Same as last solution but moved arms 10, 13, 14 to make a period of 8 work. Added notes from prev solution for ease:
So basically on the right we have a thingie that drops the blue orb in the hole and waits for it to come back. On the left we have a rotating arm on a loop of 4, and arms on loops of 5, 7, and 13. All are required to move the blue orb with exact timing back into the hole or else a few other arms will put it in the certain spot at the top giving us 5*7*13*6(from arm 10's rotation)*2(which would be 4 but the parity collides with the rotation)=once in every 5460 cycles that the orb can go back into the hole. Once the orb goes in the hole the other orbs are finally moved off the input and worked to the output, while the 5460 cycle requirement starts over.