The escapement wheel with the teeth? On most models it is held in place with two screws. Those may have become loose, but to tighten them you must remove the carriage.

Ive never owned an olympia, and the only carriages I have removed had those style escapments.  I would think that its certainly possible for the bolt to be loose, if it had a rough shipping life sometime in its life, maybe the escarpment took a beating and the bolt hole stripped and expanded a little?

KatLondon wrote:

The thing that's happening underneath is that whatever is holding the toothed wheel in place - the bolt, presumably - has clearly come out of place, because the toothed wheel, that usually controls the movement of the carriage, is loose, and is moving freely - within the confines of the small space in which it's trapped,

Sounds like it might be a relatively easy fix, which would of course make your £10 a good investment. For some reason -  I haven't been able to figure out why - the Splendid models sell for obscenely large amounts and have to be the most expensive of the Olympia ultra-portable models. I've only come across one escapement issue with the couple of dozen SF machines that I've handled, and it was a case of frozen bearings as a result of old, congealed oil/grease, which is a maintenance issue as opposed to a design weakness. Good luck in getting your Splendid working, as Valiant pointed out, they really are nice typewriters.

Hello Kat !  Your problem is caused by one of two things.  If you are lucky, the escapement wheel pivot has unscrewed itself from the machine's cast frame, leaving the escapement wheel to flap about.  If you are unlucky, the pivot will have broken clean off.  It does sound like the latter.  Remove the bottom plate so that you can see underneath the machine.  Look at the escapement area and you should see the lock nut that prevents the escapement wheel pivot from coming undone.  If it is present, the chances are that the pivot is broken off higher up.  If you cannot see the nut - just a threaded hole - you might be in with a chance.  To get proper access, you need to take the carriage off its rails.  There is a work-around which does not involve having to do this.  You need to remove the platen, paper pan and feedrolls.  There are a couple of holes in the bottom of the carriage which will line up with the escapement wheel pivot.  If the pivot has simply unscrewed itself, you can access the screwdriver slot lining it up with one of the holes.  Screw it back into place, and then you will have to find a lock nut to fit the end of the pivot from underneath to prevent it coming loose again.  I hope this helps 

We're getting off-topic for this thread, but this might help you. I've never tried going through the carriage as Tom suggested, but then again I usually remove the escapement wheel so so I can clean and oil its bearings.