publication . Article . 2017

Automatic fitting of conical envelopes to free-form surfaces for flank CNC machining

Pengbo Bo; Michael Bartoň; Helmut Pottmann;
Open Access English
  • Published: 08 Aug 2017
  • Publisher: Computer Aided Design
  • Country: Spain
Abstract
Abstract We propose a new algorithm to detect patches of free-form surfaces that can be well approximated by envelopes of a rotational cone under a rigid body motion. These conical envelopes are a preferable choice from the manufacturing point of view as they are, by-definition, manufacturable by computer numerically controlled (CNC) machining using the efficient flank (peripheral) method with standard conical tools. Our geometric approach exploits multi-valued vector fields that consist of vectors in which the point-surface distance changes linearly. Integrating such vector fields gives rise to a family of integral curves, and, among them, linear segments that ...
Subjects
free text keywords: 5-axis CNC machining, flank milling, free-form surface, tangential movability, shape manufacturing, Flank, Free form, Mathematics, Machining, Vector field, Geometry, Numerical control, Rigid body, Conical surface
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