2. On the Possibility of Classification of Part Surfaces

  1. Stephen P. Radzevich

Published Online: 21 JAN 2013

DOI: 10.1002/9781118522707.ch2

Geometry of Surfaces: A Practical Guide for Mechanical Engineers

Geometry of Surfaces: A Practical Guide for Mechanical Engineers

How to Cite

Radzevich, S. P. (2013) On the Possibility of Classification of Part Surfaces, in Geometry of Surfaces: A Practical Guide for Mechanical Engineers, John Wiley & Sons Ltd, Oxford, UK. doi: 10.1002/9781118522707.ch2

Author Information

  1. Principal Gear Engineer, USA

Publication History

  1. Published Online: 21 JAN 2013
  2. Published Print: 4 JAN 2013

ISBN Information

Print ISBN: 9781118520314

Online ISBN: 9781118522707

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Keywords:

  • circular diagrams;
  • curvature indicatrix;
  • Dupin indicatrix;
  • local surface patch;
  • planar characteristic images;
  • scientific classification;
  • sculptured part surface geometry

Summary

This chapter presents a discussion on the possibility of classification of part surfaces used in present-day engineering practice. It begins with the analysis of the possibility of developing a scientific classification of surfaces from the consideration of sculptured part surfaces. The classification includes ten kinds of local surface patches. For a more accurate analytical description of the geometry of a smooth regular part surface, the second-order parameters need to be considered. The Dupin indicatrix of a smooth regular part surface is a planar characteristic curve of the second order. In differential geometry of surfaces, Dupin indicatrices of the following five kinds are distinguished: elliptic, umbilic, parabolic, hyperbolic, and minimal. Another possibility for analytical description of the local geometry of a smooth regular part surface is associated with the so-called circular diagrams at a point within the surface patch.