Is there a safe way to feed a 240V device such as an AC or a small welder by splitting the plug and running the two lines to two separate 120V receptacles?

Unfortunately it doesn't work that way.
Voltage is a shorthand for Potential Difference, the difference in potential between two points.
Think of is as the distance an electron needs to travel, it wants to get from live to neutral.
The 120v in your supply means that the live and the neutral are 120v apart.
Every outlet in your home runs from the same live and neutral. You could feed in as many as you like (for gods sake don't) and they'd still only be 120v apart.
That's heavily over simplified.

Industrial supplies are usually three phase, this basically means they can select 120v. 240v or 360v and can potentially have outlets for each.
In your case you will need a step-up transformer, especially if you're running a welder.

Of course I meant that I would choose two 120V receptacles out of phase with each other thus supplying the equivalent of 240V at the appliance. Reason is that when using a welder in a building for instance its not always convenient to find a plug

FYI, I know that Quick 220 Systems supplies a UL approved device to accomplish this which adds the extra security of electronic lock-out if one of the legs gets disconnected. Unfortunately by the time you purchase the device, cords and shipping you're looking at close to $300.00.

If you have 240 coming into your panel and you pull 120 from each side of the panel I think you will have your 240. Never tried it but it makes sense to me.

I suppose I could wire in a 220V relay to ensure that I always have both legs connected while feeding the device. My concern is what is the down side to having each 120V leg fused as a single pole?

We will keep this post alive until TKRussell or Don can stop by and give the best answer

Using the Quick 200 device or equal is the only proper method, due to the required safety features.

Anything home made would not be OSHA, NEC, or any other agency or code approved in the workplace, (ADDED) or at home for that matter.

Sure a homemade unit can be easily made, even with relays and monitoring circuits and indicator lights.

For anyone here to provide specific details would be irresponsible.

Also, how do you know that the amperage of the device you are trying to use will not be too much for the circuit(s)? Simply asking about a "220" is pointless unless you also know the amperage.

NO, there is no safe or legal method to do this.
I have not seen this "Quick 220" device mentioned, nor do I care to . Sounds like yet another hack job to get around doing the job correctly and safely.

I agree with Stan.

You need to correctly size the conductors, receptacle and breaker for this circuit.

Ok, thanks for your input guys, much appreciated and helpful!