When examining your “Calibration Plot” and really trying to understand how the diameter of the egg affects the shape of plotted objects I made a small program in python to plot the values.
I have used a term I called ‘Aspect Ratio” which is the length of a line segment made with 1° of travel along the pen axis divided by the length of a line segment made with 1° of egg rotation. The aspect ratio is plotted as a function of position on the egg.
To have a circle appear to be round in the middle of the egg it has to be drawn as an ellipsis which is 1.48 times as wide as it is tall. At the end of the eggs the value changes to around 2.4
The plot is based on a chicken egg with 42mm diameter and 58mm length.
(To read the diameter from the plot you have to go from negative value to positive along the y-axis.) I have the pen motor shaft set 10mm lower than the egg-motor shaft and about 2mm from the middle of the egg along the length of the egg for minimum “tracking error” with this egg size.
(Red line represent the egg shape – ☺)
XKCD Style Plot
Will make a ‘Calibration plot” based on the values from this plot for verification, stay tuned.