The backlash fault (lost motion) comes from either one of 2 known faults on that model.
The
first place to check is the short belt between the Y axis motor and the
upper jackshaft. That motor is on the back wall of the printer and just
loosen the 2 screws and move the motor down to tighten that short belt.
That is the Y axis.
X axis has a totally different fault, On the
replicator 2 and 2X, the the known fault mode of failure there is the
belt clam section of the extruder carriage warps from heat from the
heater blocks nearby. This causes the belt to no longer be gripped
tight.
This is a much harder fix and requires a replacement carriage
or a creative way to clamp the belt again. I would NOT glue it as if the
carriage already warped, better to replace it.
Also the X axis belt tension is made by sliding the motor by loosening it's 4 mounting screws in the right hand side.
You
may or may not be able to use a replacement X axis carriage from
another brand like Wanhao or Flash Forge
https://ultimate3dprintingstore.com/collections/brand-new-2017/products/ultimate-3d-printing-store-parts-department-wanhao-duplicator-4-series-dual-extruders-carriageThey
use a much better clamping system on the belt, but minor mods may be
required to attach the extruder cooling bar. Nothing crazy, just I think
a little trim to allow the bar to sit on top as there was some tabs and
I know the 2X bar is much bigger.
Or, there is always Carl's trick
aluminum upgrades that solve some of this too and is compatible
https://shop.raffle.ch/shop/alucarriage-dual/Also, the X axis
idler shaft and pulley on the left needs inspected and greased. If that
pulley seizes to the shaft, then the shaft wrecks the slot in the left
arm, and then you are stuck replacing that plastic bracket.