$-$ A square$-$thread power screw has a major diameter of $32$ mm and a pitch of $4$ mm with double threads. The given data include $\backslash ($ f$=$f$\_\{$c$\}=0\mathrm{.}08\backslash ),\backslash ($ d$\_\{$c$\}=40\backslash$mathrm$\{$~mm$\}\backslash ),$ and $\backslash ($ F$=6\mathrm{.}4\backslash$mathrm$\{$kN$\}\backslash )$ per screw.

$($a$)$ Find the thread depth, thread width, pitch diameter, minor diameter, and lead.

$($b$)$ Find the torque required to raise and lower the load.

$($c$)$ Find the efficiency during lifting the load.

$($d$)$ Find the body stresses, torsional and compressive.

$($e$)$ Find the bearing stress on the first thread.

$($f$)$ Find the thread bending stress at the root of the first thread.

$($g$)$ Determine the von Mises stress at the critical stress element where the root of the first thread interfaces with the screw body.