Verification of NC machining processes using swept volumes

A numerically controlled (NC) machining verification method is developed based on a formulation for delineating the volume generated by the motion of a cutting tool on the workpiece (stock). The motion of a cutting tool is modeled as a surface undergoing a sweep operation along another geometric entity where machine tool trajectory includes translational and rotational movements. A rank-deficiency condition is imposed on the Jacobian of the sweep to determine the singular surfaces. Singular entities are then intersected to determine sub-entities that may exist on the boundary of the volume. A perturbation method is used to identify the boundary envelope of the material volume to be removed. Numerical examples