# Gears Don't Slide, They Roll

## Rolling is Efficient and has very low friction

If you mesh two gears together and rotate one - whether it's a spur gear, helical gear, or any other kind of gear - the two contacting surfaces will roll off each other, not slide. The difference may seem semantic, just a choice of words with no real consequence, but it's important to consider this all the way from gear design to gear production. This difference has a huge impact on the life and performance of the gear, and it all comes down to friction.

When one surface slides against another, like a pencil across a piece of paper, a tiny amount of material is worn off and transferred from one surface to the other. While this is all part of the design for a pencil, so the graphite is transferred to the page and marks are visible, it’s not so desirable for gears.

Gears need to work for many millions of revolutions and can’t be resharpened like a pencil. So how do gears work? Gear teeth are specifically designed with an involute profile shape so that they don’t slip or slide across each other, but roll.

#### Imagine you're rolling down a hill...

To help visualize the difference we can imagine a basketball rolling along a flat pavement. If we think of one bump on the basketball and its journey through a single rotation, we see that it starts at the top of the ball, comes down, comes in contact with the ground, then goes back to the top, and repeats the cycle. If we could zoom in to the exact point where the bump on the ball meets the ground we’d see that each spot is only in contact with the ground for one instant.

As soon as the bump is at the very bottom, it’s already started heading up and away; the bump never has time to slide or drag along the surface. In the real world the ball is not a perfect sphere, and the ground is not a perfectly flat plate, but the underlying physics still stand (there are also intermolecular forces that attract and repel the two objects but we don’t need to talk about that yet).

Arrows show the direction and velocity of each point on a circle as it rotates on the ground [1]

Gears behave the same way, as soon as the gear teeth mesh and one gear comes in contact with the other, those points become almost synced together and both move at the same time. The points don’t slip or drag, but rather come together then come part, like the bump on a basketball or someone tapping a pencil instead of drawing a line. As a result, the gears have a smooth, continuous motion that minimizes wear.

Animation of two spur gears rotating, at each instant only one point is in contact [2]

This unique and universal attribute has only been made possible through the clever utilization of the involute profile, also called the evolvent, in the gear teeth. This profile, formed by wrapping an imaginary string around a circle and “unwinding” while holding taut, has been investigated since Girolamo Cardano in 1545 and Christiaan Huygens in 1656. A proper mathematical derivation of the involute took another 120 years and the interest of Swiss mathematician Leonhard Euler in 1781. [3] Anymore, except for clocks, nearly every gear in existence uses the involute profile.

If you want to transmit power, the involute is the only way to roll.

© Evolvent Design, 2020

[1] Algarabia, Rodadura. Retrieved from Wikimedia, https://commons.wikimedia.org/wiki/File:Moglfm2207_rodadura.jpg

[2] Rocchini, Claudio. Involute Wheel. Retrieved from Wikimedia: https://commons.wikimedia.org/wiki/File:Involute_wheel.gif

[3] Radzevich, Stephen P. Gear Cutting Tools: Fundamentals of Design and Computation. Taylor & Francis Inc. ISBN: 9781439819678