Question

A gear train is made up of five spur gears as shown in the figure. Gear 2 is the driver and gear 6 is the driven member. $N_2,N_3,N_4,N_5\text{and}{N}_6$ represent the number of teeth on gears 2, 3, 5, and 6 respectively. The gear(s)which act(s) as idler(s) is/are

• A. only 3
• B. only 4
• C. only 5
• D. Both 3 and 5

Answer 1

The correct option is C only 5

Let y revolution per minute is given to driver gear 2. Gear 3 and gear 4 are compound gears.

Gear	2	3	4	5	6
No.of teeth	$T_2$	$T_3$	$T_4$	$T_5$	$T_6$
Speed	y	$-y\frac{T_2}{T_3}$	$-y\frac{T_2}{T_3}$	$+y\frac{T_2}{T_3}\times \frac{T_4}{T_5}$	$-y\times \frac{T_2}{T_3}.\frac{T_4}{T_5}.\frac{T_5}{T_6}$

Speed ratio $=\frac{\text{Speed of driver}}{\text{Speed of driven}}$
$=\frac{y}{-y\times \frac{T_2}{T_3}\times \frac{T_4}{T_5}\times \frac{T_5}{T_6}}=\frac{-T_3\times T_6}{T_2\times T_4}$

So, if the teeth of gear 5 is not in the speed ratio equation, then gear 5 will act as an idler year.

POINTS TO REMEMBER
Idler gears are given the following advantages:

• The number of intermediate gears controls the direction of rotation of the output gear.
• Idler gears serve the purpose of bridging the gap between the input and output shaft, when this centre distance is large.
• Simple way to judge idler is that gear which is connecting left and right both will be idler.