Design of a NURBS Interpolator with Predicted Tangent Constraints

Abstract

This paper focuses on proposing a tangent prediction NURBS interpolator (TP) method for reducing the machining time and improving the surface quality, which adopts predicted tangent vectors to constrain the curve shape and suppress the curve fluctuation. Although the traditional NURBS path interpolation methods have the advantageous in flexibility and can be easily implemented, those methods tend to curve distortion if insufficient interpolation points or constraints are given, which will extend the curve length and influence the accuracy of the constructed module. In this paper, the geometric module constructed by the TP method can not only ensure a smooth transition between curve sections but also decrease the curve distortion. With the proposed method, the curvature radii at some local areas may increase, which means the chord error will increase accordingly. To minimize the chord error, a curve subsection process along with a 7-segment S-shape acceleration/deceleration (ACC/DEC) process are adopted here. Meanwhile, the predictor-corrector interpolator method is applied to reduce the velocity variation and improve the accuracy of the control system. Experiments are carried out to demonstrate the ability of the method by virtue of reducing the machining time and improving the surface quality.