Problem $2(7$ points$)($Q$0$: $3100\%)$

It is desired to design a gear box as shown in the figure. Following information must be

followed:

Gears type: Spur

Smallest possible size gears

To avoid interference, number of teeth on

the smallest gear should not be less than $14$

Maintain exact speed ratio

Input and output shafts are collinear

Input speed $=3000rpm$

Output speed $=150rpm$

Module $=2\mathrm{.}5mm$

Pressure angle $=20$

Power $=7\mathrm{.}5kW$

Analyze the gear box and:

a$)$ Calculate the number of teeth of all gears.

b$)$ Determine the shafts center distance $c_1$ and $c_2($in mm $)$

c$)$ Draw FBD showing all forces on gear $3$ and $4$ with the countershaft at A and $B.$

d$)$ Calculate forces exerted by gear $2$ on gear $3$ and gear $5$ on gear $4.$

e$)$ Calculate the countershaft forces at A and $B.$

f$)$ What is the output torque of the shaft attached to gear $5?$ Neglect frictional

losses.