Open AccessRolling of a single-cavity hyperboloid of rotation on a helicoid on which it bends
Author(s) -
Тетяна Кресан,
Serhii Pylypaka,
Zynovii Ruzhylo,
I. L. Rogovskii,
Oleksandra Trokhaniak
Publication year - 2021
Publication title -
engineering review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.198
H-Index - 11
eISSN - 1849-0433
pISSN - 1330-9587
DOI - 10.30765/er.1563
Subject(s) - hyperboloid , helicoid , generatrix , rotation (mathematics) , optics , paraboloid , polygon (computer graphics) , geometry , generator (circuit theory) , physics , mathematics , surface (topology) , engineering , mechanical engineering , power (physics) , frame (networking) , quantum mechanics
The bending of a single-cavity hyperboloid with rotation while maintaining the 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 established by changing the angle between the straight line and its axis. The possibility of pure unrolling of a hyperboloid along a helicoid from the set of its bends with linear contact along a common rectilinear generator of both surfaces is shown. Using the obtained equations, the surfaces are constructed and the images of hyperboloid and helicoid with the common rectilinear generator of their contact are shown.