Generic properties of Darboux-type curves

In this paper, we present a method for constructing Darboux-type curves by using spherical curves and smooth functions. We show that all Darboux-type curves can be generated using this method. We discuss the relationship between Darboux-type curves and rectifying curves. Moreover, we establish a connection between Darboux-type curves and geodesics on a rectifying developable surface from the viewpoint of curves on ruled surfaces.