Brass bushing on my popcorn maker

Please post the make and model number of the appliance. Without that, I can only tell you to check whether the motor is getting voltage and verify that the bearings and any gears are not gummed up, worn out or jammed.

The motor output shaft bushing might have came loose I have seen where it falls out of the motor and the shaft becomes real wobbly and it will cause excessive wear in the kettle cross bar bushing too. also make sure the cross bar and lid assy. is not come loose from the kettle.

The V-1401 has a power bowl lift that is belt driven by the same motor that is used to mix. Remove top cover to check the belt. If belt is good and not slipping, is the operator handle working on /in the bowl lift gear box? If not, could be broken shear pin on handle or worn out parts in gear box. Next thing to check is the output shaft of the bowl lift gear box. If it is turning when the operator handle is engaged and the bowl lift jack shaft is not turning there is a broken shear pin between the output shaft and jack shaft. If everything is good to this point the bowl lift yoke has a large brass nut on back side of it that the jack shaft goes through. If the nut is worn the bowl lift yoke will slip, fall and/or jam. to unstick and lower the bowl , one can turn the jack shaft by hand. WARNNING : if the nut is worn enough the yoke can drop suddenly and it is very heavy.

Sounds like a worm gear problem to me, it's impossible for the motor (armature) to move far enough to not drive the gear. There are driving pins in the system from fuse gear to paddle.
1) in the fuse gear
2) inside gearbox above planetary joining shaft to bevel gear
3) through planetary and shaft

There is also one joining the little gear inside the planetary to the shaft, doubt you'd break that one though.

Replacement parts are not available for any Nostalgia Electrics equipment. Sorry.

This is a hard symptom to troubleshoot, it can have many different causes.
1. Is the stire wire in the kettle straight and spinning freely?
2. Does the agitator shaft spin freely in the crossbar?
3. Is there a small needle bearing on top of the spur gear attached to the kettle? it is a small metal circle that spins independently of the agitator shaft located ontop of the kettle spur gear, it can fall off.
4. The plastic block in the cabinet roof that has the motor spur gear coming out of it, is it cracked?
5. Does the motor turn when the switch is turned on with the kettle in the dump position?

All of these can lead to an answer of why the agitator stops turning while popping.

This is a really old question, but.

Check to verify that the needle bearing is not missing. I is a small round part above the gear on the agitator shaft. Also see how worn the crossbar bushing is. There should only be a minimum of loose play in the shaft moving it side to side.

Make sure the lid assembly is not installed backwards on the kettle casting. The lip part of the kettle is the front or left side, and the cord should come out of the bottom towards the doors/operator side.

Best guess is that the gear for 3rd speed is seized together with it's brass bushing and the center, large transmission shaft. I don't recall which gear is for 3rd, but the transmission has two gears (2nd and 3rd speed) which have brass bushings in them. The brass bushing should spin freely on the center shaft (when in final position - sometimes they pull off the shaft tough, but spin freely when in final position, my opinion is that this is OK), and the gear should spin freely of the brass bushing.
My guess is that the 3rd speed gear, being seized to the center shaft, cannot freely idle on the center shaft, which would result in being stuck in 3rd gear.

Short answer: something is worn/broken inside the mixer's transmission.

Longer answer:

Since none of the three gears operate, the problem is most likely on either the worm gear shaft (probably the brass worm gear itself) or the "transmission shaft" (ironic name as all three shafts could be called transmission shafts). If you're up to the task of disassembling the transmission, which is a very messy task, you'd probably find the problem on one of the two smaller shafts inside the transmission. You'll most likely find either a broken key or worn brass worm gear. Both of these items may have enough holding strength to operate under very light loads (such as an empty bowl) but slip once a load is presented.
Also check the planetary key. Remove the planetary by removing two nuts on the underside of the transmission, where the attachments attach (careful, as the whole thing will drop once the second, thin nut is removed). You will find a long key on the shaft (or in the planetary gear, whichever one it sticks to). Make sure it's not broken, and re-attach the planetary.

The black plastic clutch has a left-handed brass threaded insert. Temporarily remove the motor to hold the shaft and remove the brass insert by rotating clockwise.