Geometric conditions for tangent continuity of swept tool envelopes with application to multi-pass flank

By representing the swept envelope of a generic rotary tool as a sphere-swept surface, the necessary and sufficient conditions for tangent continuity of swept tool envelopes are derived. They can be applied to sequentially generate tool paths for radially tangential multi-pass flank milling of complex surfaces. It is shown that the position vector of the tool tip is uniquely determined while the unit vector representing the tool orientation should satisfy a linear constraint. This constraint function can be readily incorporated into the existing tool path optimization models and algorithms for single pass flank milling. An example is given to confirm the validity of the proposed approach for the radially tangential multi-pass five-axis flank milling.