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https://doi.org/10.30765/er.1563

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

Tetiana Kresan ; National University of Life and Environmental Sciences of Ukraine
Serhii Pylypaka ; National University of Life and Environmental Sciences of Ukraine
Zynovii Ruzhylo ; National University of Life and Environmental Sciences of Ukraine
Ivan Rogovskii ; National University of Life and Environmental Sciences of Ukraine
Oleksandra Trokhaniak orcid id orcid.org/0000-0002-4671-5824 ; National University of Life and Environmental Sciences of Ukraine


Puni tekst: engleski pdf 529 Kb

str. 106-114

preuzimanja: 49

citiraj


Sažetak

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.

Ključne riječi

single-cavity hyperboloid of rotation, bending, helicoids, linear contact, rolling, coefficients of the first quadratic form

Hrčak ID:

265976

URI

https://hrcak.srce.hr/265976

Posjeta: 135 *