I've had several similar ones apart, pretty simple. They have a shifter ring on a shaft which has two long fingers that slide in two grooves in that shaft. The fingers have nubs on the ends that slip into a little cup inside the gear which locks that gear in while all the others free wheel. Depending on where you slide ring determines which gear is locked in. I took mine apart, it was full of water and rust. I also just tore apart a 5 speed from a Murray RER and it was same setup. It seems to be a little tight going into each gear kind of what you described, but nothing looked wrong. I cleaned it and put it back together, still tight. It's my wife's coworker's, they will have to be happy with it cause nothing looked wrong and I dunno.
Here is a pic of mine I took apart, you can see the big ring across from the row of gear with the slot in the shaft, that's connected to the shifter plate on top.
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Here is a pic of mine I took apart, you can see the big ring across from the row of gear with the slot in the shaft, that's connected to the shifter plate on top.
