A real-time predictor-modification-evaluation–corrector-modification-evaluation parametric interpolator for numerical control transition curves

Abstract

A real-time parametric interpolator based on a predictor-modification-evaluation–corrector-modification-evaluation algorithm is proposed in this article, which is utilized to efficiently calculate the reference points of transition curves. Meanwhile, the stable calculation is guaranteed by analyzing the convergence condition of the predictor-modification-evaluation–corrector-modification-evaluation algorithm. Under the convergence condition, the proposed parametric interpolator and traditional line interpolators are simultaneously implemented to interpolate a two-dimensional butterfly path, which consists of quintic Bézier transition curves and line segments. Simulation and experiments are carried out, and the results demonstrate that the proposed real-time predictor-modification-evaluation–corrector-modification-evaluation parametric interpolator achieves the highest accuracy and the light stripe on the tool path is further reduced and hardly observed. Compared with other parametric interpolators, the proposed real-time predictor-modification-evaluation–corrector-modification-evaluation parametric interpolator is capable of achieving a good balance between interpolation accuracy and interpolation efficiency.