NDLI: Using an Imaginary Planar Rack Cutter to Create a Spherical Gear Pair with Continue Involute Teeth

Content Provider	Springer Nature Link
Author	Yang, Hsueh Cheng
Copyright Year	2017
Abstract	This paper presents an imaginary planar rack cutter having two parameters of motion to create a spherical gear pair with two degrees of freedom. The working region of the imaginary planar rack cutter is that of symmetrical straight lines. The relationship between the coordinate system of the imaginary planar rack cutter and that of the spherical gear pair having two parameters of motion is illustrated. The two-parameter family of imaginary planar rack cutter surfaces is obtained by using the homogeneous coordinate transformation matrix to transfer the coordinate system of the planar rack cutter to that of the spherical pinion or the spherical gear. Based on the two-parameter enveloping theory, the mathematical models of the spherical gear pair with two degrees of freedom were proposed. The developed mathematical model of the gear pair with two degrees of freedom can be used to analyze undercutting analysis of the imaginary planar rack cutter. Based on the undercutting equation, a minimum number of teeth of the spherical pinion are determined. A line of singular points on the spherical pinion’s teeth are displayed. Results show that a minimum number of teeth of the spherical pinion can be determined in order to avoid undercutting.
Starting Page	4725
Ending Page	4735
Page Count	11
File Format	PDF
ISSN	2193567X
Journal	Arabian Journal for Science and Engineering
Volume Number	42
Issue Number	11
e-ISSN	21914281
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2017-06-15
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Spherical gear Double envelope Degree of freedom Engineering Science, Humanities and Social Sciences, multidisciplinary
Content Type	Text
Resource Type	Article
Subject	Multidisciplinary

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