On rectifying curves in Euclidean 3-space

First, we study rectifying curves via the dilation of unit speed curves on the unit sphere S² in the Euclidean space E³. Then we obtain a necessary and sufficient condition for which the centrode $d(s)$ of a unit speed curve α(s) in E³ is a rectifying curve to improve a main result of {cd05}. Finally, we prove that if a unit speed curve α(s) in E³ is neither a planar curve nor a helix, then its dilated centrode β(s)=ρ(s) d(s), with dilation factor ρ, is always a rectifying curve, where ρ is the radius of curvature of α.