Formulating swept profiles for five-axis tool motions

This paper presents a methodology and algorithms for analytically formulating the swept profiles and generating topological valid swept volume of five-axis tool motions for NC simulation. For the problem of NC simulation, by using envelope theory and swept volume generation, a canonical mathematic description to formulate the swept profiles is addressed. By introducing rigid body motion theory to define a moving frame, the closed-form solutions of swept profiles for a generalized cutter geometry are obtained. For the case of common milling tools such as fillet-end, ball-end and flat-end, which are derived from the generalized cutter definition, the swept profiles are also formulated. Considering the complexity of five-axis tool motions, an analysis of the solutions and a determination of special cases are necessary to effectively enhance the robustness of the derived formulations and the proposed algorithms. The developed method can be used for NC verification and NC path optimisation, and can also be extended to the robot trajectory planning.