This is a refinement of Cut 5 Heckballs; Heckballs is an edge-lap construction-set design I developed based on some ideas Matt Heck showed me in 2005 or 2006. PDF output to send to laser cutter, parametric model in PostScript.
Cut 5 was super awesome to play with, but it still tears the octagons if you twist the joints, for example by squishing a ball flat. So it occurred to me that instead of just trying to round corners, I could make some further cuts so that that particular twisting motion wouldn’t produce such extreme deformations. As a bonus, this extra cut doesn’t add slow-to-cut corners the way the outside divots do. But it might turn out to make strength worse rather than better, since it creates a sharper corner, the sharpest possible corner in fact.
I’m trying a variety of different overcut depths on the octagons on this cut to see what works best.
This version also adds a laser-engraved logo, tapers the ends of the beams so that they won’t collide if you stick them all over a ball, and moves the parts away from the edge of the stock (since they asked me to do that).
Here are the things I still want to do but haven’t done yet:
Slit the scrap squares so they also work as connectable pieces.
The octagons (and divots, if any) should be hexadecagons so their corners aren’t as sharp, both to reduce the stress concentration factor and to make them easier on your hands.
The engineer at Max58 suggested that maybe I should let the divot slope go down into the bottom of the slits instead of letting the slit bottom be perfectly flat, thus reducing the width of the divot. Presumably after some crushing this would lead to a kind of Pringle shape at the bottom of the slit.
Sprung snap joints! That will escape the conflict between being easy to assemble and not falling apart a lot better than just fine-tuning slit widths. Even Tinkertoys have sprung joints, although without snaps; that’s what the slits in the ends of Tinkertoy beams are for.
Take more photos.
The code of this version is really messy from just hacking some things in, using the smallest change that would make them work. But that’s kind of a general feature of this design, because for things like chamfers, nesting, common-cut elimination (which is sort of part of nesting), retaining tabs (there’s probably a real name for this?), and assembly interference avoidance, I’d really benefit from a more capable CAD representation with constraint solvers and 3-D visualization and whatnot.
At some point I feel like I’m going to have to bite the bullet and either switch to a real parametric CAD system or write one. ImplicitCAD, BRL-CAD, FreeCAD, and SolveSpace have been suggested as options. I’m pretty sure I’d be unhappy with ImplicitCAD because, by design, it doesn’t have a GUI.
The worst case for beam collision is when they’re at 45° to the common axis of the two octagons in a ball; they’re both almost touching the center of the ball in that case. So the question is what angle I need to taper the beams at so that their tapered sides are parallel with those of the neighboring beam in this case, and would intersect just before the center ball.
The planes of the beams are at a 1:1 slope to the common axis, and so their intersection line is at x=y=z. The center line of one of the beams, by contrast, is at x=z and y=0. So cos θ = normalized([1, 1, 1]) · normalized([1, 1, 0]); these have components of respectively 1/√3 and 1/√2, so we have 2/√6 = 2√6/6 = √6/3 = √⅔. This suggests that θ ≈ 35.26°, which is an unexpected result, but I think correct.
It took me a while to get the math for this right, and I’m still not totally confident that the taper is okay. And I had to cut the chamfering to zero to get it to not overlap.
I shortened the slit part of the beam in order to be able to chamfer properly.
My original cost estimate was 897" and AR$359 (if engraving was free) to AR$397 (if it cost the same as cutting), but instead the quote they sent was $540. Also, they suggested that since the laser-cutter rasters horizontally to do surface engraving, maybe I should rotate the logos (and the pieces, if necessary) to be horizontal on the sheet in order to reduce the engraving time. On changing the engraving to marking, the cost went down to $420, suggesting that the cost of marking is about 1.6 times the cost of cutting, although I may be exaggerating the precision of that AR$359 number.
It took 2'25" to do the marking, which was all first. I unfortunately didn’t properly note the time to do the entire cutting and marking operation, but I think it was 17 minutes and change. The engraving involved 967 vertices and 893.2 mm of cutting (!!). If we estimate that the vertices take the same 60 ms each, they account for 58.02 seconds, leaving about 87 seconds, for about 10.3 mm/s of cutting speed.
This 2'25" would account for AR$58 at the estimated cost of AR$0.40 per second, leaving $362, almost exactly my $359 estimate.
While not exact, this should enable me to extend the cost model in a reasonably accurate way to future cuts:
The overcut thing doesn’t really work at any of the lengths tried, 0.5 mm to 9.5 mm. Twisting connected octagons until they are flat still tears the MDF; the square “tongue” at the bottom of the slit gets twisted by the other slit, which I didn’t anticipate, but should have.
This is a disappointment, because it was a lot cheaper than any of the other things I’ve tried to reduce the cracking.
The beam taper is almost exactly right, although since I didn’t account for the beam thickness, they press against each other a bit, which would be fine except that it has a tendency to lever balls apart. The shortened beams interact in a very unfortunate way with overcuts: bending stresses in beam-beam joints apply a large moment to the “tongue”, breaking it off.
I brought out Heckballs at the birthday party of my roommate’s 8-year-old son. Very rapidly I had eight or ten parents playing with them. Later, lots of six-to-ten-year-olds came inside and started playing with them. Unfortunately, one of the adults came up with the stupid idea of setting up a tower-height competition among the kids; this generated competition for resources, exclusion of the less physically aggressive kids, and unimaginative architecture.
This spectacle of a height competition with structures unavoidably consisting almost entirely of beams joined end-to-end, a metaphorical penis size competition, often listing over at one or another awkward angle, made me realize that I’d inadvertently designed the beam taper as an almost perfect cartoon penis head.
In addition to the designed-in cube and octahedron geometrical possibilities, I found that it’s possible to join twelve octagons in a ring with sixfold rotational symmetry. Each octagon is at a 135° angle to an octagon two prior to it; such alternating octagons around the ring are on a six-sided pyramid. I wasn’t expecting to be able to get sixfold rotational symmetry out of 45° and 90° angles.
The variable slit width due to laser-cutting imprecision continues to make fit tightness inconsistent and unpredictable, since I still haven’t done snap joints.