TOOLPATH BASED ON HILBERT CURVE

An algorithm for generating a toolpath for a milling machine is described. The approach to its design was interdisciplinary. The algorithm contains ideas from computer graphics and mathematics, rather than mechanical engineering alone. An artefact described by any set of curved surfaces is carved out of a workpiece in two stages. Horizontal slices are removed to reveal the roughly cut artefact, and a final pass cuts the artefact to within a present tolerance. The toolpath might seem to be needlessly convoluted, but it has substantial advantages over less sophisticated paths. Its local complexity adapts automatically to the local complexity of the artefact, so that more attention is concentrated on those parts of the artefact which require it. At the roughing out stage, the path efficiently skips over completely worked areas without retracing them with each new horizontal slice. The path minimizes the amount of tool movement which does not cut material, and minimizes the number of occasions on which the tool reenters the material. A prototype system has been developed to demonstrate that the new approach is viable.