Velocity ratio=1/3, module=4 mm, pressure angle=20 deg, Centre distance=200 mm. Determine the number of teeth and the base circle radius of the gear wheel.

Subject: Kinematics of Machinery

Topic: Gears and Gear Trains

Difficulty: Medium

​$V_{R} $= 1/3, $\phi$ = 20$^{\circ}$, m= 4 mm, C= 200 mm,

(i) $V_{R} = \frac{ N_{1}}{N_{2} }$ = 1/3 = $\frac{ T_{1}}{T_{2} }$ or $T_{2}$ = 3$ T_{2}$

And C=$\frac{(d_{1}+d_{2})}{2} = m\frac{(T_{1}+T_{2})}{2}$

Or $200 =4\frac{(T_{1}+3T_{1})}{2}=8T_{1}$

Or $T_{1}$ = 25, $T_{2} $ =25×3 =75

No. of teeth on gear wheel =75

(ii) $d_{2} = mT_{2}$=4×75 = 300 mm.

base circle radius $d_{b2} =(\frac {d_{2}}{2})\cos\phi $

= (300/2)cos 20$^{\circ}$

=141 mm.