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Orientation of natural trihedral of the spiral-helix supporting trajectory of spatial vehicle movement

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Category: Geotechnical and mining mechanical engineering, machine building

Last Updated on 17 July 2018

Published on 03 July 2018

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Authors:

V. P. Sakhno, Dr. Sc. (Tech.), Prof., orcid.org/0000-0002-5144-7131, National Transport University, Kyiv, Ukraine, е‑mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

V. V. Kravets, Dr. Sc. (Tech.), Prof., orcid.org/0000-0003-4770-0269, National Mining University, Dnipro, Ukraine, е‑mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

K. M. Bas, Cand. Sc. (Tech.), Assoc. Prof., orcid.org/0000-0003-2918-3501, National Transport University, Kyiv, Ukraine, е‑mail: This email address is being protected from spambots. You need JavaScript enabled to view it., National Mining University, Dnipro, Ukraine, е‑mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

V. V. Krivda, Cand. Sc. (Tech.), Assoc. Prof., orcid.org/0000-0002-8304-2016, National Mining University, Dnipro, Ukraine, е‑mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Abstract:

Purpose. To improve both reliability and engineering accuracy of 3D modeling of a vehicle movement.

Methodology. Orts of natural trihedral of spiral-helix supporting trajectory are expressed vectorially by means of time derivatives of a radius vector of a program movement. Quaternion matrices represent the complicated operations of vector algebra. Spatial orientation or program rotation of a natural trihedral is described with the help of Gibbs vector, Rodriguez-Hamilton vector, matrix of direction cosines depending upon kinematic parameters of the program movement.

Findings. A hodograph of program transfer of a vehicle is represented in the class of spiral-helix supporting trajectories in terms of earth reference. Unit vectors of a natural trihedral of the spiral-helix supporting trajectory have been obtained depending on the time derivatives of the program motion hodograph.

Originality. The program transfer – radius vector hodograph and program rotation (orientation) – Gibbs vector or quaternion on Rodriguez-Hamilton parameters are represented vectorially making it possible to model spatial orientation problems and problems of control of dynamic systems (i.e. vehicles) in the form of quaternion matrices.

Practical value. Calculation formulas are represented in the ordered, compacted matrix form adapted directly to computer technology. The algorithm helps solve a wide range of problems of dynamic design of vehicles.

References.

1. Qian (Chayn) Suna, Jianhong (Cecilia) Xiaa, Jonathan Fosterb, Torbjorn Falkmerc and Hoe Lee, 2016. Pursuing Precise Vehicle Movement Trajectory in Urban Residential Area Using Multi-GNSS RTK Tracking. In: World Conference on Transport Research - WCTR Shanghai, Published by Elsevier B.V. Science Direct, Transportation Research Procedia, 25, pp 2356‒2372. DOI: 10.1016/j.trpro.2017.05.255.

2. Protsiv, V., Ziborov, K. and Fedoriachenko, S., 2013. On formation of kinematical and dynamical parameters of output elements of the mine vehicles in transient motion. Naukovyi Visnyk Natsіonalnoho Hіrnychoho Unіversytetu, 4, pp. 64‒69.

3. Schmidt, S. and Mercorelli, P., 2016. Optical 3d laser measurement system for navigation of autonomous mobile robot. Optics and Lasers in Engineering Preprint submitted, IFAC Papers Online, 49(15), pp. 169‒174. DOI: 10.20858/tp.2016.11.3.7.

4. Strutinsky, V. and Demyanenko, А., 2016. The development of mechatronic active control system of tool spatial position of parallel kinematics machine tool. Journal of Theoretical and Applied Mechanics, 54, 3, pp. 757‒768. DOI: 10.15632/jtam-pl.54.3.757.

5. Pivnyak, G. G., Kravets, V. V., Bas, K. M., Kravets, T. V. and Tokar, L. A., 2016. Elements of calculus quaternionic matrices and some applications in vector algebra and kinematics, Mechanics, Materials Science & Engineering, 3, pp. 46‒56. DOI: 10.13140/RG.2.1.2466.6643.

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