  In this paper, we study the spherical indicatrices of W-direction curves in
three dimensional Euclidean space which were defined by using the unit Darboux
vector field W of a Frenet curve, in [11]. We obtain the Frenet apparatus of
these spherical indicatrix curves and the characterizations of being general
helix and slant helix. Moreover we give some properties between the spherical
indicatrix curves and their associated curves. Then we investigate two special
ruled surface that are normal and binormal surface by using W-direction curves.
We give useful results involving the char- acterizations of these ruled
surfaces. From those applications, we make use of such a work to interpret the
Gaussian, mean curvatures of these surfaces and geodesic, normal curvature and
geodesic torsion of the base curves with respect to these surfaces.
