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What is involute?

As the name suggests, an involute is a curve where points gradually move away from a fixed point (the center of the base circle).

If you wrap a line around a cylinder, with the end of the line fixed to a pen tip, and let the pen tip pull the line to gradually unwrap the cylinder and leave a trace, then this trace is a involute.

From the trajectory of your drawing, you can see that it is actually the motion trajectory of a point on a straight line as the line rolls along a circle.

In addition, there is also the cycloid, which is the trajectory of a point on a circle as the circle rolls along a straight line or curve.

In practical applications, involutes and cycloids are primarily utilized for designing the shapes of gears and racks. Since gears and racks operate through "rolling", these two curves constitute the most suitable motion trajectories for them

The involute cylindrical gear is a type of gear. When the tooth profile of a gear consists of an involute and a transition line, it is referred to as an involute gear. Due to its numerous advantages, the involute is the most widely used gear curve.

There are various forms of tooth profiles, among which the involute tooth profile is the most common. There are two main types of machining methods commonly used for involute tooth profiles, namely, the forming method and the generating method.