Precise gouging-free tool orientations for 5-axis CNC machining

Yong-Joon Kim, Gershon Elber, Michael Barton, Helmut Pottmann, Michael Bartoň

Research output: Contribution to journalArticlepeer-review


We present a precise approach to the generation of optimized collision-free and gouging-free tool paths for 5-axis CNC machining of freeform NURBS surfaces using flat-end and rounded-end (bull nose) tools having cylindrical shank. To achieve high approximation quality, we employ analysis of hyper-osculating circles (HOCs) (Wang et al., 1993a,b), that have third order contact with the target surface, and lead to a locally collision-free configuration between the tool and the target surface. At locations where an HOC is not possible, we aim at a double tangential contact among the tool and the target surface, and use it as a bridge between the feasible HOC tool paths. We formulate all such possible two-contact configurations as systems of algebraic constraints and solve them. For all feasible HOCs and two-contact configurations, we perform a global optimization to find the tool path that maximizes the approximation quality of the machining, while being gouge-free and possibly satisfying constraints on the tool tilt and the tool acceleration. We demonstrate the effectiveness of our approach via several experimental results.

Original languageEnglish
Pages (from-to)220-229
Number of pages10
JournalComputer-Aided Design
StatePublished - Jan 2015


  • Collision and gouging detection
  • Curvature matching
  • Free-form surfaces
  • Hyper-osculating circles
  • Third order approximation

All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Industrial and Manufacturing Engineering


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