@veronica @lienrag

"But the offset to the centre seems to determine the radius of the inner circle."

Do you mean the whole thing is centered on the small circle? I thought the whole thing was centered on the large circle... the small one is an anomaly.

@veronica @lienrag

Moving the pen at a constant speed won't work I think? I feel like I'm missing something obvious.

I have a clay wheel I'm going to bring it out. Hold. on.

@futurebird @veronica @lienrag I think if you move it at constant speed across the middle (with a speed of 2r per revolution time) you get a cardioid.

@ptmesis @futurebird @lienrag I think it would be a cardioid if r was outside the first circle, but again, not sure.

Radial geometry always messes with my head

@futurebird Fascinating! 🤩 Here's a slowed down version of the interesting part. It's jumpy, which indirectly shows the speed up in the middle: more distance drawn between frames. Of course, the hand has to start and end with zero speed, but it's not clear to me how close to perfect sinusoidal one needs to be to get the appearance of a circle. Probably getting the speed profile symmetric is already quite a challenge? Would love to try this! @lienrag

@veronica @ptmesis @lienrag

I think you may be right about the cardioid it seems the easiest thing to make from playing around just a bit with it.

Also it's easier if it's moving faster. I wish I had a motor.

@veronica @ptmesis @lienrag

Ok that was the wrong video hold on.

@veronica @ptmesis @lienrag

Working slowly makes the errors causes by moving the pen worse. Speed is your friend for this. The wheel in the video must have a motor or she's kicking it. My wheel is just for hand building and won't spin for long at all.

@futurebird @ptmesis @lienrag I just plotted it, and as far as I can figure out, if you stay inside the radius of the outer circle, the "cardioid" is a drop-shape, but if you move the pen a little slower at the start and end, it should be pretty circular. I think this would be a natural consequence of drawing on paper given the friction between pen and paper.

The orange line is linear in time (steps of angle), and the green line is plotted with just the radial component of the orange line.

@futurebird @lienrag when I play it at half speed, it does look like there's some variation in the velocity of the marker. Not sure what kind of variation, but it might be sinusoidal , which is what would make sense to me as well.