Before revision:  This is done by first solving the problem for spherical curves and then using the concept of osculating spheres to solve the general case. 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:  This is done by conveniently writing the curvature and torsion for a curve on a sphere. Later, we extend these expressions for the curvature and torsion , respectively, we discuss the behavior of the angle between the principal normal and a rotation minimizing vectornear these zeros.