Subject: Kinematics of Machinery

Topic: Gears and Gear Trains

Difficulty: Medium

Fig. Shows a pinion with centre $O_{1}$ in mesh with wheel or gear with centre $O_{2}$, MN is common tangent to the base circles and KL is the path of contact between the two mating teeth.

A little consideration will show, that if the radius of the addendum circle of pinion is increased to $O_{1}$N , the point of contact L will move from L to N. when this radius is further increased, the point of contact L will be on the inside of the base circle of wheel and not on the involute profile of tooth on wheel. The tip of a tooth on the pinion will then undercut the tooth on the wheel at the root and remove part of the involute profile of tooth on the wheel. this effect is known as interference, and occurs when the teeth are being cut, in brief, the phenomenon when the tip of tooth undercuts the root of its mating gear is known as interference.

Similarly, if the radius of the addendum circle of the wheel increase beyond $O_{2}$M, then the tip of the tooth on a wheel will cause interference with the tooth on the pinion. The points M and N are called interference points, obviously, interference may be avoided if the path of contact does not extend beyond interference points. The limiting value of the radius of the addendum circle of the pinion is *$O_{1}$N and of the wheel is $O_{2}$M.

From the above discussion, we conclude that the interference may only be avoided if the point of contact between the two teeth is always on the involute profile of the teeth. In other words, interference may only be prevented, if the addendum circle of the two mating gears cut the common tangent to the base circles between the points of tangency.