Electronic – Why does isolation transformer protect from shock

It's a little unclear what exactly you are trying to accomplish. If the point is just to experiment with full wave bridges and see all the signals, then do it at a low voltage like JonnyBoats said. You can probably find a old transformer somewhere that is rated in the range 6-12V AC at 1 Amp or so. That's a good size to put a full wave bridge after, and then you also get a useful DC voltage to do lots of other things with.

As Jonny mentioned, there are also wall wart type transformers that are rated for less power but you can do mostly the same things with. The advantage is that these things are cheap nowadays. You can probably find something in the 3-5 Watt range for $5. Jameco has a broad selection of such things. That's a good place to look around.

If you really want to experiment with a full wave bridge driven by a function generator, then you should power the function generator from a isolation transformer. These are 1:1 transformers meant to take line power in and put line power out, except that the output can float. These will cost a bit more since they are usually intended for 100 W or more. Sometimes they even come in a box with a line cord for the primary of the transformer and a regular output connected to the secondary. You simply plug the cord into a wall outlet, and the thing you want isolated into the outlet on the box.

One gotcha you have to be careful of with these things is that they may not come wired up fully isolated. I bunch of years ago I bought a 500 W "isolation transformer" that was just as I described above. I used it to float a device under test so that I could hook up a grounded scope to it at various places. The first time I touched the scope ground clip to part of the power supply there was nice spark and the fuse blew. It turns out there was actually a deliberate ground wire inside the isolation transformer box connecting the ground from the line cord to the grounds on the output sockets. That's not what I consider "isolation", but someone else apparently does. Once I disconnected the two sides of the transformer and carefully verified there was no conduction path, it worked as intended.

I think what you did was close, but I wouldn't leave the whole chassis floating. I'm assuming this isolation transformer comes with a standard 3 prong outlet for the output side. Just disconnect the ground connection on this outlet, but continue to let the input side ground be connected to the chassis.

Generally you want as little as possible floating at some arbitrary voltage. There will be plenty of other things around at the normal ground potential, so the chassis of the transformer isn't going to make anything worse.

I agree with Dave in that I don't understand why isolation transformers come with the grounds connected. I got one that way too many years ago, but didn't expect it. I actually blew out a fuse before realizing that the grounds were connected together inside the box. I don't know what they think isolation means, but different from what I had assumed.

By the way, beware of inrush currents on a 500 W isolation transformer. All the ones I've seen are toroidal cores. These can retain residual magnetism depending on what part of the power cycle they were turned off at. If this happened to be at one peak and you turn it on next time near the other peak, there will be a very large inrush. I once blew a 30 A breaker with such a transformer, even though I had switched it on a number of times previously on the same circuit. Unfortunately this was on a weekend and the breaker was in a different locked room. Argh. Often you want to adjust the voltage anyway when you're debugging power circuits where you want isolation. In that case, put the variac before the isolation transformer instead of after it. If you bring the variac voltage up and down with the knob, there won't be much inrush.