the worktable of a CNC machine tool is driven by a Positioning system which consists of a Stepper motor and lead screw. The lead screw has $1\mathrm{.}52$ threads$/$cm and is coupled directly to the motor shaft $($gear ratio$=1$:$1).$ The table has been programmed to move a distance of $30$ Cm at afeed rate$=0-35$ m$/$min$.$ the stepper

motor has $45$ step angles $6$ marks

$(1)$ 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 spool