Abstract <p>Helical surfaces are of great importance in toolmaking. The inverse problem of helical groove profiling, using the main known methods, is solved for wear-free wheels. The degree of grinding-wheel wear depends on its actual service life, which affects the shape of the machined helical groove of the product. Therefore, this paper examines the relationships between the parameters of the grinding wheel’s position relative to the workpiece that take into account the influence of the toroidal section profiling the rake face and other conical wheel parameters on the key parameters of accuracy of shaping the helical surface (rake angle and groove profile opening angle in the radial cross section). Basic recommendations are proposed for grinding helical surfaces with different toroidal section rounding radii on the grinding wheel.</p>