A single link of a robot arm is shown in Figure. The arm mass is m and its center of mass is located a distance L from the joint, which is driven by a

motor torque Tm through two pairs of spur gears. We model the arm as a pendulum with a concentrated mass m. Thus we take the arm's moment of inertia IG, to be zero. The gear ratios are N1 =2 (the motor shaft has the greater speed) and N2 = 1.5 (the shaft connected to the link has the slower speed). Obtain the equation of motion in terms of the angle θ, with Tm as the input. Neglect the shaft inertias relative to the other inertias. The given values for the motor and gear inertias are
Lm = 0.05 kg.m2
IGl = 0.025 kg.m2
IG2 = 0.1 kg.m2
IG3 = 0.025 kg.m2
IG4 = 0.08 kg.m2
The values for the link are
m = 10 kg
L = 0.3 m

Arm Gears N% Gi Tm Gi Motor