Two stepping motors $($shown in figure below$)$ are used in open loop system to drive the leadscrews for x $-$y positioning machine. The range of each axis is $200$ mm $.$ The shaft of motors are connected directly to the lead screws. The pitch of each lead screw is $2$ mm $,$ and the number of step angles on the stepping motor is $120.$ A metallic piece is fixed on the table for a machining process.

a$)$ How many pulses are required of each stepping motor to move the table a distance of $75$ mm in x direction?

b$)$ What are the required pulse rate and corresponding rotational speeds of each stepping motor in order to drive the table at $\backslash (250\backslash$mathrm$\{$~mm$\}/\backslash$mathrm$\{$min$\}\backslash )$ in a straight line from point $(\backslash ($ x$=100,$ y$=0\backslash ))$ to point $(\backslash ($ x$=130\backslash$mathrm$\{$~mm$\},\backslash$mathrm$\{$y$\}=180\backslash$mathrm$\{$~mm$\}\backslash ))?$

Motor A $($y axis$)$

Motor B $($X axis$)$