Oblique projection approach to generating trajectory along arbitrary direction on NURBS surfaces

Abstract

Aiming at geometric rules of trajectory generation, the oblique projection approach is proposed to generating trajectories along arbitrary direction to improve reach-ability and provide more choices for 5-axis machining. First of all, a middle plane is constructed with the normal direction at the center point and passing through the center point of the encapsulating box. Secondly, a set of parallel and equidistant lines in the middle plane is constructed as the source object of oblique projection, and the inclination angles of the line set are uniformed as any value in the range of 0 to 2π. Thirdly, oblique projections are employed to produce projection trajectories on the machined surface. Finally, a user function APathGenerator V1.0 is developed in UG NX. The algorithm is robust and provides a feasible way to control direction angle and trajectory gap for the 5-axis machining of any smooth surfaces whether concave, convex or mixed.