## Number of Teeth on the Smaller or Driving Sprocket or Pinion

**Introduction:**

In order to have smooth operation, the minimum number of teeth on the smaller sprocket or pinion may be taken as 17 for moderate speeds and 21 for high speeds.

**Number of teeth on the smaller sprocket:**

**Fig: Number of teeth on the smaller sprocket**

- Consider an arrangement of a chain drive in which the smaller or driving sprocket has only four teeth, as shown in Fig (a).

- Let the sprocket rotates anticlockwise at a constant speed of N r.p.m. The chain link AB is at a distance of d / 2 from the centre of the sprocket and its linear speed is given by

where d = Pitch circle diameter of the smaller or driving sprocket in metres.

- When the sprocket rotates through an angle θ/2, the link AB occupies the position as shown in Fig. (b).
- From the figure, we see that the link is now at a distance of from the centre of the sprocket and its linear velocity is given by

- The linear velocity of the sprocket is not uniform but varies from maximum to minimum during every cycle of tooth engagement.

- This results in fluctuations in chain transmission and may be minimised by reducing the angle θ or by increasing the number of teeth on the sprocket.

- It has been observed that for a sprocket having 11 teeth, the variation of speed is 4 percent and for the sprockets having 17 teeth and 24 teeth, the variation of speed is 1.6 percent and 1 percent respectively.

In order to have smooth operation, the minimum number of teeth on the smaller sprocket or pinion may be taken as 17 for moderate speeds and 21 for high speeds. The following table shows the number of teeth on a smaller sprocket for different velocity ratios.

**Note:** The number of teeth on the smaller sprocket plays an important role in deciding the performance of a chain drive. A small number of teeth tends to make the drive noisy. A large number of teeth makes chain pitch smaller which is favourable for keeping the drive silent and reducing shock, centrifugal force and friction force.