Abstract: A working tool having a linear working edge is secured to a tool holding arm which is rotatably arranged about a focus shaft extending in parallel with a Z axis and is slidable linearly in parallel with an XY plane. A workpiece is secured to a workpiece mounting member in such a manner that its center axis extends in an X' direction which is inclined by an angle (.pi./2-.theta.) with respect to an X axis. A longitudinal direction of the working edge is inclined by the angle .theta. with respect to a line which is obtained by projecting a sliding direction of the tool holding arm. When the working tool and the workpiece are moved relative to each other, the workpiece is cut into a quadric surface in accordance with a quadric surface formed by the working edge as an envelope of tangents.

Abstract: An optical lens having a hyperboloid surface is formed by cutting or grinding a workpiece made of glass or plastics while rotating it about its axis, while a cutting or grinding tool having a linear working edge is rotated or swung about a central axis, the working edge is separated from the center axis by a given distance and is inclined with respect to the central axis by a given angle. The envelope of the working edge forms a hyperboloid of one sheet of revolution along which the workpiece is cut or ground. An eccentricity of the hyperboloid curve can be adjusted by changing the inclined angle of the working edge with respect to the central axis.