav Martynov, Galina Morozova, Volodymyr Danylenko, Boris Krivoshey, Oleksandr Kovalov

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.

A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.