Optimum circular interpolation for plane curve contours

In NC manufacturing of curve contours, the circular interpolation is widely used. It has not been completely resolved of how to determine the parameters of circular arcs satisfying the desired interpolation accuracy and how to make the arc number minimum, simultaneously. This paper describes a new circular interpolation algorithm for a continuous curve contour. The method is based on the principle of minimax approximation and has two features: 1) the interpolation error is uniform and smooth in any monotone interval of the radius of curvature of profile curve, continuous at the connecting points between two monotone intervals and less than or equal to the specified accuracy value; and 2) the parameters of the circular arcs are determined dependent on the desired interpolation accuracy and the arc number is minimum. The algorithm is simple and convenient to apply to NC contour manufacturing. As an example, the interpolation results for the profile of a plane cam are shown.