The authors study ruled surfaces obtained from the motion of the Frenet frame
of one curve
along a second curve
. The ruled surfaces in question have
as director line and the direction
of a ruling is fixed in the moving Frenet frame of
. Particular emphasis is put on the cases where
is one of the Frenet basis vectors. After providing criteria for the developability of these ruled surfaces, the authors compute certain differential invariants like harmonic curvature, angle of pitch, length of pitch and the distribution parameter.