The workings of a carburettor are mysterious... Well, they're a mystery to most folk...

In order to correctly "fuel" an engine from it's lowest "idle" speed, right through to it's WOT* maximum revs, there has to be a great deal of flexibility in the way that the carb operates.
*WOT = Wide Open Throttle...
In order to create this flexibility, carb design adopts a number of separate "systems", each controlling a specific part of the engine's RPM range and working together to fuel the engine right through that range...
The basic systems are:
Choke or "Cold Start Enrichment Device" - Enables the carb to provide a fuel rich mixture in order to start a cold engine.
Idle Mixture Circuit - Sets the fuel/air ratio to enable the engine to idle smoothly.
Carb Slide and Needle Jet - Allows a variable fuel/air ratio for engine speed between idle and 4k - 5k RPM.
Carb Venturi and Main Jet - WOT - Sets the fuel/air ratio between 4k - 5k RPM and maximum revs.In this write up, I'll be trying to explain the idle mixture circuit. How it works, what goes wrong and what to do when it has already gone wrong...
This 'ere's a piccie of a set of carbs from an 'early XS1100...

Item 34 is the idle mixture screw. 33 is a tamper-proof can to stop you fiddling with the idle mixture screw and 35 is a spring that prevents the idle mixture screw from vibrating away from its' pre-set position.
What does it do..???The idle mixture screw, together with its' very closely machined recess, acts as a precise fuel metering jet.
The screw sits atop a tiny hole in the top of the carb venturi. As air is drawn through the venturi
(by the descending piston and through the gaping inlet valve, etc, etc...) a vacuum is formed at the mouth of this tiny hole and air is drawn out of it... The drawing of air causes the vacuum to pass through the series of drilled passages, past the idle mixture screw and down a long tube to the carb's float bowl... This tube is immersed in fuel
(you hope) and the vacuum causes that fuel to rise up the tube, through the passages, past the idle mixture screw and appear
(as if by magic) at the tiny hole, where it is immediately atomised by the rushing torrent of air through the venturi... (bye bye little drop of fuel...)

All this happens in the blink of an eye... It happens constantly (as long as the engine is running) and the effect is that the fuel through the idle mixture circuit appears as a fine mist in the venturi and is completely atomised before entering the engine...
I said, "What does it do..???" Fatty..!!OK... The idle mixture screw adjusts the amount of fuel that is drawn through the idle mixture circuit. It does this by changing the size of the tiny aperture in the venturi. Here's a piccie of an XS1100 Idle Mixture Screw:

The head has a single slot for adjustment... The thread is a metric "super fine" M6 x 0.5mm for ultra precise adjustments of the fuel metering and the taper is normally snapped off and stuck into the carb body

More on that later...
The recess in the carb body that the idle mixture screw fits into is of a similar shape. However the tapered section is arranged such that the screw will actually seal the tiny hole off completely if screwed too far in...
BTW: Not shown in either pic... Under the screw, in the screw's recess, are fitted a spring, washer and o-ring. The spring prevents vibration moving the screw, the washer prevents the spring tearing the o-ring and the o-ring prevents air being drawn down the screw threads and buggering up the lovely vacuum-driven mechanism, thingy...So... What Goes Wrong..??Actually...It's a very reliable part of the carb... Some folk say that modern fuel types mean that changes in idle settings are neccessary, but that ain't the fault of the idle mixture screw... Is it..??!! The things that actually go wrong with this circuit are usually due to some ham-fisted fecker getting their grimy paws on it in the first feckin' place...!!
#1 - Corrosion..!! #1 'cos it's the #1 problem... These screws sit in a vertical channel. On most EU bikes there isn't a tamper proof cap fitted and that channel can easily fill with lovely, mineral-loaded, rainwater... The screw is brass. The carb is zinc alloy... After about 20 years of soaking in rainwater it's difficult to say which starts or stops where... There are MANY tips on how to get a seized idle mixture screw out of a carb...
Some of 'em work too...!!
#2 - Maladjustment: Maladjustment in itself ain't the problem... It's what happens when these screws are maladjusted that IS the problem... "Correct" adjustment of an idle mixture screw will always start with the phrase "gently wind the screw clockwise, until slight resistance is felt..." Unfortunately, the words "gently" and "slight" are often completely feckin' ignored by the hastily shaved apes who are entrusted with such delicate adjustments...!!!
NOTE: IF YOU WIND AN XS1100 IDLE MIXTURE SCREW TOO FAR IN YOU WILL WEDGE THE END OF THE SCREW INTO THE TINY HOLE IN THE VENTURI. THIS WILL DEFORM THE TINY HOLE. AS YOU HASTILY ATTEMPT TO WITHDRAW THE SCREW
(HOPING THAT NO-ONE HAS NOTICED YOUR CLUMSY BODGERY) THE TINY SHARP END OF THE SCREW WILL BE NEATLY SEVERED FROM IT'S END
(RATHER LIKE WALLACE TAKING SLICES OF CHEESE FROM THE MOON IN "A GRAND DAY OUT" - A FINE FILM AND FUN FOR ALL THE FAMILY...)Really clever thing,
and a bit vicious too, about this fault is that you don't know that you've done it..!! The screw appears unaffected and moves exactly as it should (apparently). But adjusting the screw now is no feckin' use at all... You've bunged the hole up you witless wassock..!!

*
The repair for this fault is: Remove the carbs.
(Even if you're a feckin gynaeocologist and a proctologist you ain't gonna get your finger into this one..!!) Take a gander from the engine end... You'll see the tiny hole up near the throttle valve... Easier if you hold the throttle open... Can you see the hole..?? Try running a finger over the top of the inside of the venturi.... Bleeding..? You've found the tip of yer screw then...

Before a new screw can be fitted, that'll have to come out..!! It MUST be shoved out upwards... (Tapered remember...)
Once the tip is out, a new screw is needed... They often come as a "kit", complete with the spring, washer and o-ring...
#3 - Sh!te in The Klystron: (An ol' radar term, but I'm sure you get my drift...) In this context, the "Klystron" is usually the tiny brass tube that draws fuel from the float bowl... It's orifice is at the bottom of the bowl, where it's best placed to gather all sorts of unfiltered nasties... If the worst should happen and water gets into the float bowl, these have been know to block almost solidly... If it ain't clear, it won't idle properly and the only effective cleaning processes are solvents, compressed air and ultra-sonic baths (all at the same time if you can get help...)
Apart from that and the highly contentious subject of "how many turns out", my last on this is that every single manual you'll read states to set the idle mixture screws the same on each carb... Why..? it's clear that a common pre-set position is desirable, but the final setting should be reached empirically... "Suck it and See" As the circuit works by allowing or restricting fuel flow, it's a VERY good thing to remember that screwing it in makes the air/fuel ration weaker, screwing it out makes it richer...
HTH
Miti* BTW: If you think you MAY have snapped the end off your idle mixture screw, start the engine and unwind the screw completely... (It's a SOD to remove with the carbs in place, but you'll probably get it...)
Clue #1... Did the idle alter at all when you were unscrewing the screw..??? If not, it's probably stuck in there...
Clue #2... Has your screw lost it's tip..?? Well personal problems ain't dealt with 'ere mate... You're on yer own..!!