Two 28BYJ48 stepper motors L₁/L₂ positioning system

I used two 28BYJ48 stepper motors recently for αβ as well as xy positioning systems already, see below.
This time I used them for L₁/L₂ positioning system.
Not something new, the technique has been used by many blackboard drawing robots.

I did need this in order to move a black ball slowly, simple gravity pendulum was too fast
(animation speed below is 5.0).
Details as well as Arduino sketch can be found in this posting (again “two drops of superglue for the 28BYJ48s”):
https://www.raspberrypi.org/forums/viewtopic.php?f=43&t=252176&p=1570443#p1570443

“4 drops of superglue result in high precision PT camera system”

“Lego Arduino (28BYJ48 stepper motor) nanometer xy positioning table”

P.S:
For completeness, (only a single 28BYJ48 stepper motor used):
“How to build high precision (0.122µm accuracy) linear actuator”

b

P.P.S:
With three stepper motors (only one being a 28BYJ48):
‘“Uno” µm xyz positioning system for 0.21µm/pixel microscope(Raspberry HQ camera)’

Until now all my stepper motor controls were direct, mostly superglued.

Recently I added same technique used to focus microscope contactless to focus my telescope as well:

Now I used same stepper motor for turning turntable contactless (up to 25kg). This is first time I used timing belt pulley with timing belt, but not the standard way. 1:23.5 gear ratio results in very fine grained positioning, 4096/360*23.5=267(!) steps per 1° of turntable rotation with half stepping. I will use this for horizontal positioning of my telescope, standing with its tripod on turntable:
https://www.raspberrypi.org/forums/viewtopic.php?f=43&p=1771898#p1771898

I will add vertical positioning of telescope soon.
All three steppers will be controlled via 4x4 keypad and Arduino Uno, as described here:
https://www.raspberrypi.org/forums/viewtopic.php?f=43&p=1771898#p1761298