But how does that work?
The "sensor backlash" is easy to measure automatically, with something like a homing routine or even as part of the normal homing routine.
Because it contains two components;
1. The electronic Hall switch/magnet hysteresis (should remain constant)
2. The actual machine mechanical backlash (the remainder)
if the first component can be quantified once, then every time the test is performed the remainder of the value must be the machine's mechanical backlash.
Quantifying the Hall sensor hysteresis
Well this process actually quantifies the machine backlash, and we work out both component 1 and 2 at the same time.
The easiest way is using a dial gauge, a tool used on metalworking Lathes and is commonly available for $40 or so.
Using the dial gauge to measure machine backlash
I used the setup seen below, which is just a metal block screwed down to my CNC machine table, and the magnetic base hold the dial gauge in position.
As the X axis moves right-left this moves the dial indicator. My dial gauge is just on 0.001" divisions (it's a cheap one), but it still shows pretty well to 0.0002" (ie; one fifth of a thou, maybe one tenth of a thou if I get fussy).
Measuring backlash has issues...
I knew from previous backlash testing on my machine there are some issues. The backlash should be tested in a "settled" position, as the vibration of your router and stepper motors will settle the position a certain amount.
I did the settling by pushing the axis hard with my hand, then releasing it and tapping it VERY lightly with a plastic screwdriver handle a few times. Then pushing hard the other way, and after releasing and tapping again checking the dial gauge.
Backlash on my machine at this point (machine is cool);
X = 0.0025" = 0.06 mm
Y = 0.0021" = 0.05 mm
That made me fairly happy, the machine has plastic leadnuts and there seems to be no wear at all after many months of use (although intermittant use).