a$)$ The worktable of a CNC machine tool is driven by a positioning system, which consists of a stepper motor and leadscrew. The leadscrew has $1\mathrm{.}52$ threads$/$cm and is coupled directly to the motor shaft $($gear ratio $\backslash (=1$: $1\backslash )).$ The table has been programmed to move a distance of $30$ cm at a feed rate $\backslash (=0\mathrm{.}35\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$min$\}\backslash ).$ The stepper motor has $45$ step angles.

$[6$ Marks$]$

i$)$ How many pulses are required by the control system to move the programmed distance?

ii$)$ Rotational speed of the motor to make the move

iii$)$ Pulse rate to achieve the desired table speed?