Before revision:  Finally, since Frenet frames and osculating spheres are not well defined at the zeros of the curvature and torsion , respectively, we discuss the behavior of the angle between the principal normal and a rotation minimizing vectornear these zeros.
After revision:  Finally, since Frenet frames and osculating spheres are not well defined at the zeros of the curvature and torsion of a generic curve by studying its behavior near an osculating sphere, i.e., we describe them in terms of spherical analogs. Finally, we also address in this work the problem of characterizing those curves whose position vector, up to a translation, lies on a (moving) plane spanned by the angle between the principal normal and a rotation minimizing vectornear these zeros.