||High speed high accuracy machining holds the dominant position in modern manufacturing industry. Seeking a direct approach to increase the productivity and speedup the operation becomes more and more stringent. In this thesis, research is focused on real-time parametric curve interpolator in the motion control systems. A common requirement of all motion control systems is to generate coordinated movement of the separately driven axes of motion in order to achieve the desired path of the tool. This involves the generation of signals prescribing the shape of the produced part by interpolators. In the conventional interpolation method, the part geometric data is decomposed by the CAD/CAM system into a sequence of straight lines and circular arcs that approximate the desired geometric path with a given tolerance. However, the requirements of high speed high accuracy machining of dies, molds, and aerospace parts with sculptured surfaces cannot be fulfilled by the traditional interpolator. Parametric interpolator fills the gap between the well-developed CAD/CAM softwares and conventional CNC systems in terms of the methods available for defining geometry. In contrast to the traditional method, parametric interpolators can deal with the parametric curves transferred substantially from CAD/CAM system. Therefore, the drawbacks mentioned above could be subsequently eliminated. Before the trajectory generation part in the interpolator, we first establish a cutter path planning module which can approximate the original successive fine line segments to piecewise parametric curve within the pre-defined tolerance requirement. The second order continuity is fulfilled to guarantee the smoothness of the generated cutter path. In the trajectory generation we focus on the development and implementation of the speed-controlled parametric interpolator, especially the NURBS curve parametric interpolator, with the scheduling of jerk, acceleration/deceleration, and vector feed speed control along the tool paths incorporated. The integration of machining dynamics and the computational simplicity is taken into consideration. The experiment is carried out on the two dimensional X-Y table and the part positioning table in the CNC milling machine to validate the feasibility of the cutter path planning module and the NURBS interpolation algorithm.