Before revision: In this work we furnish characterizations of spherical and plane curves using rotation minimizing frames. Due to their minimal twist, in many contexts these frames are preferable over the usual Frenet one, such as in motion design, sweep surface modeling, computer visualization, and in geometric considerations as well. Here, we first furnish an alternative proof for the characterization of spherical curves by using osculating spheres described in terms of a rotation minimizing frame. In addition , we show how to find the angle between the principal normal and a rotation minimizing vector for a spherical curve.
After revision: In this work , we study plane and spherical curves in Euclidean and Lorentz-Minkowski 3-spaces by employing rotation minimizing (RM) frames. By conveniently writing the curvature and torsion for a curve on a sphere , we show how to find the angle between the principal normal and a rotation minimizing vector for a spherical curve.