Continuous path verification in multi-axis NC-machining

Ron Wein*, Gershon Elber, Oleg Ilushin, Dan Halperin

*Corresponding author for this work

Research output: Contribution to conferencePaperpeer-review


We introduce a new approach to the problem of collision detection between a rotating milling-cutter of an NC-machine and a model of a solid workpiece, as the rotating cutter continuously moves near the workpiece. Having five degrees of motion freedom, this problem is hard to solve exactly and we approximate the motion of the tool by a sequence of sub-paths of pure translations interleaved with pure rotations. The detection problem along each sub-path is then solved by using radial projection of the obstacles (the workpiece and other parts of the NC-machine) around the tool axis to obtain a collection of critical surface patches in ℝ3, and by examining planar silhouettes of these surface patches. We thus reduce the problem to successive computations of the lower envelope of a set of planar curves - this reduction is exact, and incurs no loss of accuracy. We have implemented our algorithm in the IRIT environment for solid modeling, using an extension package of the CGAL library for computing envelopes. The algorithm, combined with the proper data structures, solves the collision detection problem in a robust manner, yet it yields efficient computation times as our experiments show. Our approach produces exact results in case of purely translational motion, and provides guaranteed (and good) approximation bounds in case the motion includes rotation.

Original languageEnglish
Number of pages10
StatePublished - 2004
EventProceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04) - Brooklyn, NY, United States
Duration: 9 Jun 200411 Jun 2004


ConferenceProceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04)
Country/TerritoryUnited States
CityBrooklyn, NY


  • Lower envelopes
  • NC-machining
  • Path verification


Dive into the research topics of 'Continuous path verification in multi-axis NC-machining'. Together they form a unique fingerprint.

Cite this