Towards efficient 5-axis flank CNC machining of free-form surfaces via fitting envelopes of surfaces of revolution

Pengbo Bo, Michael Barton*, Denys Plakhotnik, Helmut Pottmann

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

60 Scopus citations


We introduce a new method that approximates free-form surfaces by envelopes of one-parameter motions of surfaces of revolution. In the context of 5-axis computer numerically controlled (CNC) machining, we propose a flank machining methodology which is a preferable scallop-free scenario when the milling tool and the machined free-form surface meet tangentially along a smooth curve. We seek both an optimal shape of the milling tool as well as its optimal path in 3D space and propose an optimization based framework where these entities are the unknowns. We propose two initialization strategies where the first one requires a user's intervention only by setting the initial position of the milling tool while the second one enables to prescribe a preferable tool-path. We present several examples showing that the proposed method recovers exact envelopes, including semi-envelopes and incomplete data, and for general free-form objects it detects envelope sub-patches.

Original languageEnglish (US)
Pages (from-to)1-11
Number of pages11
JournalCAD Computer Aided Design
StatePublished - Oct 1 2016


  • 5-axis CNC machining
  • Flank milling
  • Free-form surface
  • Shape manufacturing
  • Tangential movability

ASJC Scopus subject areas

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

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