关键词： 可展曲面, 曲线, 直线族

Abstract: In this paper we discuss how to obtain  a developable surface from some families of straight along a curve.The main results are:(1) The ruled surface generate by a directrix Γ：r=r(s)  and the rulings α(s)cos θ(s)+γ(s)sin θ(s) is developable if and only if tan θ(s)=k(s)/τ(s),where α and γ are the unit tanqent vectors and binormal vectors of Γ respectively,k and τ are curvature and torsion functions of Γ respectively；(2) Let Γ be a curve on the surface S,then the  ruled surface can be generated by the directrix Γ and the rulings ε(s)cos θ(s)+n(s)sin　θ(s)  is developable if and only if θ(s)=∫ss0τg(s)ds＋θ0,where n(s) is the normal vector of S at s,ε=n×α,τg is the gesdesic torsion of S along Γ.

Key words: development surface, curve, family of straight lines