The Research Of The Continuous Line Segments Fitting By Arc And The Separation Of NURBS Curve

There are three kinds of cutter location in NC machining. The continuous line segment path, arc path and NURBS curve. The continuous line segment path is constructed by a series of small lines. This tool path just approximates the original contour in shape. It cannot satisfy the accuracy and smooth. If we fit the continuous line segments by arcs, the surface of the machining modeling will become smoother. The NURBS curve is widely used in the design of the modeling, however, most CNC systems do not support NURBS curve interpolation, the common method is fitting NURBS curve by the continuous line segments.In this dissertation, the least squares algorithm for the fitting by arcs is introduced. As the algorithm does not consider the influence of the bad points, it will generate the wrong fitting arcs. A new method called the half-constraint least squares algorithm is proposed. In this algorithm, we calculate the new link points to avoid the influence of the bad points and guarantee the fitting precision. However, both of the above algorithms do not consider the smoothness of the path. For the arc path, we just consider the derivability of the link points. Firstly, the strict derivability in the link points is considered, we find the restriction is so severe that there is fewer arc after fitting. Then the derivable tolerance at the link point is proposed. It can guarantee the curve smoothness by restricting the tolerance. Then a simulation experience is made to prove the correctness of the algorithm.For the NURBS curve separation, the algorithms of the equal chord length separation and the equal error separation are introduced. Then both the algorithms are tested by MATLAB. From the result of the simulation, we can find out the two above methods cannot make the continuous line segment path approximate the NURBS curve. They even generate the sharp points. Basing on the original algorithm, the equal chord length, the equal error and controllable deflection angle segment algorithm is proposed. This algorithm mainly produces a relative smooth continuous line segment path by dividing the interval of the curve and analyzing the relationship of the chord, error and the deflection angle. The path after separating by this algorithm is much more suitable for CNC machining.