Intersection of Rays With Parametric Envelope Surfaces Representing Five-Axis NC Milling Tool Swept Volumes

Abstract

Abstract A technique based on the theory of envelopes is presented to formulate a parametric representation of the surfaces swept by an axis-symmetric convex solid under general rigid body motion. The resulting swept surfaces are used to build a complete and precise swept volume model of the moving solid. Finally, an algorithm for finding the intersection of a ray with a swept volume is presented. The algorithm is sufficiently general to be useful in a variety of applications, including robotic path planning, design of mechanisms, and the simulation and verification of numerically controlled (NC) milling programs. Several examples of the algorithm are presented demonstrating ray intersections with swept volumes generated by a general seven-parameter NC milling tool model undergoing typical five-axis motion.