中文摘要：

为解决采用滤波技术对NURBS曲线进行插补时导致的滤波后连接点和极值点的速度发生改变这一不足，基于移动平均技术，提出移动平均的位置不变性推论。该方法具有可扩展性，可实现加速度、加加速度及位移对时间更高阶指令的连续性，有效地减小了机床振动。最后对所设计的算法进行了实例验证，验证结果表明了所提出算法的有效性及可行性。

英文摘要：

Due to solve the shortcomings of the speed and position altering of the interpolation points near the extreme point and the junction point by filtering technology, the inference of moving- average of the position invariance was derived based on moving-average technology. By means of this inference, the shortcomings can be solved. And the method was scalable. It can achieve the acceleration of continuous,and jerk very easily and displacement for time of more-order differentiabiiity of contin- uous. Thus the proposed algorithm can reduce the machining vibration. Finally, the implementation and experimental results were given in detail. The experimental results show the effectiveness and fea- sibility.