Cassette replacement
 

I recently replaced a worn chain on a bike with a Shimano 10 speed cassette, 11-26. Of course, the chain is now skipping around the cassette a bit and I believe I need to replace the cassette. My question is whether I can replace the 11-26 cassette with a 11-28 or preferably, a 12-30, without replacing or adding additional links to the chain? Any thoughts?

That depends on how the replacement chain was sized. If it was done by the method of big/big plus 1" then likely no, the chain will be too short with the larger big cogs.


But if the chain was sized the way I do, by small/small and the der's ability to wrap the chain so no droop exists, then maybe yes. The chain might be long enough to handle the new big/big.


BTW your rear der's ability to both clear a larger cog as well as wrap enough chain is at play here. Ultimately only by trying will one really know. This is why working with a LBS can be a good choice. Trial fit at the shop and no purchase made with only assumptions or hopes at play. Andy.

the replacement chain was sized by matching the new chain to the old chain, matching link for link.

But we don't know what method, if any, was used to size the chain.

Put the chain on the biggest ring & cog.
Take 2 skinny screw drivers or similar.
On a long run of chain, insert them a few links apart.
Keeping them parallel, move them closer to each other and see how much chain slack you have.
If you have an inch, you're "safe".
You would theoretically only need 1/2" additional, but you don't want the chain "taut" or close to.
Give it a bit of slack for cogs/rings that may have a bit "eccentricity" in their rotation.

You need the 1" to account for the chain having to climb over the teeth when shifting, ½" isn't quite enough to reliably shift in and out of the big cog. Then you need another ½" to go from 26 to 28, and so on.

I had the same issue. I replaced the chain then the cassette didn't work so I had to change the cassette. I went from an 11-25 to 11-28 and the new chain worked. Probably if I had gone bigger, I would have had to replace the derailleur as well as the chain.

The 28 should work - it's effectively only one tooth more chain and you can't actually add one link. The 30 might work but you would need to take a look - plus you need to ensure your rear derailleur can handle the 30.
Like Andrew, on road bikes I usually run the maximum amount of chain that the derailleur will handle. On MTB I run the minimum.