Another message so I can then attach photos....

The 'rotor' is the drawband drum and it does have a mainspring inside. Did this suddenly happen or was the typewriter like this when you received it?
 

I'm not familiar with the drawband that was originally used on that typewriter, but it looks like someone has replaced it, which is fine; I use fishing line myself for such repairs. Since the carriage is moving properly through half of its travel, it probably isn't a broken mainspring, which is also good. With any luck you'll just need to add more tension to the drawband to fix it the problem.

 ​First thing to do is to hold down the carriage release and make sure that the carriage moves very freely throughout its entire range of left to right motion. There shouldn't be any resistance or tight spots. Next, with the carriage all the way to the right, you'll want to make sure that the drawband (the clear fishing line in your photo) is not binding or getting caught on or is passing through any mechanical components underneath the carriage. Nothing should be impeding its movement as the carriage moves from right to left. You also want to verify that the drum is not binding on anything either, and that it's turning freely as it pulls the carriage back.

If all is good, then you'll want to add some tension to the drawband. To do this you'll need to wrap more of the drawband around the drum. In you bottom photo you can see the slack in the drawband, which should never be there. Take that slack and work it around the drum. It can be a bit of a finicky process, so be patient. You'll probably have to spin the drum manually (counterclockwise in your photo) to give you enough extra drawband to get it around the drum again. The goal is to have tension on the drawband at all times, but not too much, so only add one loop at a time and fully test the carriage movement before adding another loop. You might need to add more than one. Good luck.

Please try following my instructions for adding more tension to the drawband as your video reinforces my belief that is the problem you're experiencing. Although it is possible but unlikely, if you had a broken mainspring your carriage wouldn't function the way it does right now. Most broken mainsprings that I've had to deal where in drums that completely freewheeled and could not develop any tension at all. In a few cases, where the break or problem occurred where the mainspring hooks to the drum, it would build some tension before slipping back to a repose condition.

First rate close up photos! A pleasure to look at just for their quality, and the subtle use of Totem and Taboo as a support is intriguing - I suppose sometimes a book is just a book,

What did you use to take the photos?