  In this paper, we define some new associated curves as integral curves of a
vector field generated by Frenet vectors of tangent indicatrix of a curve in
Euclidean 3-space. We give some relationships between curvatures of these
curves. By using these associated curves, we give some methods to construct
helices and slant helices from some special spherical curves such as circles on
unit sphere, spherical helices, and spherical slant helices. Finally, we give
some related examples.
