So far, we have the dimensions that we need to ensure that each arm grabs the pendulum at the right location and releases it at the right location. Now, we need to make sure that all arms release all pendulums

*at the same time*.

After doing a little sketching, I came up with a simple mechanism that works. Other than the arm, there are two components in this mechanism. To mess with the electrical engineers, I will call them the rotor and stator.

R_c is the sum of s (not big S from the previous problems) and the edge length of the arm (not shown) beginning at the pin. As mentioned on the previous step, the actual length of the arm is different than the value R we calculated previously. Additionally, the angle Ï is different than the angle Ï just calculated above. Sorry for any confusion.

The actual length, by Pythagoras, is:

R_actual= SQRT((R^2-t^2/4)

where t is the thickness of the arm.

So,

R_c = R_actual + s.

In order to find s, we need to find the value for α, the angle opposite of s.

From the diagram, we see that α = 180 - (Ï + 90 - β/2) => α = 90 - Ï + β/2

where Ï = asin(h/R), and β/2 = asin(t/(2*r)).

So, α = 90 - asin(h/R) + asin(t/(2*r)).

tan(α) = 2*s/t => s = t*tan(α)/2 => s = t*tan(90 - asin(h/R) + asin(t/(2*R)))/2

Thus,

**R_c = SQRT(R^2-t^2/4) + t*tan(90 - asin(h/R) + asin(t/(2*R)))/2**
For my pendulum wave, I chose the release thickness (t) to be 1/2".

We designed each arm in the release mechanism to let go of its respective pendulum when the rotor is at a constant angle (Ï). Thus, each rotor can be coupled to all other rotors. The implication of this is that since all rotors (when coupled) have the same angular velocity, and all pendulums will be released when the rotor is at angle Ï, all pendulums will be released at the same time.