If you're thinking about removing the carriage on your typewriter, stop. In rare cases does a typewriter carriage need to be removed when cleaning or servicing a typewriter. I run into people all the time who have taken the carriage off their typewriter and have trouble reinstalling it. Many antique typewriters end up in the trash for that very reason.
There are exceptions to every rule and this one is no different. A few typewriters are made in such a way that the carriage comes off the machine fairly easily. I'm thinking about standard Olympia typewriters as an example. By moving a couple of levers, the entire carriage assembly can be lifted off the machine. I love that! However, that's not usually the case. Of course removing the carriage isn't usually the problem. REINSTALLING the carriage is where people run into difficulty and sometimes get in over their head. Small ball bearings get lost. Any number of things can go very wrong when installing a typewriter carriage.
Of course, if you have specific questions, I'd be happy to try and help. Just shoot me an email at firstname.lastname@example.org.