Real-time CNC interpolators for precision machining of complex shapes with Pythagorean-hodograph curves

Computer numerical control (CNC) machining is the prevalent means for precision fabrication of mechanical parts. CNC systems have traditionally employed real-time interpolators that can only interpret piece-wise linear/circular (G code) tool paths: free-form geometry must be approximated by many short linear/circular segments before being downloaded to the CNC system. Such G code approximations can seriously degrade the ability of the controller to accurately realize rapid and smooth tool motions, especially in the high-speed machining of complex shapes.; The restriction to piecewise-linear/circular tool paths stems from the impossibility of exact real-time computation of reference points along general curved paths, traversed according to prescribed federate functions. Many researchers have proposed approximate interpolators for free-form parametric curves. However, only the interpolators for Pythagorean-hodograph (PH) curves offer essentially exact real-time computation of reference points at constant or varying feedrates.; In this thesis, new algorithms for PH curve CNC interpolators, are developed and tested empirically on an open-architecture 3-axis CNC milling machine. The proposed new methods include (i) least-squares approximations of existing G code part programs by PH curves; (ii) physical-constraints feedrate analysis, to determine feedrates and feed accelerations within the torque and power capacity of the drives; (iii) algorithms for general time-dependent feedrates along PH curves; and (iv) variable-feedrate interpolators for general Bézier curves, based on Taylor expansions. These techniques comprise a comprehensive software library that offers powerful motion planning capability, and the accurate and smooth realization of rapid tool motions. The methods have been verified by extensive experiments that compare the relative performance of G code and PH curve interpolators. Adoption of these methods can have a significant impact on the accuracy, reliability, and flexibility of high-speed machining applications.