泰勒展开NURBS曲线插补算法

Study on NURBS Interpolator with Taylor Expansion

分别利用一阶、二阶泰勒展开公式逼近NURBS样条参数,对NURBS曲线插补算法进行了研究.算例证明该算法可以获得与指令速度几乎完全一致的插补结果.给出了一阶、二阶泰勒展开方法的速度波动与曲率的关系,弦误差与插补周期的关系.指出泰勒方法NURBS曲线插补对于误差控制是一种开环方法,但是它忽略了机械系统的输出能力,当机械系统的输出能力不足时将会出现较大的加工误差.

The NURBS （non-uniform rational B-spline） interpolator was studied with the first and second order Taylor expansion to approximate NURBS parameter. Numerical example results proved that the interpolation velocity is almost the same to reference velocity. The relationships between curvature and velocity fluctuating and between chord error and interpolation period in the Taylor expansion were given. It was found that the NURBS interpolator with Taylor expansion is actually a kind of open loop method. However, it ignores the output capability of a mechanical system and, therefore, big processing error may occur when the output capability of the mechanical system is insufficient.