GCMC includes cycloids.gcmc, a test program producing a fixed set of hypotrochoids and epitrochoids, more commonly known as Spirograph patterns:
I’m using them to get familiar with bCNC’s Workspace Coordinate System settings and to exercise the MPCNC hardware; ya gotta plot before you can cut.
Most came out fine, but some showed distinct wobbles:
Tight curves and higher speeds produce more wobbles:
You’d probably never feed a wood router over 6000 mm/min = 240 inch/min, so this isn’t as much of a problem as it might appear. Also, I expect a few pounds of router will have fewer wobbulations than a weightless pen hung on a thin plastic mount:
Just one more thing to keep in mind.
The Smell of Molten Projects in the Morning 
Just think how difficult it would be to get those extra wobble patterns IF you wanted them! Most are probably from what are already obvious to you; a thin plastic frame on a long moment arm supported by a single screw and using a pen attached with a nylon tie. I remember making lissajous patterns attached to motors with duct tape using front surface mirrors decades ago that changed based on motor rpm and centrifugal force acting on the duct tape. It was pretty random until the mirror let loose from the tape!
The mildly surprising part was how repeatable they are: re-drawing the same pattern with a different pen overlays the first, including the wobbles! Of course, given the same stimulus, it should produce the same output, but …
Most likely it’s a combination of belt slap and torque around the big central assembly. There’s no damping worth mentioning anywhere in the thing, so any resonances have free reign.
Try plotting a step response like you would on an oscilloscope, that could be interesting and useful especially if you try it in both axis, … GRBL might interfere in completely square corners, so maybe try rounding them a bit.
Good idea!
I think truly square corners will test the acceleration settings, too, because GRBL should slow down in order to maintain the cornering tolerance, which is what I want in the general case. A testcase of high-speed squares, each rotated by 5 (-ish) degrees from the previous one, should shake out the wobbles.
Interesting on the star cycoid that the wobbulations start/end right at the pen-up/pen-down point — do you know offhand which it is (i.e. which direction that was drawn)?
I think the wobbles happened going counterclockwise around the figure just before the pen went up; it’s oriented roughly as in the upper picture, with the start/finish star point aimed toward +X. So the pen was decelerating to the stop along more-or-less the same angle as when it accelerated along the upper edge.
Having spent far too long leaning over the thing, there’s no obvious place where the resonances happen: touching / pressing various spots doesn’t change the sound or the vibration in any way. Which means it’s buried inside the central assembly or I just haven’t risked my fingers enough.