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the first 555 is a one shot timer. It outputs one pulse from pin 3 to pin 2 of second 555 (trigger input)
the second 555 is an bi-stable timer. It controls the third timer set up as an astable timer (outputs a train of pulses instead of just one pulse.)
the output of the second controls the third timer.
this circuit can be reconfigured so only one 556 (2-555"s in one package) can be utilized.
Haven't figured out why they put the bi-stable (acts like a toggle switch) in the mix.
look at this site as it explains all of this LM555 Timer Circuits
with that posted link - the train can only go in one direction for the circuit to work.
working on an idea that detects model train coming from either direction, using only 2 IC's or using one micro-controller.
also using reed switches is not as reliable as a photo-transistor arrangement.
will get back to you if your interested.
the third 555 is being powered by the second 555 output-I don't think this is a good idea as the output won't drive it or it may cause eratic behavior
at least that's my take on this schematic as well as the train can only go one direction for it to work
planning on using a D flip flop.
have it almost configured by using a divide by two 4013 circuit.
train starts the one shot then the one shot triggers a D flip flop hen when train finishes passing over last sensor the 4013 resets for next train, regardless of direction of travel.
this would be so easy using a PIC but configuring using cmos or TTL is kinda fun.