Following might be relevant:
Speed: timeframe for movements, slowest and fastest acceptable.(General operation parameters, air pressure, flow throttle)
Accuracy of force. (Cylinder diameter and air pressure)
Accuracy of stroke length. (Limit switches)
Precision of coordinated movement. (Adjustment of regulating devices)

General common advice for an operation of several cylinders in parallell is to have large enough common air feedstock, components, pipelines, layout and air supply to feed and empty all cylinders simultaneously.

As an example solenoid valves with 1/4" diameter might for instance have internal borings up to 1/4", but also down to 5% of this or less. It will be better to have wide openings all over and restrict by air pressure regulators or simple needle valves.

The rest is a detailed layout, done by an expert.

Good luck!

Also you need to think about how fast these items go and how you want or need to control speed and movement.

It sounds like (please fill in the gaps) like this is some sort of gripping machine where most? of the travel is free movement followed by application of force.

If you don't have a variable restriction on air then the pistons could move very fast with all sorts of shock loading when they reach the middle.

A 2" stroke should be ok for a fixed velocity until it grips the thing in the middle.

There are many many pneumatic control and equipment suppliers and vendors out there.

e.g. https://www.pneumatictips.com/pneumatic-design-101...
https://uk.rs-online.com/web/c/pneumatics-hydrauli...

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

Thank you gerhardl and LittleInch. That was was helpful. I didn't realize anyone had answered. I'm still learning to navigate the ETF board. I think what I must do after reading your replies is consult with a vendor's technical advisor, tell them what I want to do and have them set me up with a package. I just don't know enough to figure out what items I need by myself. Thanks, again.

That's it!

The art of being an engineer is the art of knowing when you need to know more, and how to find more information! Good vendors have very often updated specialists!

Again: Good luck!

Many persons here tend to forget that half the fun of trying to help is getting back a progress report!

Thank you for star and your thoughts!

Fair enough and thanks again for your support, gerhardl. I will report back. I got my "working papers" today. Very official looking stuff. Seems I'm an essential manufacturing worker in keeping with the Emergency Act having to do with national defense. You'd think that they would at least furnish us with some government issue tissue. No perks. A lot of risk but it's an income. All that they tell us is "wash your hands often".

I have been redirected to peruse electric linear actuators for this application which is metal forming, in case I didn't mention it. The situation will require a good amount of static force over a period of time but at least they can be coordinated more easily by electronic controller adjustment. Computer I guess. I'm not convinced that linear actuators like being restrained under a load in stasis for too long by a dead-stop. The static force is about triple their dynamic rated force. I'll need the static force in this case. Are they designed to do that?

OK Here's an update. I hope I still have everyone's attention. I've redesigned the setup using only two air cylinders which will be installed “nose to nose” opposing, with metal forming going on in between using rollers while it spins. To be clear, the idea is to spin-form an aluminum tube over a mandrel into a taper as the rollers under force travel down the length of it on a lathe. The total stroke length will be less than 1–1/2″ from two 4″ cylinders with 1″ dia rods. They need to arrive at the target very close to the same time and exert equal force. Because we're spinning the taper over a mandrel it has to be done in short length increments as well a diametrical, feeding the tube out onto the mandrel little by little with final full length sweeps as it nears the final shape. I’ve done this manually before using three rollers driven by a cam system and a hand lever. This tube is much bigger and thicker. Here's the idea. I would very much like your thoughts. Would electric linear actuators be better or would that be a similar problem?

Electric actuators will need force balancing, which is possible if the motors are fed from a common supply...I think.

But your pneumatic cylinders, if fed from a common plenum, will tend to be automatically force balanced, i.e. have equalized pressure on the driving side of the cylinder, as the flow will automatically balance cylinder pressure when one cylinder makes contact and the force to cause further motion increases.

Thanks, btrueblood. In this case the "plenum" would be the shop's common air compressor tank which delivers about 120 psi going into two 4" pneumatic cylinders should yield something over 1500 lbs force each....all things being equal, which seems to be the question. Unless advised otherwise again (I'm hoping for more advice), I'll need a manifold for splitting the compressed air path and cylinder return exhaust and a regulator to control the pressure and filter the in-going air etc and an activation switch of course. This is all new to me. It needs to get done though. I wouldn't be asking if I was sure.

" I'll need a manifold for splitting the compressed air path"

Right. And it wouldn't hurt to oversize this manifold, i.e. make the i.d. a size or two larger than the lines from it to the cylinders, so that the pressure has a chance to better equalize b/n both drive sides.

I'm assuming there are radial supports for the reduced rod somewhere off to the right in your picture? If not, then you may want to think about adding them, or have a secondary drive that holds the effective center of the reduction within some small distance of the center of rotation of the chuck or whatever that is on the left.

Yes. What's going on to the right is a steady-rest (when needed) and an a live center at the very tip. I've done this before with a manual/mechanical set-up using a rotary cam plate and a long hand lever and it worked. This is just bigger, longer and meaner requiring more force. Thicker wall tube. It's done incrementally with graduating lengths and diameters feeding the tube little by little on to the mandrel which never changes position. The cylinder ports are 1/2 NPT.