A few days ago I wrote about the mechanical sequencer built by Tim Robinson out of Meccano. I emailed him for some more details, and here is what I found out.
In this diagram, the red shaft on the left goes through a hole in the large crown gear; it is not attached to the crown gear. When the crown gear is rotated, then assuming that both shafts are free to move, there will be no drag on the central bevel gear, and so both shafts will rotate in the same direction at the same rate as the crown gear.
If, however, one of the shafts is prevented from moving, then the central bevel gear has to rotate, and the other shaft continues to rotate, this time at twice the rate of the crown gear.
Now imagine a finger extending radially outwards from each of the shafts. I can stop the rotation of a shaft by blocking the movement of that finger with, say, a rod. By pulling out the rod and letting the finger go, the shaft can move again. If I move the rod into position again, the shaft can only complete one rotation, and then the finger hits the rod and the shaft stops.
By timing the blocking rod movements correctly, I can choose when and how many rotations the shaft may make. This is the essence of Tim's sequencer. The movements of the blocking rods are controlled by a drum with bumps on it.
Again, being Meccano, these things are hellishly expensive. The cheapest bevel gear sold by meccanoman.co.uk is £4.94, or nearly USD 8. And they're made of brass. That's just nuts.