Assuming the wiring to the outlet has 2 loads and one neutral, isolate one load from the outlet and use the neutral as the common. Be sure to ground from the receptacle to your conduit or ground lead. You should also replace the corresponding breaker with a 120 volt single breaker.
Previously when something like the timer needed 110V, it used one of the hot legs and the neutral. This outlet is essentially ungrounded although the chasis ground in the dryer was usually connected to the neutral lead. Which is contrary to every other application... so it was changed.
Now the wire that runs to a dryer has four wires in it. The two hot legs.. (220V across them) the neutral (for 110V items) and the ground; to ground the chassis. Where does that leave you?
You can buy a replacement plug (or pigtail as they are sometimes called) with the four prongs. The two outside ones are the hot leads. When you wire it, obviously the hots go to the new hots.
Then separate the neutral wire from the ground strap on the machine. The ground can then go to the ground and the neutral to the neutral...That all makes sense?
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