In Conclusion

The oscillatory fan mechanism was built to allow for the oscillatory motion of a fan from point A to point B. This mechanism is successfully achieved through an efficient design.
A single motor allows for rotation to be transmitted to oscillation.
Omega experiences a speed reduction due to the gear box between the fan motor and the four bar mechanism; this speed reduction ensures that the same motor that spins the fan's blade is also the motor that allows for the fan's oscillation. This makes for an efficient design as it eliminates the existence of a second motor).
The position, velocity and acceleration of the fan's head and mechanical advantage of the fan system has been analyzed in this report. At any rpm, the fan's head range of position is given to be about 100 degrees, wide enough to allow for the side-to-side cooling of a room. Angular velocity and acceleration are fairly constant as fan moves from point A to B right after changing direction. There are spikes in these values with corresponding spikes in mechanical advantage of the system just when the fan's head reaches max position and turns.
It is sufficient to say that the analyses in this report prove that the fan works the way it was intended when designed.