RD still wont shift gears Schwinn 12 speed
 

I have a Suntour allegro 12 speed rear derailleur that wont shift it just stays in the center gear shown. I can push down all the way on the shifting lever on the handlebar stem. RD remains motionless as you try to shift. Its not the tension screw either because I can loosen and tighten.
Maybe its the H & L limit screws? They're hard to turn.

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OK, start with a basic process of elimination. Remove or slacken the cable, and see if you can get the RD to move by pushing the lower body in while pedaling. If so, and if with the cable off, the RD can be pushed in and springs back, then it's OK.

OTOH - if you cannot move the RD by pushing the lower body in, then you need to look within it for why. Possibly a prior owner brought the limits in against each t er to lock it in position, or possibly the pivots are corroded and bound.

Either way, the detective process starts with narrowing the list of suspects to a few, then checking them out one by one.

With the chain off check to see if the pivots move freely. I've seen a ton of old derailleurs gummed or rusted up. If frozen then remove and spray/soak in wd40 or your preferred penetrating oil. I've saved a few by doig this. Sometimes the pivots are rusted solid and depending on the model it may not be worth taking apart to rebuild. The lube will probably help free up the limit screws as well.

It could be for a number of reasons but it sounds like the High and Low screws are in to far. it also could be a stiff cable its worth checking the cables moves freely