Generating conjugate shapes using piecewise cubic spline functions Original Research Article

This paper proposes a method called “piecewise generation” for generating conjugate shapes from sets of data points on original cutters using cubic spline functions to fit the points. The differences between conventional generation methods and piecewise generation are presented. The main advantage of this method is that the analytical form of the cutter need not be provided. Therefore, only sets of data points on the cutter either derived from analytical form or measured with coordinate measuring machines (CMMs) are necessary for the conjugate shape to be derived using this method. It provides a practical and useful tool for conjugate-pair design verification and reverse engineering applications.