The paper presents a geometric investigation of collision-free 3-axis milling of surfaces. We consider surfaces with a global shape condition: they shall be interpretable as the graphs of bivariate functions or shall be star-shaped with respect to a point. If those surfaces satisfy a local millability criterion involving curvature information, it is proved that this implies globally gouge-free milling. The proofs are based on general offset surfaces. The results can be applied to tool-motion planning and the computation of optimal cutter shapes.
Geometric Criteria for Gouge-Free Three-Axis Milling of Sculptured Surfaces
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Pottmann, H., Wallner, J., Glaeser, G., and Ravani, B. (June 1, 1999). "Geometric Criteria for Gouge-Free Three-Axis Milling of Sculptured Surfaces." ASME. J. Mech. Des. June 1999; 121(2): 241–248. https://doi.org/10.1115/1.2829450
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