My toilet flapper will not fall in my toilet, there is slack in the chain. I have tried every length and replaced the flapper itself. Nothing works. I am curious as to what exactly the mechanism is that prompts the flapper to fall?

Two things make the flapper fall, one is the weight of the flapper itself and the other is the water going out of the bottom of the tank causes a suction and pulls the flapper down.

Now what we need to find out is what make it not fall, one of the most common is the fact that the chain is too tight and will not let it drop but you have already said that is not the problem. Another is that the handle mechanism is corroded up and down not work up and down as it should, the handle arm should drop on its own even before the ball drops. One other thing is the flapped could have a foam center in it and this piece of foam is not letting the flapper fall because it keeps floating on top of the water.

One other thing that I have seen cause the flapper not to fall is the water coming into the tank is too fast and some how is keeping the flapper up, so you might turn your cut off behind the commode down some to slow the water down to see if this might change things.

Let me know what you find wrong.