Abstract
The article describes the creation of the normal cycloidal curve by rotation of the point about the normal of the circle on the spherical surface and binormal cycloidal curve created by rotation of the point about the binormal of the previous cycloidal curve. Cycloidal cyclical surfaces are created by moving circles along the curves lying in the normal plane of the curves. Described cycloidal cyclical surfaces are projected on the spherical surface. Varying parameters of the curves are generated different ornaments on the spherical surface.