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The involute gear profile, sometimes credited to Leonhard Euler, [1] was a fundamental advance in machine design, since unlike with other gear systems, the tooth profile of an involute gear depends only on the number of teeth on the gear, pressure angle, and pitch. That is, a gear's profile does not depend on the gear it mates with.
Profile of a spur gear Notation and numbering for an external gear Notation and numbering for an internal gear. The tooth surface (flank) forms the side of a gear tooth. [1] It is convenient to choose one face of the gear as the reference face and to mark it with the letter “I”. The other non-reference face might be termed face “II”.
The involute gear system maintaining these conditions follows the fundamental law of gearing: the ratio of angular velocities between the two gears must remain constant throughout. With teeth of other shapes, the relative speeds and forces rise and fall as successive teeth engage, resulting in vibration, noise, and excessive wear.
A line drawing of a spur gear with an involute profile. This was drawn in Solid Edge and Inkscape using Unwin's Construction. The pitch diameter is 12mm and there are 18 teeth, giving a module of 2/3. Date: 25 August 2007: Source: Self-made
In involute gears, the tooth profile is generated by the involute of the base circle. The radius of the base circle is somewhat smaller than that of the pitch circle Base pitch, normal pitch, p b In involute gears, distance from one face of a tooth to the corresponding face of an adjacent tooth on the same gear, measured along the base circle
Involute spline where the sides of the equally spaced grooves are involute, as with an involute gear, but not as tall. The curves increase strength by decreasing stress concentrations. Crowned splines where the sides of the equally spaced grooves are usually involute, but the male teeth are modified to allow for misalignment. Serrations
Illustrations by the Renaissance scientist Georgius Agricola show gear trains with cylindrical teeth. The implementation of the involute tooth yielded a standard gear design that provides a constant speed ratio. Some important features of gears and gear trains are: The ratio of the pitch circles of mating gears defines the speed ratio and the ...
The same involute gear may be used under conditions that change its operating pitch diameter and pressure angle. Unless there is a good reason for doing otherwise, it is practical to consider that the pitch and the profile angle of a single gear correspond to the pitch and the profile angle of the hob or cutter used to generate its teeth.