In current industrial practice, the transformation of Computer-Aided Geometric Design surfaces into Computer Numerical Control (CNC) machine tool axis commands is performed with the aid of Computer-Aided Manufacturing software and a closed CNC machine tool controller. The advent of new technologies such as Open Architecture Control has enabled the rethinking of motion command generation.

This thesis describes a five-axis motion command generation architecture and algorithms in which a parameterized tool-path is interpolated off-line and the inverse kinematics mapping is performed in real-time, on the CNC controller. This architecture eliminates the need for time consuming repost-processing of the tool-path in the event of kinematic changes and additionally introduces the benefits of parametric splines with controlled feedrate.

To deterministically attain a near constant feedrate tool-path, near arc-length parameterized splines are prepared off-line. The C² position spline which is near arclength parameterized improves on the previously reported research. The orientation unit vectors are interpolated with a C² spherical Bézier spline. These two splines are then synchronized by means of a monotonic reparameterization spline. This results in reduced effective feedrate oscillation. The interpolated tool-path and axis commands are demonstrated to be smooth and C² continuous. To cope with actuator saturation, a feedrate interpolation algorithm is developed which ensures C² continuity but allows the feedrate to be adjusted as needed. The developed algorithms were simulated for two tool-paths and two five-axis machines tools. A test part was cut to demonstrate geometric correctness.