Abstract: A lathe for cutting an aspherical surface on a workpiece, such as a contact lens blank, comprises a headstock mounted for linear reciprocating movement relative to a radius cartridge having a tool post for mounting a cutting tool so that the tool can swing at a preset radius about an axis perpendicular to the rotational axis of the headstock spindle in the same plane as the spindle axis. The radius cartridge is coupled to the headstock via an eccentric mechanism, a connecting rod and a slidable bearing assembly for the headstock leadscrew so that the headstock is reciprocated in synchronism with oscillating movement of the radius cartridge to cause the tool to cut a predetermined aspherical surface on the workpiece. The headstock may be intermittently advanced towards the cutting tool, independently of its reciprocating movement and while the cutting tool is stationary, by means of the leadscrew in order to provide for incremental removal of material from the workpiece.