Force Required To Pull Two Links Straight?

What is the weight of the chain? Pins? distance between links?

In theory, if all things are equal and perfectly made you might be able to estimate the force. However, weight and size of chain, variations in lubrication, manufacturing, burs, dirt, o-ring condition (if that type). what is the load capacity and condition of equipment being operated. On a simple bicycle type setup you may overun the torque on the wheels and barely need tension to ride down the road. Turn around and go up the hill and things change. Look at the bottom of the chain and it could be super tight or so sloppy it's hitting the chain guard. But at the same time the working side of the chain has the same necessary tension to properly complete the work required. Depending on what equipment or work is being performed there are as many different ways to determine or adjust the tension required.

In theory, (assuming pins as points and no friction) they cannot be pulled straight: Any tensioned chain always hangs with a catenary, because the straighter it gets the poorer the leverage. The moment tending to straighten the chain gets increasingly tiny, while the moment tending to force it into a curve remains nearly constant for small angles.

Practically speaking, you would never want the chain bow string tight for the same reason: you'd be putting unnecessary loads on the bearings, etc.

The inverse of this is seen in sailboat rigging, which can be tensioned to (for example) 2000 lb, but which can be deflected by a ounces of finger force.

The angle between the links will approach 0 as the tension T approaches infinity.

I love it when someone says in a couple words, what it took me zillions to say!