Rolling of a single-cavity hyperboloid of rotation on a helicoid on which it bends

Authors

  • Tetiana Kresan National University of Life and Environmental Sciences of Ukraine, Heroiv Oborony Str., 15, Kyiv, Ukraine http://orcid.org/0000-0002-8280-9502
  • Serhii Pylypaka National University of Life and Environmental Sciences of Ukraine, Heroiv Oborony Str., 15, Kyiv, Ukraine http://orcid.org/0000-0002-1496-4615
  • Zynovii Ruzhylo National University of Life and Environmental Sciences of Ukraine, Heroiv Oborony Str., 15, Kyiv, Ukraine
  • Ivan Rogovskii National University of Life and Environmental Sciences of Ukraine, Heroiv Oborony Str., 15, Kyiv, Ukraine http://orcid.org/0000-0002-6957-1616
  • Oleksandra Trokhaniak National University of Life and Environmental Sciences of Ukraine, Heroiv Oborony Str., 15, Kyiv, Ukraine http://orcid.org/0000-0002-4671-5824

Keywords:

Single-cavity hyperboloid of rotation, Bending, Helicoids, Linear contact, Rolling, Coefficients of the first quadratic form

Abstract

The bending of a single-cavity hyperboloid of rotation with the preservation of rectilinear generator is considered. The resulting bending surfaces are a plural of open skew helicoids, including partial cases of oblique closed and open ordinary helicoid s. The parametric equations for the continuous bending of these surfaces are made by changing the angle between the straight line and its axis. The possibility of a pure rolling of a hyperboloid along a helicoid from the set of its bends with linear contact along a joint rectilinear generator of both surfaces is shown. According to the obtained equations, the surfaces are constructed and the hyperboloid and helicoid images are shown with the joint rectilinear generator of their contact.

Author Biographies

Tetiana Kresan, National University of Life and Environmental Sciences of Ukraine, Heroiv Oborony Str., 15, Kyiv, 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, Heroiv Oborony Str., 15, Kyiv, 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, Heroiv Oborony Str., 15, Kyiv, 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, Heroiv Oborony Str., 15, Kyiv, 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, Heroiv Oborony Str., 15, Kyiv, 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

2021-12-20

Issue

Engineering Review, Vol. 41, No. 3

Section

Articles

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