Hey dear polargraphers,
I've managed to build my own polargraph according to the two instructables (http://www.instructables.com/id/Polargraph-Drawing-Machine/ and http://www.instructables.com/id/XY-Plotter-Drawing-Robot-Arduino-Polargraph/) and with some reading on this forum and the github.
It draws nice with some problems 🙁

Machine Specs:
Clone Adafruit v1 motorshield from ebay
L293D IC Chips which i had to piggy pack two times, put a DIY Heatsink with
thermal paste on them and added a 8cm Pc case fan to it. Now they get warm but not hot.
This might not be the best solution but it works ....

Nema 17 Steppers from Banggood (according to the second instructable i used 400steps per revision, 32MM per revision and a Step multiplier of 1)
Rated current (single-phase): 1.5A DC
Rated voltage: 4.8V
Power rating: 6.6W
Resistance: 3.2Ω
Step angle: 1.8 °
Static torque: 320mN.m (I = 1.5A)
Location moment: 12mN.m
Moment of inertia: 38g.cm2
The maximum load starting frequency: ≥1500pps
The maximum no-load operating frequency: ≥8000pps
Inductance: 3MH

Several Power Supplies:
Playstation One Power Supply
7,5V and 2,0A
Pc Power Supply
12V and 19A
5V and 2A
And the cheap one from Banggood (haven't tried this because it is making a relatively loud
beeping noise when plugged into the wall socket)
3/4,5/6/7,5/9/12V and 3A
I do have a couple more on my attic.

While using the PC power supply (12V and 5V) the Stepper Drivers (L293D) got insanely hot so i stopped using it.

Servo
The servo I ordered from Banggood arrived broken so i used one out of a Arduino starter kit
which works just fine
TowerPro MicroServo 9g SG90

I'm using an Arduino Uno with a Raspberry Pi 0wh (instruction from the github page). This combo works fine aswell. So i send the queue text file to the pi and the pi is sending it to the Uno.

Machine settings:

Here are some images of my machine

So now to my problems:
In short tests it all works finde but in my latest test which was much longer: i had some difficulties with the steppers and the power supply. Both got warm. I didn't burned my hand while touching them but they still got alot warmer then before.

Also the drawing got distorted. Wether its swaged or lengthened.

And it seams that on some point while drawing the machine looses it's homepoint and continues somewhere the page. I guess it's importand to say that it only very rarely moves the pen of the page so i think that my page dimension must be almost correct.

Here are some more pictures from my imgur album: https://imgur.com/gallery/QSbgd

Thank you for the very comprehensive description and pictures - really helpful!

Your test circle looks a bit distorted, but nothing a bit of tuning won't fix. As you've said, your page dimensions are probably almost right. This doesn't seem like a settings or a software problem, otherwise you wouldn't get anything recognisable at all. The bottom-left corner of your square looks like the pen or counterweight got stuck on something.

For your longer drawing, it definitely looks like you're skipping or dropping steps somewhere, but unfortunately it's something that's hard to diagnose without watching it actually move. Or knowing what sequence it is expected to draw in.

Some of it has drawn OK. Superficially, it looks like the lower half is where the most errors are. Perhaps you have insufficient weighting so the motors are struggling to move the gondola to the bottom half of the drawing surface? I can only guess.

If you watch it, and you see it jerk or fall suddenly then there is your clue, but it's hard to see. Actually usually easier to hear than to see.

You can easily test it though, just by using "move to point" to move the gondola to all the different points on the surface, getting further and further out from the centre until it stops being accurate. Until it starts skipping or falling. Or you could try drawing your square over and over and over, and you should end up with the same line over and over again.

You could try shrinking your drawing to fit more into a small area, and that might tell you if the problem is the length of time taken to draw, or if it's some mechanical problem with moving to certain areas.

I'll be blunt: I'm amazed that this even works as well as it does. Those 1.5A motors are seriously overloading even piggy-backed L293Ds - they're simply the wrong motors for the shield.

sn

I really think that distortion is due to your gondola design. Because the attach points don't pass through the pen center and they also don't allow the gondola to sit vertically, your gondola has an offset that grows the further you get from the center line.

You can see in the video that the pen is rotated away from where the machine thinks it is.

-Shorn