Editing Involute (section)

==Application==
The most common profiles of modern [[gear]] teeth are involutes of a circle. In an [[involute gear]] system, the teeth of two meshing gears contact at a single instantaneous point that follows along a single straight line of action. The forces the contacting teeth exert on each other also follow this line and are normal to the teeth. 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. For this reason, nearly all modern planar gear systems are either involute or the related [[cycloidal gear]] system.<ref>V. G. A. Goss (2013) "Application of analytical geometry to the shape of gear teeth", [[Resonance (journal)|Resonance]] 18(9): 817 to 31 [https://link.springer.com/article/10.1007%2Fs12045-013-0106-3 Springerlink] (subscription required).</ref>

[[Image:Two moving spirals scroll pump.gif|frame|Mechanism of a scroll compressor]]
The involute of a circle is also an important shape in [[gas compressor|gas compressing]], as a [[scroll compressor]] can be built based on this shape. Scroll compressors make less sound than conventional compressors and have proven to be quite [[mechanical efficiency|efficient]].

The [[High Flux Isotope Reactor]] uses involute-shaped fuel elements, since these allow a constant-width channel between them for coolant.