The article has described the simplicity machining method of the tilted edge fingerlike gear cutter with uniparted hyperboloid matching tooth shape and the straight generatrix of the uniparted hyperboloid as the blade curve.

This article not only discusses the ruled surface features of uniparted hyperboloid and its application in archtecture engineering but also discusses the teaching of the ruled surface.

It is proved that the surface organized by all the straight lines which are coplanar with three u-family rectilinear generators of an uniparted hyperboloid,which are not coincident with each other,is exactly the primal uniparted hyperboloid.

Potential distribution of charged conductorwith surface of hyperboloid of one sheet;

From the hyperboloid of one sheet of special section line,the article analyzes its property of ruled surface and deduces the parameter equation of another trigonometric function form,which agrees with the definition of the ruled surface.

The paper proves that the surface normal,which is followed by rectilinear generators on hyperboloid of on sheet,comstructs the hyperbolic paraboloid generated by two same parabola,when rectilinear generators go through the vertex of waist ellipse,and it also deduces that the hyperboloid of one sheet is constructed by surface normal through a certain rectilinear generator.

For a given three screws, this paper, using the theory of quadric surface, finds the hyperboloid which is defined by the three given screws.

This article discussed the method used to create complicated spatial contour surface of roller gear cam, built the functions of roller gear cam contour surface, established the parameterized design system of roller gear cam complicated spatial contour surface model by using UG OpenAPI programming interface.