How can I repair take up reel when it doesn't spin?

I don't know exactly your make of projector but I have experience with Eumig 8mm and Eiki 16mm projectors. You need to check the drive belt/spring/clutch which drives the take up reel.
Sometimes the clutch pads don't pressurize enough or the drive to it from the motor may have a broken drive belt or dried up grease. You need to unplug (of course) and see if you can open the projector up and see what the issue is. I take it that the film moves through the projector ok and the take up reel is not turning.

Raymond
February 2018

Tread mill will start. Run for about 8 seconds. Stops at speed 3

Kay
May 2017