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I know that I shouldn't have, but I had a go on my son's bike (https://www.giant-bicycles.com/au/xtc-street-20-2012).

I think that I stretched the chain. It's sagging now with about 3" of vertical play at the point between the cogs.

So - can I buy a chain breaker and just shorten the chain, or should I get a new one?

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    True chain stretch is very small (we talking a couple millimeters, not 3 “ of vertical play), happens through wear, and changes the effective pitch of the chain. Sounds like the rear wheel changed position in the frame. – Rider_X Mar 15 '18 at 5:04
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    It looks like you fell prey to the X Y problem. I took the liberty of editing your question to make things clearer. – sleske Mar 15 '18 at 10:56
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    A chain doesn't really "stretch", it wears, such that each link gets more loosely connected to the adjacent ones. You might see significant wear in a week of riding gravel roads in the rain, but not from a single outing. And if the chain really is "stretched" (ie, worn) this much you should replace it, since it will cause the sprockets to wear much more rapidly. – Daniel R Hicks Mar 15 '18 at 12:38
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If this happened over the course of 1 ride, it sounds like the wheel just slipped forward in the dropouts. If you loosen both nuts on the rear wheel axle and pull it backwards evenly, you should be able to retension the chain to proper working specs. Then just tighten it back to a torque of pretty f**ckin tight so it doesn’t slip again!

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    +1 for the torque value of “PFT” - I’ll have to remember that one. – RoboKaren Mar 15 '18 at 16:51
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    Damien Sawyer -- While looking at that image above, imagine grabbing the chain at about the 2 o'clock position of the sprocket and pulling it up and towards the front to try to lift it off the sprocket. A new chain on a new hub will rise up about half the height of a sprocket tooth. As the chain wears you will be able to pull it further. When it gets up to almost the height of the tooth then the chain is too worn. – Daniel R Hicks Mar 15 '18 at 17:02
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    @DanielRHicks That's a good measuring rule-of-thumb for a chain. – Criggie Mar 15 '18 at 23:52
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I think that I stretched the chain.

No, you most likely did not. Bicycle chains are very strong (and chains on children's bicycles are usually similar to chains on adult bicycles). Plus, if a chain is really overloaded, the links will separate (i.e. the chain will tear) before the force is great enough to actually stretch the chain material (which is usually hardened steel).

Note that bicycle chains do get longer due to wear on the material. This is often referred to as "stretch", but that is misleading - the chain does not lenghten due to being pulled, like a rubber band, but because the friction in the links wears down the material.

So something else must have happened to make the chain sag. The most likely explanation is that the back wheel was pulled out of its dropouts, as indicated in BillSkiCO's answer.

It is also possible that the chain was already sagging before, you just did not notice. On bicycles without a derailleur, chains can sag quite a bit without causing problems.

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    Check the seat-stays and chain-stays whether they are still straight. The weight of an adult could have caused permanent deformation on a bike that was meant to be ridden by a lighter rider. – Carel Mar 15 '18 at 20:28
  • Thanks @sleske for a great explanation of stretch! That makes a lot of sense. carel, I've had a look and can't see any obvious deformation. I'll check those areas again more carefully. – Damien Sawyer Mar 15 '18 at 22:44
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When you stretch a chain the distance between pegs become longer than designed. Even fatal chain stretch cannot be easily identified by looking at the chain.

There are very simple yet accurate chain scales used to identify whether the stretch is none (new chain), fair, acceptable, "replace the chain", "replace all chain and sprockets". Another way to estimate the chain stretch is to try to lift the chain from the sprocket. The further you can lift it, the more stretched chain you have.

One can see the chain is stretched far above the "replace the chain ASAP" level when the teeth on small sprockets are no more symmetrical and become worn from the rear side (upper teeth of the rear sprocket). When the chain starts skipping over the teeth, whole drivetrain it worn out and the chain still looks quite good to many people and is still very strong in tension and the peg-to-peg distance is stetched in orders of tenths of milimeters.

Another reason for not-stretching a chain is the momentum one can produce on such bike. The crank arm is shorter on kid bikes than on the "full size" bikes. Therefore the tensile force you have applied to the chain was lower than you are able to apply on your bike.

Since you were able to load the chain with weaker forces and even hard stretch will be negligible to wrong setup the only option left is that you have moved the rear wheel a bit front. Realign it, as others already suggested, and tighten it.

It is worth nothing to get the chain measured for the wear, though.

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