Abstract: A lathe for generating spherical surfaces of selected radiis on workpieces in the usual manner but which is provided with curve-selecting adjustable means for generating aspherical surfaces which deviate from the spherical surfaces in a predetermined relationship. The lathe is provided with a spindle which carries the workpiece for rotation about its axis and a feed carriage which carries a suitable surface forming tool for swinging about a fixed pivot in contact with the face or surface of the workpiece. The feed carriage for supporting the tool includes means for supporting it for axial floating movement into contact with the surface of the workpiece. The curve-selecting adjustable means for causing deviations from spherical in the surface produced on the workpiece includes a mechanical linkage having a link pivotably interconnected to the feed carriage along its centerline which passes through the fixed pivot, and to a mount positioned in predetermined relationship to the fixed pivot.