On the trajectory ruled surfaces of framed base curves in the Euclidean space

In this paper, we study trajectory ruled surface of a curve with singular points in the Euclidean 3‐space as an application of singularity theory of a space curve with singular points. By considering notion of framed curve, we investigate the trajectory ruled surface and give some results about invariants of these surfaces. Then, we give some examples of trajectory ruled surfaces. Moreover, we determine local diffeomorphic image of these surfaces.