Optimal Linear Interpolation of Planar Curves for NC Contour Machining

In NC machining of planar contours, the cutter path is frequently approximated by linear interpolation to a contour curve as target. In this situation, the interpolation error should be measured along the normal direction of the contour curve, and it is desired that only the fewest linear segments are needed with respect to the specified accuracy. However, how to determine the parameters of segment to match these requirements has not been completely solved. This paper presents a new linear interpolation approach for this problem. The approach is named as the optimal linear interpolation method and has three features which include: (1) the interpolation error along the normal direction of object curve satisfies the specified accuracy, and the number of the required segments is the fewest simultaneously; (2) the connection between any two adjacent segments on generated cutter path is natural and smooth, and the generation of extremely short segment is avoided as much as possible; (3) the algorithm is simple and with a high computation efficiency. The effectiveness of the proposed approach has been sufficiently confirmed by applying it to two interpolation examples of planar cam contours. At the same time, the reduction effect of interpolation data has also been verified through comparing the segment number required by the proposed method and Nishioka’s method, which is specially developed to precision machining of planar cam contour, relative to the same interpolation conditions.