A lathe-based system may include chucks to retain a glass core rod, an arm, a slip joint, an actuator system, and a control system. The slip joint may couple the arm and a first chuck in fixed relation against relative axial motion with respect to an axis of rotation. The slip joint may also couple the arm and the first chuck in two-dimensionally movable relation with respect to a plane normal to the axis of rotation. The actuator system may be configured to two-dimensionally adjust a position of the first chuck in the plane. The control system may measure straightness of the glass core rod and control the actuator system in response to optical measurements of the straightness. In this manner, the system may straighten the glass core rod. The system may simultaneously elongate the glass core rod as it straightens the glass core rod.