Exercise $3$

The geared system shown in Figure $2$ represents

an elevator system. The motor has inertia $I_1$ and

supplies torque $T_1.$ Neglect the inertias of the gears

and assume that the cable does not slip on the pulley.

The pulley radius is $R$ and the shafts are rigid.

$($a$)$ How many degrees of freedom does this sys$-$

tem have? Explain why.

$($b$)$ Derive a dynamic model of the system in

terms of the speed ${}_1$ and the applied torque $T_1.$

Figure $2$: Idealized Elevator