TOOL-PATH GENERATION FOR POCKETS WITH FREEFORM CURVES USING BEZIER CONVEX HULLS

The objective of this paper is to generate tool paths for pockets with freeform curves, i.e. Bezier curves or B-spline curves. Time efficien cy and overcut avoidance are two of the most important factors in NC m achining. A method based on the convex hull property of Bezier curves, is thus developed so that the portion of the boundary defined by a Be zier curve is replaced by parts of its convex hull on the cavity side. Therefore, the new pocket boundary, redefined by only segments of str aight lines, can be solved efficiently based on current algorithms wit hout overcuts. Cutting tool paths can be generated for pockets with is lands avoiding computation of higher degree curve/curve intersections. Furthermore, recursive subdivisions on Bezier curves are used to impr ove the accuracy of the cut with an allowance criterion based on sizes of convex hulls. The portion of the boundary defined by a B-Spline cu rve is transformed into piecewise Bezier curves. The tool-path generat ion for pockets with B-spline curves can thus be solved by reducing th e problem to one of pockets with Bezier curves.