The arm of a robot is carrying a load of $20$ Kg as shown in Figure Q$1$c$.$ Itis moved by a d$.$c$.$ motor of maximum speed $1200$ rpm acting through a$60$:$1$ reduction gearbox.The motor supplies a maximum torque of $2\mathrm{.}0$ Nm and has a moment ofinertia of $0\mathrm{.}06$ Kg m$2.$ The $20$ Kg load is at an effective distance of $0\mathrm{.}75$ mfrom the pivot of the arm. The arm has a moment of inertia of $1\mathrm{.}8$ Kg m$2.$Calculate:$($i$)$ The maximum initial motor acceleration.$($ii$)$ The maximum initial load acceleration.$($ii$)$ The maximum load speed.