Chapter 3, Problem 3.25P

The geared system shown in Figure P3.25 is similar to that used in some vehicle transmissions. The speed ratios (which are the ratios of the gear radii are

$\frac{{\omega }_2}{{\omega }_1}=3\frac{{\omega }_3}{{\omega }_2}=\frac{3}{5}\frac{{\omega }_4}{{\omega }_3}=\frac{13}{11}$

1. Determine the overall speed ratio ${\omega }_4/{\omega }_1$ .

Derive the equation of motion in terms of the velocity ${\omega }_4$ , with the torque $T_1$ as the input. Neglect the inertias of the gears and the shafts.

Figure P3.25