Abstract:Based on the basic theory and characteristics of space curves in classical differential geometry,a new kind of moving construction——the spherical Frenet construction of this kind were finany obtained in 3D Euclidean space,as well as the 3D curves Frenet construction field were introduced to inspect the spherical curves in 3D Euclidean space.Bertrand,Mannheim,rectifying curves,and special curves of this kind were finally obtained in the 3D E3 space,giving spherical curves in 3D Euclidean space which can be described by firstorder ordinary differential equations with respect to curve’s curvature and torsion,and producing a lowlevel curve representation for the corresponding differential equation.The new characteristics of spherical curves were verified and the calculation process was simplified.