On rectifying curves in Euclidean 3-space

First, we study rectifying curves via the dilation of unit speed curves on the unit sphere S-2 in the Euclidean space E-3. Then we obtain a necessary and sufficient condition for which the centrode d(s) of a unit speed curve alpha(s) in E-3 is a rectifying curve to improve a main result of [4]. Finally, we prove that if a unit speed curve alpha(s) in E-3 is neither a planar curve nor a helix, then its dilated centrode beta(s) = rho(s)d(s), with dilation factor rho, is always a rectifying curve, where rho is the radius of curvature of alpha.