Collision-free five-axis milling of twisted ruled surfaces

Ruled surfaces (generated by straight ruling lines) are a special kind of free form surfaces which plays an important role, e.g., in aerodynamic surfaces (rotary engines). They are particularly well suited for five axis milling by the flank milling method. In the case of twisted ruled surfaces, however, the obvious milling method of having the cutter touch these ruling lines along a generator of its own flank leads to collision problems. The nature of these twisted ruled surfaces is analyzed and conditions for their collision free milling by a cylindrical cutter are established. Efficient milling strategies are found.