The hinges are pretty simple. Basically two hoops stuck to the wall, one hoop between them stuck to the door and a pin down the middle.
Just in case anyone is thinking of coming round to my house and breaking in by removing the pins and taking the door off, I should tell you that there are allen screws holding the pins in, that can only be accessed when the door is open. Also, even if you did get the pins off, there are plates and grips on the hinge side of the door so it will only open by swinging. So when it's locked, it's locked. The door designers are one step ahead of burglars, although I sometimes think the people who made our windows have similar moral solvency.
Although simple, the geometry of the door means that the axis of the hinges must be in the same place, so we couldn't just replace the hinges with any others: we had to get the same hinges.
To replace the broken hinge, they needed to
1. take all three pins out,
2. remove the door,
3. remove the screw from the broken part of the hinge,
4. replace it with a new unbroken part,
5. put the door back in again,
6. put the pins back in.
Sounds simple, but the door weighs over 100 kg.
I was expecting them to have some fancy door installing equipment that would be able to hold the door in the right orientation and steadily move it away from the opening. They put a blanket underneath the door, and one of them rather quickly took the bottom pin out while the other was holding on to the door. I wrote above that the first step was to take all three pins out, but in fact the top hinge was free from the door, so only two pins needed removing.
I suggested they should put something a bit more substantial under the door to keep it at the right height. They first asked if I had a piece of wood, but then I held on to the door while they fetched some from their van.
I began to think that I could have done this myself, with the help of a couple of strong mates. But they did the job quickly and effectively. Fancy equipment was not necessary, and they didn't need to use lasers to set anything up. They just had to take out the old part and replace the new one, and it would be in the right place if they counted the number of exposed threads.
After fixing our front door, they were then very helpful fixing a problem with our other door. I'd already replaced the latch plate, which is definitely within my mechanical ability.
The other external door has been gradually sagging, since once again the manufacturers seem to have skimped on the part. This has meant the whole door is five or six millimetres lower than it should be, leaving a gap at the top allowing cold air to rush in.
They recommended getting new hinges, but to fix the problem in the medium term they cut out rectangular shims, and while one of them was lifting up the door with a combination of bits of wood and a crow bar, the other unscrewed the hinge and put the shims underneath. This lifted the door up, and the difference to the airtightness of the door is amazing. There are no longer icy blasts of air coming into that room, and a couple of days later it was back to the temperature in the rest of the house. Just in time for the end of winter!