This paper presents a method of real-time CNC interpolation for complex curved profiles which can be described with NURBS equations. The real-time interpolation algorithm is based on second order Taylor’s expansion with the principle part being a formula for updating parametric value u after each sampling period. | Vietnam Journal of Science and Technology 55 (5) (2017) 650-657 DOI: A METHOD OF REAL-TIME NURBS INTERPOLATION WITH CONFINED CHORD ERROR FOR CNC SYSTEMS Nguyen Huu Quang*, Banh Tien Long Hanoi University of Science and Technology, 1 Dai Co Viet, Hai Ba Trung, Ha Noi, Viet Nam * Email: Received: 8 February 2017; Accepted for publication: 10 April 2017 ABSTRACT This paper presents a method of real-time CNC interpolation for complex curved profiles which can be described with NURBS equations. The real-time interpolation algorithm is based on second order Taylor’s expansion with the principle part being a formula for updating parametric value u after each sampling period. With the updated value of u, a new interpolated point is calculated based on the DeBoor’s algorithm. Chord error caused by the interpolation algorithm depends on two main factors which are machining feedrate and radius of curvature of the NURBS curve. In this paper, an efficient method of limiting chord error is also presented with the basic idea of reducing machining feedrate at positions with a radius of curvature smaller than a critical value. Simulation results on Matlab software verify effectiveness of the proposed method. Keywords: CNC interpolation; CAD/CAM; NURBS; DeBoor’s algorithm. 1. INTRODUCTION Nowadays, parametric curves such as Bezier, B-spline, NURBS, etc. are being widely applied in well-developed CAD systems to design parts with complex curved profiles. On the other hand, conventional CNC machines typically only support motion along straight lines (G01) and circular arcs (G02,G03). To bridge the gap between CAD systems and CNC machines, there are two main approaches: In the first one, original parametric curves is approximated by a sequence of short linear segments with the use of CAM softwares; And in another one, a new parametric interpolator is suggested to be developed for CNC systems, so that it has the ability of .
