PURPOSE: To enable the highly accurate cutting of a work on a paraboloid of revolution, by rotating a single point cutting tool while controlling the distance between the work and the center of rotation of the cutting tool in accordance with the rotary angle of the cutting tool such that the edge of the cutting tool will draw the parabolic curve on the work cutting face.

CONSTITUTION: A servo motor 15 and a rotary motor 16 for moving the work supporter 20 and a tool supporter 11 relatively in the direction of the rotary axis in a plane parallel with the rotary plane of the edge. In the pulse trains of the simultaneous two axis produced from a numeric controller 30, one is provided to the rotary motor 15 to rotate a tool shaft 17 while the other is provided to the servo motor 15 to move a spindle table 13 thus to control the relative movement of the work W against the center of rotation of the cutting tool 18 and to rotate the rotary table 21 with low speed thus to cut the paraboloid of revolution while satisfying the condition shown on the drawing. Here (a) is the focus distance on the paraboloid of revolution, (d) is the diameter of revolution of the cutting tool 18, θ is the rotary angle of the cutting tool 18 and Y is the displacement.