(^702) „„„„„ A Textbook of Engineering Mechanics
Multiplying equation (ii) by (i),
32
21
N N
NN
× =^21
32
TT
TT
×
or
3
1
N
N

1
3
T
T
∴ Speed of the follower
Speed of the driver

No. of teeth on the driver
No. of teeth on the follower
Similarly, it can be proved that the above equation also holds good, even if there are any
number of intermediate wheels. It is thus obvious, that the velocity ratio, in a simple train of wheels,
is independent of the intermediate wheels. These intermediate wheels are also called idle wheels, as
they do not effect the velocity ratio of the system.
34.11. COMPOUND TRAIN OF WHEELS
We have seen in Art. 34.10 that the idle wheels, in a simple train of wheels, do not affect the
velocity ratio of the system. But these wheels are useful in bridging over the space between the
driver and the follower.
But whenever the distance between the driver and follower has to be bridged over by interme-
diate wheels and at the same time a great (or much less) velocity ratio is required then the advantage
of intermediate wheels in intensified by providing compound wheels on intermediate shafts. In this
case, each intermediate shaft has two wheels rigidly fixed to it, so that they may have the same
speed. One of these two wheels gears with the driver and the other with the follower attached to the
next shaft as shown in Fig. 34.8.
Fig. 34.8. Compound train of wheels.
Let N 1 = Speed of the driver 1
T 1 = No. of teeth on the driver 1,
Similarly N 2 , N 3 , ...N 6 = Speed of the respective wheels
T 2 , T 3 , ...T 6 = No. of teeth on the respective wheels.