What is the maximum tooth sprocket you could fit on the back using a Deore DX rear derailleur?

setting H and L screws should have no effect on the derailleur beyond what they are designed to do - ie limit how far inboard and outboard it can move. If something has caused damage its far more likely its because one of those limits is set incorrectly and the derailleur has crashed into either the frame or (far more likely) the wheel spokes - think you would notice that however!!

Another thing that could break it is overly tight chain tension (ie incorrect chain length or obviously over capacity setup where it can't take up the slack properly or gets stretched out too much)

I think this is another point where some photos of your setup would MASSIVELY help anyone see what might be up - I think if you put your mind to it you could sort some out :)
 
sounds like the chain wasn't routed properly between the jockey wheels and the cage maybe? (or buggered links that stick out can cause catching issues also)
 
Well that was an hour I’ll never get back, hoping there was a happy ending as to the fitment of massive cogs.
Here are my examples;
I recently bought a 26” wheel Cotic Bfe and rode it yesterday for the first time. 1x11 all XT M8000 with a whopping 40t on the back. Can’t remember the front but will check. The first three gears were totally useless, even uphill and tired. Legs spinning like crazy and 1+2 were moving the bike so slow it was hard to balance it and stay on. The mech is obviously sitting a lot closer to the ground which clearly isn’t a good thing. Not in my opinion.
A key one for me is - on another bike I’m building I put a short cage M735? XT r/m to do good old 11-28 and 24/34/46 the other day and when I realised it wouldn’t work I gave in and bought another mech. I could have just accepted that I’ll never use big/big or small/small but you never know and I didn’t like the idea of either accidentally ripping off the mech or having the chain so slack I could run over it.
My Five on 26” wheels runs 2x10 with 11-34 cassette. I use most of it. For me personally that’s enough on that particular bike. The mech is a long cage but doesn’t need to be, I just don’t have a shorter one and not buying one for the sake of it.
My Cotic Soul runs 1x9 using 32/11-34. I only muck around on it so it’s great for my needs. Works perfectly, despite being old.
My Karakoram has a full 27speed M570/M750 group which is great for that bike and its use. Correct sized cogs and mech.
I’ve never tried a mech hanger extender, I didn’t even know they existed.

While I noticed that the bike when I got it had new brake cables it seems the gear cables are old so perhaps that is the issue. The outer casings look good and not worn but looking at the exposed cable it is dirty and rusty so could be decades old. Could that cause indexing issues?
Yes. Even cables that look good are often not. On a mission like this you 100% need brand new quality cables as the very first step.
I notice people like to discourage me from tinkering as they think I am not qualified to do it. They think I not able to process information and will end up doing nothing, which is not accurate. I bought a bike and am improving it. Nothing complicated about that but people say I am 'over analytical' for asking questions to improve my bike.

Since you have added 40t to your old bike I see we are similar! Nearly everyone else discourages such experiments!

Yes I am sure extension would stop it but was trying to avoid using one and use as last resort. If that is the best idea then I will use it but I wonder if there is any problem with how it is currently with the cassette just being very close to the jockey wheel.
I like to push the boundaries but the square will never go in the triangle hole without significant changes such as making the square into a triangle.
I have switched to 2x now anyway since I never used the big cog on 3x anyway. Never understood why you would want to pedal when going downhill.
In most cases, to go faster, in order to get up the other side. To get more air off jumps. To swallow more flies.
I no longer need to hope, I have achieved it and ridden it. I have tasted the fruit of the gods.

I did run the numbers and 22/40 is almost identical to 20/36.

I find the pushback about low gearing peculiar. I don't see people complaining at people riding e-bikes which takes away much more of the physical aspect. Seems some subconscious issues about all the low gear shaming. Maybe e-bikes are so far removed as to not be a threat.
Then you’re not trying hard enough. Search the forum - there’s plenty of dislike towards E-bikes around here.
Oh ffs!!!

I am now in a world more trouble.

I was following the park tool article for setting the H-screw.

I got it to what seemed correct and was going through the indexing process as per the guidance.

I got everything what seemed close and as I went to take it for a ride suddenly the derailleur kept catching on itself as I pedaled.

I then went back to base to take a closer look and it looks like the derailleur has now packed in somehow! I thought the cage might have gotten bent somehow. Maybe too much tension when doing the H-screw exercise? Really did not have time to give it proper inspection in the last spurt of light.

When pedaling the bottom jockey wheel will not take up the chain.

I looked at the hanger and I am not able to tell really if it is that. I don't see how that could bend in that pedestrian process I was just doing. I didn't drop it or 'owt.

It was going dark and had to pack everything away at peak frustration not having got to the bottom of what has happened, having cocked it up farther than ever before and the light dwindling.

Oh FFS indeed.
No disrespect, but this is a total waste of time. Get the right kit for the job and be done with it. When you’ve accumulated 10+ years of parts and a heap of bikes you can take time out to muck around trying new ideas.
You seem to have discovered that when in the higher gears the top jockey wheel is too far from the cogs to give a smooth shift. The derailleur and cassette are designed to work together to avoid this. Let’s say you change your front gears. You have moved the chain over by 6mm or so. That has no effect on the rear. Why? Because it’s so far away. See what I mean? Enough people have asked for photos now to see exactly what it is you’re up to and you really ought to share some.
The most important thing is to enjoy the hobby and I can see you are doing that, which is a good thing, but some things are better left alone.

Edit - spelling mistake.
 
setting H and L screws should have no effect on the derailleur beyond what they are designed to do - ie limit how far inboard and outboard it can move. If something has caused damage its far more likely its because one of those limits is set incorrectly and the derailleur has crashed into either the frame or (far more likely) the wheel spokes - think you would notice that however!!

Well the crashing into the spokes might well be it!

When I adjusted the H screw I noticed everything was tighter and when I came to do the L screw, after the indexing process as advised by park tool, I crashed the RD into the spokes several times as it seemed everything was shifted over to how I had it before. When this happened I just changed gear and pedaled out so this could have bent the cage?

Another thing that could break it is overly tight chain tension (ie incorrect chain length or obviously over capacity setup where it can't take up the slack properly or gets stretched out too much)

Chain is not tight, I don't think. What constitutes tight? I can push my finger on it and it moves freely and tried in big-big.
 
Ok! So I started early on it this morning.

I took off the derailleur and took it apart and it didn't look bent so put it back together.

As I looked more closely at the hanger while the derailleur was off I thought maybe it was bed inward slightly.

I then did a 'cold set' aka break out the vice grips and bent it outboard 3mm or so. Now this looked straighter to my eye.

I then put the derailleur back on and the clattering issues seemed less however later I noticed that now it looks scew whiff when in big cogs. When looking face down while riding it looks like it is bending outward a bit.

When I had put everything back together and tried pedaling again to see how things were I somehow noticed that I think the jockey wheel not taking the chain is related to looseness and also chainline as it only seems to happen in the small cog. I think it was happening across a lot of the cassette yesterday so I think the hanger change did improve that.

I tried the indexing and again issues but back to the most being indexed but one side not. Having been for a 3 hour ride today and giving the gears a good workout I can say that thumbies seem the way to go as I was twiddling around with the barrel adjuster while riding to try and fine tune but it would not improve matters.

I hadn't even put the b-screw back on and was ok without but maybe the grumbling about shifting into the biggest cog sometimes was due to that. Might try the hanger soon as the b-screw doesn't seem to do much anyway and it is extremely awkward to do the reverse having to prize the spring back manually while angling the derailleur up to screw in.

Of course pictures will help but I was riding for 3 hours today and tired, I can look into it another day.
 
Oh and the 14" gear got used today! I would switch between 18, 16, 14. First time I have had a proper ride on the new gearing.

I would say the middle gets used a lot more and the granny gets engaged less frequently but still a fair bit. When the going gets tougher it is time to kick into granny gear!

I went to the steepest hill I know in my area to test it out and even that gearing does not give you a free lunch, It was still a hard climb up that. It isn't that long, maybe 1/4 of a mile but extremely steep in spots.

I was still fighting to get up it. That hill is pretty exceptional though.

For longer more gradual climbs though the lower gears really soften things up.

I still felt 'bonked' after 3 hours riding.

The hard gears still hardly get used at all. There are barely even indexed with multiple clicks not doing anything in the middle then suddenly dumping down to the couple smallest cogs. I do not feel at much of a loss without those indexed because mostly I just coast and barely use those harder ones but still it would be nice to access them all properly.

I would make better use of the middle of the cassette if it was working. I found myself having to avoid some of those gears on climbs as I knew they would ruin my cadence with loads of crunching around to find the gear if it changed at all.
 
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Does using thumb shifters also give you more leeway with a somewhat out of alignment hanger?

The realignment seems like a fussy job and, especially since it is part of the frame and not replaceable, I don't want to keep messing with it if I can avoid it. I think I may even have made it less aligned than before :LOL: I don't know but by eye it looks straighter and the derailleur seems to be better but looks squiffy on the low gears.

Btw what to do if the hanger attached to the frame gets cocked up? I am sure they stopped making them for the obvious reason that it was not a good idea to have it fused to the frame! So what happens if it did break or overzelous realingments make it weak and just come away from the frame with one too many adjustments!?
 
I’m starting to think this is a wind up now. After all the advice you have been given, you are still bending your mech hanger 3mm at a time with a pair of pliers. If it snaps off I would say you asked for it.
 
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