EXTERNAL ROLLING OF A POLYGON ON CLOSED CURVILINEAR PROFILE

Authors

DOI:

https://doi.org/10.14311/AP.2020.60.0313

Keywords:

Equilateral polygon, curvilinear profile, external rolling, differential equation, centroids

Abstract

The rolling of a flat figure in the form of an equilateral polygon on a curvilinear profile is considered. The profile is periodic. It is formed by a series connection of an arc of a symmetrical curve. The ends of the arc rely on a circle of a given radius. The equation of the curve, from which the curvilinear profile is constructed, is found. This is done provided that the centre of the polygon, when it rolls in profile, must also move in a circle. Rolling occurs in the absence of sliding. Therefore, the length of the arc of the curve is equal to the length of the side of the polygon. To find the equations of the curve of the profile, a first-order differential equation is constructed. Its analytical solution is obtained. The parametric equations of the curve are obtained in the polar coordinate system. The limits of the change of an angular parameter for the construction of a profile element are found. It is a part of the arc of the curve. According to the obtained equations, curvilinear profiles with different numbers of their elements are constructed.

Author Biographies

Tetiana Kresan, National University of Life and Environmental Sciences of Ukraine

PhD, Associate Professor of Department of Design of Technical Systems of Separated Subdivision of National University of Life and Environmental Sciences of Ukraine Nizhyn Agrotechnical Institute, Nizhyn, Ukraine.

Serhii Pylypaka, National University of Life and Environmental Sciences of Ukraine

Doctor of Technical Sciences, Professor of Department of Descriptive Geometry, Computer Graphics and Design of National University of Life and Environmental Science of Ukraine

Zynovii Ruzhylo, National University of Life and Environmental Sciences of Ukraine

Ph.D, associate professor, Dean of Department of Engineering Reliability of Faculty of Design and Engineering of National University of Life and Environmental Sciences of Ukraine

Ivan Rogovskii, National University of Life and Environmental Sciences of Ukraine

Prof. Ph.D. Eng. of Department of Occupational Safety and Environmental Engineering of Mechanical and Technological Faculty of National University of Life and Environmental Sciences of Ukraine

Oleksandra Trokhaniak, National University of Life and Environmental Sciences of Ukraine

Ph.D, associate professor of Department of Engineering Reliability of Faculty of Design and Engineering of National University of Life and Environmental Sciences of Ukraine

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Published

2020-09-01

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Section

Articles