The mechanism shown is designed to move the tool at H while keeping it oriented vertically...

The mechanism shown is designed to move the tool at H while keeping it oriented vertically. To do so, the rotor in the motor M is attached to the gear A, which drives the gear B. In turn, gear B drives the gear C, which is rigidly attached to the arm EF. Arms EF and DG both have length L and are parallel to one another. The radii of gears A, B, and C are rA, rB, and rC, respectively.

If the motor A rotates with angular speed ωA and angular acceleration in the directions shown, determine the velocity and acceleration of the tool H as functions of the angle θ .

Figure P6.30