Formulating the swept envelope of rotary cutter undergoing general spatial motion for multi-axis NC machining

Based on the tangency condition in envelope theory and the body velocity representation in spatial kinematics, a closed-form solution of the swept envelope of a general rotary cutter moving along a general tool path defined in the NC programs is derived. No additional moving frames or local frames are required, and the computational formulas are independent of the types of the machines. The results can be applied to NC machining simulation, tool path optimization, and CAD/CAM of spatial cams.