a$)$ Design a typical cotter joint $($with drawing$)$ shown below to transmit a load of $50$ kN in tension or compression. Consider that the rod, socket and cotter are all made of a material with the following

allowable stresses:

Allowable tensile stress $($oy$)=150$ MPa

Allowable crushing stress $($oc$)=110$ MPa

Allowable shear stress $($ty$)=110$ MPa.

b$)$ Also, suggest a unique way to overcome the challenges of using cotter joints in agricultural machinery in cost$-$effective manner on rough terrain jerks and vibration by engaging and disengaging the cotter using the clutch system.

c$)$ A multiple$-$disc wet clutch is to be designed for transmitting a torque of $85$ N$.$m$.$ Space restriction limit the outside disk diameter to $100$ mm$.$ Design values for the molded friction material and steel disks to be used are f$=0\mathrm{.}06($wet$)$ and pmax $=1400$ kPa. Determine appropriate values for the disc inside diameter, the total number of discs, and the clamping force.