Here's a more detailed explanation and a video.
Conditions:
The wheel rotates counter clock-wise.
A rectangle with two weights attached to each end.
Four rod locking constraints that turn on and off at appropriate angles as the wheel turns. They are attached to the main wheel and to the weights. The rod locks are not shown.
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Operation:
A Rod lock is initially engaged at P2 at the 12 o'clock position.
Blue Weight swings from P1 to P3 through the green arc.
Wheel rotates 270 degrees. P3 is now at 12 o'clock.
Rod lock at P2 is disengaged and Rod lock at P3 is engaged. Red Weight swings from P2 to P4 through the red arc.
Wheel rotates 270 degrees. P4 is now at 12 o'clock.
Rod lock at P3 is disengaged and rod lock at P4 is engaged. Blue weight swings from P3 to P1 through the cyan arc.
Wheel rotates 270 degrees. P1 is now at 12 o'clock.
Rod lock at P4 is disengaged and rod lock at P1 is engaged. Red weight swings from P4 to P2 through the blue arc.
Wheel rotates 270 degrees. P2 is now at 12 o'clock. The wheel is now 'Reset'.
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With each swing of the weights you 'gain' 90 degrees so the wheel only has to rotate 270 degrees to set up the next swing of that mechanism.
There are four swings before the system resets, and each rotation you only need 270 degrees to set up for next swing, so 4 x (3/4) = 3 rotations.
So with this square setup and four swings, you need 3 wheel rotations before the system resets.
The rod lock/unlock mechanisms will not use a (modulus angle, 360), they will use a (modulus angle, 1080).
And then figure out where in those 1080 degrees of rotation you need to turn on/off each of the rod locking mechanisms.
The sim uses invisible 'marker' circles that are backed off from zero degrees a certain amount for each mechanism. An invisible output meter tracks the orientation of the marker circles with a (mod 1080) adjustment, and the ActiveWhen statements of the rods look at the output meter to determine when to trigger their lock and unlock.
There is a background square attached to the main circle and is not shown. This is used as a stop mechanism instead of the ring and allows better locking control of weights at the end points of the swing.
The second part of the sim adds springs that are Active and Not Active based on certain orientations of the wheel (mod 1080).
Observations:
With a square geometry you can only have 3 mechanisms. If you add a fourth mechanism its movement will overlap one of the other three.
With a triangle geometry, you can only have 2 mechanisms before duplication becomes an issue.
If you had a 6 sided polygon, this would be two triangles so you could probably only have 4 mechanisms until the mechanisms started to become duplicates of each other.
A 7 sided polygon could have 6 mechanisms before one would duplicate another.
If you run the sim at too high an angular velocity the lock/unlocks miss their correct lock position because the weights have not fallen into position yet. The lock will still occur, but not at the edge of the wheel, and the sim starts to fall apart at that point.
Possible improvement would be a different spring system that is perhaps more mechanical so the spring disengages after the extension.
Youtube video here:
https://youtu.be/iRdxbqZvb4s
