Drilling machine plus drill bit smallr than the bolt diameter

just drill into it then?all the way through it?

Yes, just drill all the way through it. Really though you need stud extractors and a drill that's a bit smaller than the tapping size drill and then it's easy. It's basically one of them jobs - you have the right tools it's a doddle!
If it's loose, spray it with something like WD40 and leave it soak for a bit. Then using a something sharp try turn it very carefully and it will eventually come out but this method only works if it's loose ok.

Pillar drill makes life much easier.

Centre punch the broken bolt and drill exactly down the middle with a small drill and gradually increase the size of the drilling. You can try extractors but be careful with small sizes 0- they can be brittle and snap easily and then you have real problems.

Or you continue to drill it out untill all you have left is the threads - then pick those bits out / run a tap thru it

seems all my bits are next to useless. They don't appear to be making any progress through the thing!

to continue on what others have said, the ideal size drill is the same as the shaft of the bolt. That's the diameter of the bolt at the narrow point between the threads. If you can get it dead straight then the thread should come out in a coil.

takes time and patience but gives a great feeling when done. especially when its a spark plug :-\

Goto halfords or b n q and buy a sharp drill bit, you wil do more damage than good trying to force a blunt drill in.

very very carefully

left handed drills are very useful for this. Usually better than stud extractors ime.

Well normally you drill something out with a drill.... 🙄

Not sure what else you could use.

Not sure how you have ended up with some bolt stuck in the mech, if it sheared I would have thought you maybe have at least some bolt still outside the threaded out for you to turn.

Make sure you start in the very centre of broken stud.
Start with small drill and then gradually work up to tapping size if necessary of the broken stud.
eg. an 8mm bolt is in a hole which is drilled 6.8mm
Take your time and make sure it drills in line with stud also.
I have had the pleasure of removing an array of items,extractors,drills,taps and various other stuff, in the unsuccessful attempts of others.
Sometimes the use of a very sharp centre punch can be used to turn out the offending stud if it isn`t too seized.

HTH

Not had much luck trying to remove those in the past, they never shear off flat, so even wth a well placed centre-punch the drill tends to wander, they're such an awkward shape that it's difficult to clamp them up to fit a pillar drill, and the bolts seem to be the only ones on a bike that aren't made of cheese,so resist drill bits quite nicely.I don't like to be defeatist, and always have a go at removal, but usually end up scrapping the mech.