Multipatched B-Spline Surfaces and Automatic Rough Cut Path Generation

A method is proposed to generate rough cut machining tool paths for multipatched B-spline surfaces. For a group of B-spline surfaces, smoothly connected, separated or intersecting one another, this method can guarantee generating paths without overcutting any of the surfaces under consideration. The use of multipatched surfaces to construct complex surfaces can greatly increase the controllability and friendliness in the design of surfaces. A method for rough cut planning by convex hull boxing is proposed to generate paths guaranteeing no over-cut. Since no computation for solving nonlinear equation is involved, the rough cut plan is robust and efficient.     

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 efficiency and overcut avoidance are two of the most important factors in NC machining. A method, based on the convex hull property of Bezier curves, is thus developed so that the portion of the boundary defined by a Bezier curve is replaced by parts of its convex hull on the cavity side. Therefore, the new pocket boundary, redefined by only segments of straight lines, can be solved efficiently based on current algorithms without overcuts. Cutting tool paths can be generated for pockets with islands avoiding computation of higher degree curve/curve intersections. Furthermore, recursive subdivisions on Bezier curves are used to improve 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 curve is transformed into piecewise Bezier curves. The tool-path generation for pockets with B-spline curves can thus be solved by reducing the problem to one of pockets with Bezier curves.