Geometric relations for transforming a helically wound cylindrical pipe into a curvilinear branch

A calculation model for transforming a cylindrical pipe wound on a deformable mandrel into a curvilinear branch whose shape corresponds to the section of a circular torus is presented. The conditions of inextensible filaments and invariable twist angle are considered. Formulas for changing the winding angles on the branch, relations for determining the parameters of a billet and the branch, and limitations on the choice of winding angles for the billet are found.