Computational Nanotechnology Issue №1 — 2023

The Trajectories Construction of the Universal Joint Movement in the Configuration Space in ℝ3
( Pp. 60-66)

Lamotkin Alexey E. Misyura Natalia E. Mityushov Evgenii A.

DOI: 10.33693/2313-223X-2023-10-1-60-66

Lamotkin Alexey E. senior lecturer at the Department of Fundamental Education
Ural Federal University
Ekaterinburg, Russian Federation Misyura Natalia E. Cand. Sci. (Eng.); associate professor at the Department of New Materials and Technologies Mityushov Evgenii A. Dr. Sci. (Eng.), Professor; Professor at the Department of New Materials and Technologies

Abstract:

In this paper, the study of the movement of the universal joint using the quaternion formalism was carried out, the law of movement of the cross of the universal joint was established with a known law of rotation of the drive shaft. A method of visual interpretation of the law of motion of the crosspiece is proposed, using the mapping of unit quaternions into a three-dimensional ball with radius 2π.

How to Cite:

Lamotkin A.E., Misyura N.E., Mityushov E.A. The Trajectories Construction of the Universal Joint Movement in the Configuration Space in ℝ3. Computational Nanotechnology. 2023. Vol. 10. No. 1. Pp. 60–66. (In Rus.) DOI: 10.33693/2313-223X-2023-10-1-60-66

Reference list:

Willis R. Principles of mechanisms. London: John W. Parker, 1841.
Poncelet J.V. Traité de mécanique appliquée aux machines. Part 1. Liége: Librairie scientifique et industrielle, 1845.
Frolov K.V. et al. Theory of mechanisms and machines. Moscow: Vysshaya shkola, 1987.
Karadere G., Kopmaz O., Güllü E. A new approach to the ki-nematic analysis of universal joints. Part 2: Investigation of various assemblings. Materials Testing. 2010. Vol. 52. No. 5. Pp. 332–337.
Zhilin P.A. Vectors and second-rank tensors in three-dimensional space. St. Petersburg: Nestor, 2001.
Gorshkov A.D. Defenition kinematic characteristics of hooke joint by the analytical method. European Science. 2016. No. 2 (12). Pp. 26–30. (In Rus.)
Jomartov A.A. et al. Modeling of dynamics of cardan shaft on software complex SimulationX. Reports of National Academy of Science of the Republic of Kazakhstan. 2014. Vol. 3. Pp. 27–34. (In Rus.)
Yadav K., Jain H. Modeling and finite element analysis of universal joint. Advancement in Mechanical Engineering and Technology. 2021 Vol. 4 Issue 1. Pp. 1–4.
Amelkin N.I. Kinematics and dynamics of a rigid body. Moscow: Moscow Institute of Physics and Technology, 2000.
Golubev Yu.F. Quaternion algebra in rigid body kinematics. Preprints of the Keldysh Institute of Applied Mathematics. 2013. No. 39.
Mityushov E.A., Misyura N.E. A quaternionic description of kinematics and dynamics universal joint. J. Phys.: Conf. Ser. 2021. Vol. 1901. P. 012121.
Mityushov E.A. et al. Modeling the kinematics and dynamics of universal joint. Computational Nanotechnology. 2022. No. 4. Pp. 48–54. (In Rus.)
Branets V.N., Shmyglevskii I.P. The application of quaternions in problems of rigid body orientation. Moscow: Nauka, 1973.
Arnold V.I. Geometry of complex numbers, quaternions and spin. Moscow: MCCME, 2002.
Zhuravlev V.F. Foundations of theoretical mechanics. Moscow: Fizmatlit, 2001.
Lamotkin A.E., Misyura N.E., Mityushov E.A. Designing the program trajectory for steering a spacecraft under arbitrary boundary conditions // IOP Conference. Series: Materials Science and Engineering. 2020. No. 747 (1). Pp. 1–9.
Mityushov E.A., Misyura N.E., Lamotkin A.E. Quaternionic description of the Euler trajectories of a rigid body in various configuration spaces // Polynomial Computer Algebra. 2021.

Keywords:

quaternion, quaternions mapping in ℝ3, universal joint, cardan gear.