Editing Involute gear (section)

==Advantages and design==
The involute gear profile, sometimes credited to [[Leonhard Euler]],<ref>{{Cite web |title=MOZIMTEC |url=http://www.mozimtec.de/a1.html |access-date=2024-01-03 |website=www.mozimtec.de}}</ref> 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. Thus, n and m tooth involute [[spur gear]]s with a given pressure angle and pitch will mate correctly, independently of n and m. This dramatically reduces the number of shapes of gears that need to be manufactured and kept in inventory.

In involute gear design, contact between a pair of gear teeth occurs at a single instantaneous point (see figure at right) where two involutes of the same spiral hand meet. Contact on the other side of the teeth is where both involutes are of the other spiral hand.  Rotation of the gears causes the location of this contact point to move across the respective tooth surfaces. The tangent at any point of the curve is perpendicular to the generating line irrespective of the mounting distance of the gears. Thus the line of the force follows the generating line, and is thus tangent to the two base circles, and is known as the [[gear#Line of Action|line of action]] (also called ''pressure line'' or ''line of contact''). When this is true, the gears obey the ''fundamental law of gearing'':<ref>Norton, R.L., 2006, ''Machine Design: An Integrated Approach'', 3rd Ed, Pearson/Prentice-Hall, {{ISBN|0-13-148190-8}}</ref>
<blockquote>''The angular velocity ratio between two gears of a gearset must remain constant throughout the mesh.''</blockquote>
This property is required for smooth transmission of power with minimal speed or torque variations as pairs of teeth go into or come out of mesh, but is not required for low-speed gearing.