申論題

4. Fig. D shows a single-link robot driven by a DC servomotor. To amplify the torque τm generated by the motor, a gear transmission with gear ratio n Gie. H= teeth number of Gear 2 / teeth number of Gear 1) is used between the motor shaft and the robot link. Let Im be the moment of inertia of the motor shatt and Gear 1 combination, and It be the moment of inertia of the robot link together with Gear 2. A rotational damper of coefficient b_m is placed at the end of Gear I to model the possible viscous friction.

(a) What is the relation between the motor speed ω_m and the link speed ω_L, and determine the equivalent moment of inertia referred to the motor shaft. (5%)