ON TWO METHODS FOR NONLINEAR MODELING OF THE DYNAMICS OF PARAL-LEL MANIPULATORS

Main Article Content

Krasinskiy A.Ya.

Abstract

The control loops of modern mechatronic systems have the potential to implement control algorithms of almost any degree of complexity. However, a necessary condition for their effective use is the availability of an adequate mathematical nonlinear model of the controlled object. The development of methods for creating such models is hampered not so much by the technical complexity of the system under study, as by the fact that often in the study of a specific really functioning device, fundamentally new problems that have never been encountered before in the corresponding theory. Their solution requires research by theoretical specialists on the further development of the relevant areas of analytical mechanics, applications of the nonlinear theory of stability, mathematical control theory with incomplete information, information technologies, etc. would be distant from each other areas of knowledge. However, the use of new results in modern engineering practice is complicated by the fact that methods based on those sections of mathematics, mechanics and control theory that have never been included in the curricula of standard engineering education are used to rigorously substantiate these results. Based on this, one of the main problems, the solution of which, in our opinion, could significantly expand the practical application of the latest results in engineering practice, is the development of such a presentation of algorithms for their qualified application, which does not require a complete understanding of all the abstract-theoretical foundations of their justification.

Article Details

How to Cite
Krasinskiy A.Ya. (2022). ON TWO METHODS FOR NONLINEAR MODELING OF THE DYNAMICS OF PARAL-LEL MANIPULATORS . Journal of Engineering and Technology Development Research, 1(1). Retrieved from https://a-publish.com/ojs/index.php/jetdr/article/view/41
Section
Artciles

References

J. Gajek, J. Awrejcewicz,”Mathematical models and nonlinear dynamics of a linear electromagnetic motor,” Nonlinear Dyn (2018) 94:377–396. https://doi.org/10.1007/s11071-018-4365-0.

L. -W. Tsai, “Robot Analysis, The Mechanics of Serial and Parallel Manipulators,” Wiley, New York, 1999.

H. Cheng; G.F. Liu; Y.K. Yiu; Z.H. Xiong; Z.X. Li “Advantages and dynamics of paral-lel manipulators with redundant actuation,” Proceedings 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems. Expanding the Societal Role of Robotics in the the Next Mil-lennium (Cat. No.01CH37180) DOI: 10.1109/IROS.2001.973354/

A. Elkady, G. Elkobrosy, S. Hanna and T. Sobh (April 1st 2008), “Cartesian Parallel Manipulator Modeling, Control and Simulation from Parallel Manipulators, towards New Ap-plications,” Edited by Huapeng Wu, Intech Open, DOI: 10.5772/5435. Available from: https://www.intechopen.com/chapters/833.

Z. Pandilov, V. Dukovski, “Comparison of the characteristics between serial and paral-lel robots,” ACTA TEHNICA CORVINIENSIS – Bulletin of Engineering Tome VII [2014] Fasci-cule 1 [January – March] Pp.143-160.

C. Gosselin, L-T. Schreiber, “Redundancy in Parallel Mechanisms: A Review,”Appl. Mech. Rev. Jan 2018, 70(1): 010802 (15 pages). Paper No: AMR-16-1071 https://doi.org/10.1115/1.4038931.

A.Ya. Krasinskiy and A.N. Ilyina A.N, “The mathematical modelling of the dynamics of systems with redundant coordinates in the neighborhood of steady motions,” Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, vol. 10. No. 2, 2017, pp. 38-50.

A.Ya. Krasinskiy, A.N Il'ina and E.M. Krasinskaya, “Stabilization of Steady Motions for Systems with Redundant Coordinates,” Moscow University Mechanics Bulletin, vol. 74, No. 1, 2019, pp. 14-20.

E. J. Routh. Dynamics of a system of rigid bodies. Dover, 1960.

A.Ya. Krasinskiy, E.M. Krasinskaya (2020) Complex Application of the Methods of Analytical Mechanics and Nonlinear Stability Theory in Stabilization Problems of Motions of Mechatronic Systems. In: Radionov A., Karandaev A. (eds) Advances in Automation. RusAutoCon 2019. Lecture Notes in Electrical Engineering, vol 641. Springer, Cham. https://doi.org/10.1007/978-3-030-39225-3_39.

Yong-Lin Kuo Mathematical modeling and analysis of the Delta robot with flexible links. https://doi.org/10.1016/j.camwa.2016.03.018.

M.F. Shulgin, “On some differential equations of analytical dynamics and their inte-gration,” “Proc. of the Lenin Central Asian state University”, vol. 144, 1958 (in russian).

A. Krasinskiy and A. Yuldashev, "On One Method of Modeling Multi-link Manipula-tors with Geometric Connections, Taking into Account the Parameters of the Links," 2021 3rd International Conference on Control Systems, Mathematical Modeling, Automation and Energy Efficiency (SUMMA), 2021, pp. 190-193, https://doi: 10.1109/SUMMA53307.2021.9632056.

A. Krasinskiy and A. Yuldashev, "Nonlinear Model of Delta Robot Dynamics as a Ma-nipulator with Geometric Constraints," 2021 3rd International Conference on Control Systems, Mathematical Modeling, Automation and Energy Efficiency (SUMMA), 2021, pp. 115-118, https://doi: 10.1109/SUMMA53307.2021.9632138.