Question

A compound gear train with gears P, Q, R, and S has a number of teeth 20, 40, 15 and 20 respectively. Gears Q and R are mounted on the same shaft as shown in the figure below. The diameter of the gear Q is twice that of the gear R. IF the module of the gear R is 2mm, the centre distance in mm between gears P and S is

• A. 40
• B. 80
• C. 120
• D. 160

Answer 1

The correct option is B 80


Centre distance between P and S.

$=(\text{Radius}{)}_p+(\text{Radius}{)}_Q+(\text{Radius}{)}_R+(\text{Radius}{)}_S$

$\Rightarrow D_Q=2\times D_R$

$M_R=2\text{mm}$

$\therefore M_R=\frac{D_R}{T_R}$

$\therefore D_R=T\times M_R$

$=15\times 2=30\text{mm}$

$D_Q=2\times 30=60\text{mm}$

$\text{and}{T}_Q=40$

$\therefore M_Q=\frac{D_Q}{T_Q}=\frac{60}{40}=1.5$

Since Q meshes with the P module of gear Q is equal to the module of gear P.

$D_P=M_P\times T_P=1.5\times 20=30.0\text{mm}$

Since S meshes with R module of S and R will be same

$\therefore$ $\text{Module}S=2\text{mm}$

$D_s=M_s\times T_s=2\times 20=40\text{mm}$

$\therefore \text{Centre distance}=15+30+15+20$

$=80\text{mm}$