Abstract: A lathe and a method of using the lathe are disclosed for forming an aspheric surface on a workpiece, in which the workpiece is mounted to a holder that is rotatably carried by the spindle, headstock and bed of a lathe, with that spindle and workpiece being rotated about the axis of the spindle with the workpiece being engaged by a forming tool which forming tool is moved through an arcuate path about an axis that is generally transverse to the spindle axis. The method and apparatus provide further for determining the time-varying angular position of the forming tool along the arcuate path, for determining the time-varying angular position of a point on the workpiece about the spindle axis and for reciprocating the workpiece holder and the workpiece held thereby relative to the lathe headstock and to the forming tool in synchronization with the movement of the forming tool and with the rotation of the workpiece about the spindle axis to form the desired contoured surface.

Abstract: A lathe and a method of using the lathe are disclosed for forming an aspheric surface on a workpiece, in which the workpiece is mounted to a holder that is rotatably carried by the spindle, headstock and bed of a lathe, with that spindle and workpiece being rotated about the axis of the spindle with the workpiece being engaged by a forming tool which forming tool is moved through an arcuate path about an axis that is generally transverse to the spindle axis. The method and apparatus provide further for determining the time-varying angular position of the forming tool along the arcuate path, for determining the time-varying angular position of a point on the workpiece about the spindle axis and for reciprocating the workpiece holder and the workpiece held thereby relative to the lathe headstock and to the forming tool in synchronization with the movement of the forming tool and with the rotation of the workpiece about the spindle axis to form the desired contoured surface.