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Determination of the velocities of the points of the third-class mechanism with three leading links using the graph-analytical method

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Category: Content №2 2025

Last Updated on 26 April 2025

Published on 30 November -0001

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Authors:

S.Koshel, orcid.org/0000-0001-7481-0186, Kyiv National University of Technology and Design, Kyiv, Ukraine, е-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

V.Dvorzhak, orcid.org/0000-0002-1693-9106, Kyiv National University of Technology and Design, Kyiv, Ukraine, е-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

H.Koshel*, orcid.org/0000-0003-1862-1553, Open International University of Human Development “Ukraine”, Kyiv, Ukraine,  е-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

M.Zaliubovskyi, orcid.org/0000-0002-9183-2771, Open International University of Human Development “Ukraine”, Kyiv, Ukraine, е-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

I.Panasiuk, orcid.org/0000-0001-6671-4266, Kyiv National University of Technology and Design, Kyiv, Ukraine, е-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

* Corresponding author e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

повний текст / full article

Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu. 2025, (2): 137 - 146

https://doi.org/10.33271/nvngu/2025-2/137

Abstract:

Purpose. To develop sequences of actions and conduct a kinematic study of a complex planar mechanism of the third-class with three leading links by the graph-analytical method to determine the actual values of the angular velocities of individual and linear velocities of all points coinciding with the centres of the kinematic pairs of the mechanism.

Methodology. The kinematic study of the twelve-link mechanism was carried out using the course provisions of the theory of mechanisms and machines about the theory of the structural scheme of mechanical systems and the kinematic analysis of lever mechanisms by the graph-analytical method. Graphic constructions were made in the automated design and drawing system Autocad, which allowed us to bring the accuracy of graphic constructions to the generally accepted level of engineering calculations.

Findings. Using the principles of the theory of mechanisms structure of higher course classes of the theory of mechanisms and machines, a mechanism with three degrees of mobility was considered in the form of three mechanisms, in which the influence of the movement of one leading link with predetermined kinematic parameters on the movement of the mechanism links was successively investigated, for which systems of kinematic equations were compiled with their subsequent solution in the form of graphic constructions. The calculation of the actual angular velocities of those links was obtained, absolute the movement of which is caused by their kinematic attachment to the stationary riser of the mechanism. Calculation of the linear velocities of the points that coincide with the geometric centres of the rotational kinematic pairs of the driven links of the mechanism of the third-class with three leading cranks was performed.

Originality. A plan was developed, and a sequence of actions was implemented, which made it possible to perform kinematic studies and determine the linear velocities of the points that coincide with the geometric centres of the rotational kinematic pairs of links of a complex twelve-link mechanism of the third-class with three leading links using the graph-analytical method. A sequence of studies specially developed for such a planar mechanism with three cranks made it possible to determine the actual values of the angular velocities of the links, the absolute movement of which is determined by their kinematic connection to the stationary body. This made it possible to compile systems of vector kinematic equations to determine the linear velocities of the points of the mechanism of the third-class with three leading links and solve them graphically.

Practical value. The numerical values of the kinematic parameters were obtained and compared with the parameters of the same mechanism, which were calculated using the method of mathematical modelling in the Mathcad software environment. The coincidence of the results of the research performed by two different methods with 95 per cent probability was confirmed, which is a simultaneous confirmation of the credibility of the results obtained by such methods of analysis. Expert research of complex mechanical systems using the graph-analytical method is recommended if engineering calculations are obtained using mathematical modelling technologies.

Keywords: third-class mechanism, kinematic analysis, graph-analytical method, kinematic study

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