Generation of Enveloping Surfaces: Special Cases

  • Stephen P. RadzevichEmail author


In this chapter of the book, special cases of generation of enveloping surfaces is disclosed. For this purpose, a concept of reversibly-enveloping surfaces is introduced. For generation of reversibly-enveloping surfaces a novel method is proposed. This method is illustrated by an example of generation of reversibly-enveloping surfaces in case tooth flanks for geometrically accurate (ideal or perfect) crossed-axis gear pairs. The performed analysis makes it possible a conclusion that two Olivier principles of generation of enveloping surfaces: (a) in general case are not valid, and (b) in a degenerate case these two principles are useless. Ultimately, there is no sense to apply Olivier principles for the purpose of generation of reversibly-enveloping smooth regular part surfaces. Part surfaces those allow for sliding over themselves are considered as a particular degenerated case of enveloping surfaces.


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Southfield Innovation CenterEaton CorporationSouthfieldUSA

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