Standard Sprocket and Polygonal Action

The sprocket with number of teeth, with a tooth pitch, , rotates at a constant speed, (RPM).

In the top image, the chain is tangent with the Pitch-Circle of the Sprocket.  However, when the sprocket rotates by radians, the chain link is nearer to the center of the sprocket. Therefore, as the chain moves up and down, the effective radius of the sprocket changes to give a uneven, non-constant chain velocity.

The linear speed of the chain is maximum in the top image.

The linear speed of the chain is a minimum in the bottom image.

The e Linear-Acceleration of the chain is discontinuous at the instant the chain starts to move upwards.

Polygonal-Action creates two(2) problems

•Velocity Variation in the Chain

In the general case, if a Driving Sprocket is rotating at constant Angular Velocity, the chain does not move at constant Linear Velocity.

The ratio of Maximum and Minimum Velocity increases as you reduce the number-of-teeth on the drive sprocket.

•Tension Variation in the Chain.

As a chain link engages with a tooth, the chain accelerates, and thus there is a tension variation.

Also, the pitch of the chain link is not constant.

Usually, it is recommended that you use more than 17 teeth on a standard sprocket. Bicycle sprockets have fewer, but the derailleur compensates for the velocity and tension-variations.