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

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Published

2021-12-20

Issue

Engineering Review, Vol. 41, No. 3

Section

Articles

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How to Cite

Rolling of a single-cavity hyperboloid of rotation on a helicoid on which it bends. (2021). Engineering Review, 41(3), 106-114. https://www.engineeringreview.org/index.php/ER/article/view/1563