I have made several instruments like this, namely to use in a class I plan to hold. I think it is a viable art form and is relatively unknown to the general and artistic community. People find it hard to believe you can get such detail in the lettering. Try it, I think you will like it. Disclaimer: IF YOU DON'T UNDERSTAND THE ELECTRICAL WIRING, DO NOT ATTEMPT! GET QUALIFIED ELECTRICIAN TO HELP. I have used one of these machines for 15 years with no problems, not even a broken wire. So if things don't seem to be working right, you have probably done something wrong. A few additional tips: Try to keep temperature as low as possible. You want to melt the foam, not burn it. Use only with adequate ventilation. Some people may be sensitive to the vapors produced. Use care around the wire! It is hot and will burn you. Don't let young children play with it. It is not a toy.
But I like the project, might have to do one!
I know a lot about electrical wiring. I wired the majority of my house and it hasn't burned down... It even got a seal of approval from the inspector. But it would be nice to know where you have intended each of these components to go.
Instructables are intended for the DIY'er to LEARN a little bit more then they already know, so that when they attempt to DIY their own project, it's not as much a mystery.
Thanks for giving us mystery. Thanks for enabling a desperate DIY'er to injure themselves and others when they mistakingly place the dimmer switch between the cutting wire and transformer instead of between the wall outlet and transformer... Or when they use the Nichrome to wire the dimmer switch to the transformer and the standard wire to attempt the cutting... Or when they buy a dimmer switch that is not capable of handling the electrical load.
The fact is, Leaving out the wiring diagram, not to mention the construction of the entire project, is more dangerous for the average DIY'er than sharing the diagram. Imagine giving a gun to someone and not telling them about the safety switch, or how to load the ammunition cause you don't want them to hurt someone.
I mean honestly, you spent more time talking about the "look" of this device than on how it works, or even how it all comes together.
Here, look at this pretty gun, it has a black trigger, a nice dark oak handle, and the words "Remington" carved on the stock... have fun with it. Oh, and if you have never handled a gun before, have your local gunsmith load the ammunition for you.