Figure shows a $450-mm$ inner diameter brake drum with four internally expanding shoes. Each of the hinge pins A and $B$ supports a pair of shoes. The actuating mechanism is a linkage which produces the same actuating force W on each shoe as shown. The lining material is to be sintered metal. The face width of each shoe is $70$ mm $.$ Using friction coefficient $=0\mathrm{.}3$ and maximum contact pressure of $1\mathrm{.}25$ MPa $,$ with neat free body diagrams,

$($a$)$ Which shoes are self$-$energizing, and which are de$-$energizing?

$($b$)$ What are the actuating forces and total torque for the four shoes?

$($d$)$ What is the maximum pressure on the de$-$energizing shoes?

$($e$)$ What are the hinge pin reactions as well as resultant reaction?