Calculation of the bending parameters of a flat workpiece into a twist of a helicoid torso

Helical surfaces are deployable and non-deployable. The first is the surface of a helical conoid widely used in technology, known as screw. second one an unfolding helicoid or torso-helicoid. In both cases, formed from blank - sweep form flat ring. If case can be calculated approximately, since exact does not exist due to properties non-expanded surfaces, then it exactly. However, this mean that just possible ready-made product twist torso. contrast during manufacture which workpiece subjected complex stretching compression deformations, expanded obtained by bending with minimal plastic magnitude depends on thickness sheet. Bending occurs along rectilinear generators, theoretically located workpiece. process bending, location these generators should change. theory differential geometry, such described analytically called continuous bending. With regard torso-helicoid, means gradual increase step desired value. work contains parametric equations describe method At same time, only axis coil occurs, but also its twisting around axis. A comparison two movements was made found relationship between them linear. gives formula describing dependence. According it, when uniformly stretched axis, angle increases according dependence close quadratic. work, examples use torso-helicoid given, visualized, graphs constructed. Confirmation reliability results quadratic change bent