Cylindrical helices and Bertrand curves are studied from a new point of view: they are considered as curves on a ruled surface. It is shown that a ruled surface is the rectifying developable of a curve

$\gamma $ if and only if

$\gamma $ is the geodesic of the ruled surface which is transversal to rulings and whose Gaussian curvature vanishes along

$\pi $. As a consequence of this theorem, a new characterization of cylindrical surfaces is obtained. Another essential theorem states that a ruled surface is the principal normal surface of a space curve

$\gamma $ if and only if

$\gamma $ is the asymptotic curve of the ruled surface and has vanishing mean curvature along

$\gamma $. Applying this result, consequences on Bertrand curves and an interesting characterization of helicoids are deduced.