10. Generation of Enveloping Surfaces: Special Cases

  1. Stephen P. Radzevich

Published Online: 21 JAN 2013

DOI: 10.1002/9781118522707.ch10

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) Generation of Enveloping Surfaces: Special Cases, in Geometry of Surfaces: A Practical Guide for Mechanical Engineers, John Wiley & Sons Ltd, Oxford, UK. doi: 10.1002/9781118522707.ch10

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:

  • enveloping surfaces;
  • Olivier principles;
  • reversibly enveloping part surfaces

Summary

An enveloping surface is generated by a smooth regular part surface which is performing a certain motion in relation to a reference system the generated part surface will be associated with. This chapter presents a few special cases of enveloping. It begins with consideration of one special case of enveloping, namely the case where the envelope allows for sliding over itself. The chapter then discusses the generation of reversibly enveloping surfaces following an example of generation of tooth flanks in geometrically accurate crossed-axis gearing (CA gearing) having line contact between the interacting tooth flanks. The Olivier principles for generation of enveloping surfaces in general cases are either incorrect, or they are useless when valid. The application of Olivier principles is valid in degenerate cases, when one of the part surfaces allows for sliding over itself in the direction of the enveloping motion.