Direction curves of principal normal indicatrix of a curve

Helices and slant helices are curves which are often encountered in nature and science and have a wide range of uses including computer aided geometric design, fractal geometry, kinematics, and DNA double. In this paper, direction curves of principal normal indicatrix of a curve in Euclidean 3-space are defined and some relationships between Frenet vectors and curvatures of these curves are found. By using these direction curves, some useful methods to construct helices and slant helices from spherical curves are obtained. Finally, a related example is given