A gear box is to be designed to reduce the input speed of $4800$rpm to $30$rpm$.$ Available modules are $5$ mm$\mathrm{.}8$ mm and $10$ mm and available pressure angles are $20$

$$

and $25$

$$

$.$ The gear box should be as small in size as possible, without having the issue of interference. a$)$ Clearly stating reasons, select appropriate module and pressure angle and design the gear box $[7]$ b$)$ Neatly sketch the drive $[2]$ c$)$ Find the contact ratio between the gears in the stage that has the largest reduction ratio $[3]$ Z$=$

$($r

p

$$

$+$a

p

$$

$)$

$2$

$($r

p

$$

cos$)$

$2$

$$

$+$

$($r

g

$$

$+$a

g

$$

$)$

$2$

$($r

g

$$

cos$)$

$2$

$$

$$Csin$$