Do half link chains work on any bike?
What is the purpose of a half link chain?
I've noticed that only BMXers and DJers use them, and that leads me to believe there is a technical reason behind that.
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From the internet:
"Half Link BMX chains were designed to help dial in the chain length on frames with short dropouts and small gearing, making sure your rear wheel is exactly where you want it. Dan's Comp offers a wide variety of half-link BMX chains for both race and freestyle."
Basically, you can break your chain at smaller increments to get a more precise chain length. 1/2" instead of 1".
Half link chains should work with most single speed set-ups, but not with any bike with multiple sprockets / chain rings.
As mentioned in another answer, the main purpose of half link chains is to have more control over the chain length and hence the wheelbase of your bike (assuming you have rear facing or slideable drop-outs). A centimetre difference in wheelbase will change the feel of the bike quite a bit, especially on a short bike like a BMX.
Half link chains can only be used on single speed bikes* because their side profile won't match/mesh with the ramps that help lift it onto the next gear.
Half link chains also won't work with thick/thin chainrings as every link is thin on a half link chain.
Half link chains most commonly come in 1/8" width for BMX and general single speed use. You can also get them in 3/32" width for use with a mountain bike drivetrain, a lot of dirt jump mountain bikes run a mountain bike crankset with a 3/32" chainring for example.
Note: Modern mountain bike chains are actually a little bit narrower than 3/32" once you get to 9 speed or more. The difference is enough to stop a 3/32" chain working with 9+ speed gears but a 3/32" chain will still work with a 12 speed compatible chainring.
Using a 1/8" chain on a single speed mountain bike drivetrain might work but there would be a lot more side to side play which can't be good for wear! It also might not fit through a chain device designed for 3/32".