To realize the high precision and real-time interpolation of the NURBS （non-uniform rational B-spline） curve, a kinetic model based on the modified sigmoid function is proposed. The constraints of maximum feed rate, chord error, curvature radius and interpolator cycle are discussed. This kinetic model reduces the cubic polynomial S-shape model and the trigonometry function S-shape model from 15 sections into 3 sections under the precondition of jerk, acceleration and feedrate continuity. Then an optimized Adams algorithm using the difference quotient to replace the derivative is presented to calculate the interpolator cycle parameters. The higher-order derivation in the Taylor expansion algorithm can be avoided by this algorithm. Finally, the simplified design is analyzed by reducing the times of computing the low-degree zero-value B-spline basis function and the simplified De Boor-Cox recursive algorithm is proposed. The simulation analysis indicates that by these algorithms, the feed rate is effectively controlled according to tool path. The calculated amount is decreased and the calculated speed is increased while the machining precision is ensured. The experimental results show that the target parameter can be correctly calculated and these algorithms can be applied to actual systems.
本文首先介绍B样条曲线,并推广到B样条曲面及B样条体,然后在此基础上介绍直接操作自由变形技术(Direct Manipulation of Free Form Deformation),将此技术应用于曲面模型上,使得物体发生变形。在此基础上,对直接操作自由形式变形进行了改进,提出了以Nurbs曲线作为变形基函数的变形方法;并且讨论了Nurbs曲线的控制点和权因子的改变对变形的影响;然后,结合Nurbs曲线控制点和权因子的变化,完成DMFFD变形;最后,比较了以Nurbs作为变形基函数与以B-spline作为变形基函数变形的不同。实验结果表明,改进后的DMFFD变形有更好的选择性和自主性。
