## 23 August 2017

### Contact ratio of gears

Arc of contact :

The distance travelled by a point on either pitch circle of the two wheels during the period of contact of a pair of teeth is called the arc of contact.

It is the length of the pitch circle traversed by a point on it during the mating of a pair of teeth.

Thus, all teeth laying in between the arc of contact will be meshing with the teeth on the other wheel.

Number of teeth in contact n = Arc of contact / Circular pitch

As we mentioned above the ratio of the arc of contact to the circular pitch is also the contact ratio, the number of teeth is also expressed in terms of contact ratio.

For continuous transmission of motion, at least one tooth of one wheel must be in contact with another tooth of the second wheel. Therefore, n must be greater than unity.

If n lies between 1 and 2, the number of teeth in contact at any time will not be less than one and never more than two.

If n is between 2 and 3, it is never less than pairs of teeth and not more than three pairs, and so on.

If n is 1.6, one pair of teeth are always in contact whereas two pairs of teeth are in contact for 60% of the time.