Rolling of a single-cavity hyperboloid of rotation on a helicoid on which it bends
Keywords:Single-cavity hyperboloid of rotation, Bending, Helicoids, Linear contact, Rolling, Coefficients of the first quadratic form
AbstractThe 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.
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