  In this study, we define the generalized normal ruled surface of a curve in
the Euclidean 3-space $E^3$. We study the geometry of such surfaces by
calculating the Gaussian and mean curvatures to determine when the surface is
flat or minimal (equivalently, helicoid). We examine the conditions for the
curves lying on this surface to be asymptotic curves, geodesics or lines of
curvature. Finally, we obtain the Frenet vectors of generalized normal ruled
surface and get some relations with helices and slant ruled surfaces and we
give some examples for the obtained results.
