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.

(b) Using τw as the control input and the rotation angle (say, θ) of the link as output, obtain the transfer function describing the dynamic relation between the torque im and the output angle  θ. (5%)