I have a new welder (230v 21amp) with a NEMA 10-30P cord. I also have an electric dryer (230v 30amp) which attaches to a NEMA 10-30R. The dryer circuit has two hots and a common, no ground. The welder has a hot, common and a ground wire. How would I set up connections so the welder and the dryer can use the 230v 30amp circuit from the panel (obviously only one devise could be operating at a time)?

 

No the dryer has two hots and a combined neutral and ground. No. If it is 240v it has two hots and no neutral. You could run the welder from the receptacle but you would not have a ground assuming what you are calling "common" is in fact an insulated white neutral. You need to either run a new circuit for the welder or change the dryer to 4-wire and use an adapter for the welder.

Above assumes there is not continuous metal conduit to the breaker box.