In this paper, we address a new version of Darboux frame using a common tangent vector
field to a surface along a curve and call this frame the rotation minimizing Darboux frame (RMDF).
Then, we give the parametric equation due to the RMDF frame for a sweeping surface and show that the
parametric curves on this surface are curvature lines. Consequently, necessary and sucient conditions
for sweeping surfaces to be developable ruled surfaces are derived. Also, we analyze the conditions
when the resulting developable surface is a cylinder, cone or tangential surface. We also provide some
examples to illustrate the main results.