Problem $9$: A $3-$phase stepping motor is to be used to drive a linear axis for a robot. The motor output shaft will be connected to a screw thread with a screw pitch of $1\mathrm{.}5$ mm $.$ We want to be able to have a spatial control of at least $0\mathrm{.}1$ mm $.$

a$)$ How many poles should the motor have? $(5$ points$)$

b$)$ How many pulses are needed from the controller every second to move the linear axis at a rate of $\backslash (20\backslash$mathrm$\{$~mm$\}/\backslash$mathrm$\{$sec$\}\backslash )?(5$ points$)$