(^708) „„„„„ A Textbook of Engineering Mechanics
Now assume* T 4 = 8 and T 3 = 4 T 4 = 4 × 8 = 32
Substituting the values of T 3 and T 4 in equation (i),
T 1 + T 2 = 32 + 8 = 40
∴ T 1 = 40 – T 2 ...(iii)
Now substituting the value of T 3 and T 4 in equation (ii),
T 1 × 32 = 12 × T 2 × 8 = 96 T 2 ...(iv)
∴ T 1 =3 T 2
Substituting this value of T 1 in equation (iii), 3T 2 = 40 – T 2
∴ T 2 =
40
10
4

Now substituting this value of T 2 in equation (iii),
T 1 = 40 – 10 = 30
∴ T 1 = 30; T 2 = 10; T 3 = 32; T 4 = 8 Ans.
Since the number of teeth are within the given limit (of 40), therefore the arrangement of
the teeth is correct.
34.14.EPICYCLIC GEAR TRAIN
In the previous articles, we have discussed the cases of
gear trains in which each wheel is free to revolve about it own
axis. But sometimes, one of the wheel is fixed and the other makes
revolution about the fixed wheel with the help of an arm. Such a
system is called an epicyclic gear train.
In Fig. 34.12 is shown wheel A and an arm C having a
common axis at O 1 , about which they can rotate. The wheel B
meshes with the wheel A and has its own axis on the arm at O 2.
Now, if the arm C is considered to be fixed, the wheels A and B
form a simple gear train. But, if the wheel A is fixed and the arm
is rotated, the system forms an epicyclic gear train.
34.15.VELOCITY RATIO OF AN EPICYCLIC GEAR
TRAIN
The following two methods may be used for finding out the velocity ratio of an epicyclic
gear train :

1. Tabular method, and 2. Algebraic method.


2. Tabular method
   Let TA= No. of teeth on wheel A, and
   TB= No. of teeth on wheel B.

* This assumption is by trial and error. If we assume the value of T 4 as 1, 2 and 3, the no. of teeth on the

other wheels obtained are not complete integers. If we assume T 4 as 4, we get T 1 = 15, T 2 = 5, T 3 = 16, and

T 4 = 4. The no. of teeth on each wheel is too less for practical purposes. Similarly, if we assume the values

of T 4 as 5, 6 and 7, the no. of teeth on the other wheels obtained are not complete integers.

It will be also seen that if we assume the values of T 4 as 9, 10 and 11, the no. of teeth on the other wheels

are not complete integers. If we assume T 4 as 12, we get T 1 = 45, T 2 = 15, T 3 = 48, T 4 = 12. This is contrary

to the given condition (i.e., no wheel should have more than 40 teeth).

Fig. 34.12. Epicyclic gear train.