Variational gridding algorithms to optimize a tool-path of a five-axis milling machine

We present a new application of variational grid generation techniques to optimize the tool-path of an industrial milling robot. Our approach is based on a global approximation of the required surface by a virtual surface composed from tool trajectories. The procedure combines inverse kinematics techniques and a variational gridding method endowed with constraints related to the required scallop height. The proposed technique allows one to generate a tool-path for workpieces with complex geometries comprising "islands" and/or boundaries with sharp edges requiring a combined "spiral-zigzag" pattern. Finally, our proposed technique provides a significant increase in the accuracy of milling.