3) Kinematic Analysis

All the graphs were obtained from the provided MATLAB script and are based off a motor speed of 1000 rpm. For reference, point A is located at the connection between the big gear and the oscillating arm, while point B is on the other end of the arm. The graph below maps out the position of point A, resulting in a circle with a smaller radius than the big gear.

The position of point B traces out the end of the arm, which forms a perfect line of length 11 cm. This makes sense because the end of the arm is restricted to move in only one direction.

The velocity of point A is at a constant value of 3.927 cm/s due to the gear rotating with no angular acceleration. The gear is being driven by a motor with constant angular velocity, resulting in the gear itself having constant angular velocity.

The velocity of point B resembles a rectified wave. The velocity equals zero when the arm is in toggle position and has maximum values of about 4 cm/s.

The graph below shows the angle the fan forms with respect to it original, forward-facing position. This graph helps visualize the oscillation best and provides maximum angles of turning for the fan. As seen, the fan can turn about 16 degrees in both directions given its specifications, resulting in a total of 32 degrees of area coverage.

As for the oscillation of the fan, these properties can be determined from the properties of the arm, since the arm is directly connected to the body of the fan. The angular velocity is a wave form with peak values of about 12 deg/s which occurs when the fan is facing forward (in its original position).

The angular acceleration graph is a scaled mirror of the angular velocity graph. This makes sense because acceleration is simply the derivative of velocity. Here, we see that the fan reaches maximum values of 8 deg/s^2 when it's at its maximum displacement angle.