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 the usual spindle which carries the workpiece for rotation about its fixed axis and a feed carriage which carries a suitable generating tool for swinging about a fixed pivot in generating contact with the face or surface of the workpiece. The feed carriage for supporting the generating tool includes means for supporting it for axial floating movement and means for constantly biasing it into contact with the surface of the workpiece.