Yavuz, Ayse2024-02-232024-02-2320211844-9581https://doi.org/10.46939/J.Sci.Arts-21.4-a16https://hdl.handle.net/20.500.12452/16600The main purpose of this paper is to investigate unit speed curve with constant geodesic, normal curvature and geodesic torsion of curve on a surface in the Euclidean 3-space. In accordance with this scope, the position vector of a curve is stated by a linear combination of its Darboux Frame with differentiable functions. Some special results have been obtained within the scope of this position curve and differentiable functions. As a physical application of obtained results, differential geometric properties of a surface with binormal motion of a given curve are given with the obtained characterization of the curve.eninfo:eu-repo/semantics/openAccessBinormal MotionDarboux FrameSurface-Twisted CurveArticle410431056WOS:00075666580001610.46939/J.Sci.Arts-21.4-a16