This is a refinement of Cut 4 Heckballs; Heckballs is an edge-lap construction-set design I developed based on some ideas Matt Heck showed me in 2005 or 2006.
Cut 4 came out more fragile than I wanted, and the smaller scale didn’t help its strength the way I thought it would. So this version makes the following changes, which took me a couple of hours:
The octagon size is increased back to 100 mm across the flats again.
The array of octagons is just 4×4 this time on the theory that I can reduce costs that way.
The tabs that hold the parts together during cutting are reduced back down to 800 μm tab width.
The divot diameter is reduced from 6 mm to 3 mm, which isn’t much stress relief, but also won’t weaken the pieces as much.
The corners of the slits are generously chamfered to ease assembly.
The slit opposite the elongated slit is removed, for strength and stiffness, because you can’t use them both at once anyway, and to cut down on cutting time.
Beams are added! They should put octagon centers four times as far apart as if the octagons were just edge-lapped at their edges. Also, the octagons they link should be coplanar, while they would have been in perpendicular planes if they had been connected with three intermediate octagons. The beams are a bit more area than the octagons. They still won’t work for the angled constructions I was originally envisioning because they will collide with other beams, and they have sharp corners, but it’s a start.
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 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.
I’d like to add some kind of engraved “JECVALZ” logo so that curious people can google it. I don’t know how much extra laser time that will add.
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.
This is by far the best version yet! This version is super awesome! The divots don’t prevent damage when octagon balls are squished, but they do reduce it noticeably. The 30-micron slop means that some slits still slide apart under the weight of just an octagon, while others are comfortably snug, but the chamfers greatly reduce the assembly difficulty I noticed with the tight 50mm version. Snap-fit joints (or bent or curved slits) will eliminate this inconsistency.
When I first compared the beam length against a string of octagons, I thought I had screwed up the beam length calculation, but I think I just hadn’t put the octagons together tightly. If it’s incorrect, it’s very close to correct.
This version took 13 minutes and 47 seconds to cut, almost exactly the same as the version yesterday, which didn’t have beams but had 32 small octagons instead of 16 big ones. The long sides of the new 259-mm-long beams took about 12 seconds each to cut, about 22 mm per second. The small octagonal double-divot slit bottoms took about 3 seconds each to cut, which is closer to 3 mm per second, so we can confidently say that the cutting cost there was due primarily to the 8 corners, so we can estimate that each corner costs about 400 ms.
All of this is happening on Max58’s fabulous Universal Laser Systems cutter (whose model number I haven’t noticed), driven by VLS6.60 with a 60-watt CO₂ laser. This means potentially about 24 joules per corner or about 2.7 joules per millimeter.
This works out to a higher cost of about AR$0.42 per second of cutting, including the materials and setup, while the previous two jobs were roughly AR$0.38 per second. This allows us to calculate that, within about 5%, each millimeter of cut on 3-mm MDF costs about AR$0.018 (US$0.0012), and each vertex costs about AR$0.16 (US$0.011).
When I write some code to measure the edge length and count vertices from the PostScript designs, I should be able to refine these numbers a bit, but I think it already provides me with an adequate linear model to use for cost optimization!
The beams still collide if I try to use a pair of octagons to assemble a vertex of an octahedron with beams for the octahedron edges. I can taper the beam tips to prevent this in the next version. For now, I’ve assembled a partial octahedron with five octagons at its top and bottom vertices, no horizontal edges (since I only have 8 beams), and an octagon or two at each of the other four vertices.
The 400 ms per corner means that cutting the “JECVALZ” or “JECVALS” logo I've been thinking about, which would contain 23 vertices, would cost about 9.2 seconds per logo. This would have added 2½', or about 18%, to the fabrication time. Laser-engraving the surface is likely to be faster, cheaper, and adequately durable.
I noticed my hands were itching a little, maybe from the creosote generated by the laser cutting, so I read through the US EPA’s information on creosote exposure. Apparently wood creosote can cause contact dermatitis and “comedones”, which are blackheads, and in serious cases can sensitize skin to sunburn; if eaten, it can lead to liver damage, but they say this is not a danger from dermal exposure. It also mentioned that rats died from being fed creosote-contaminated food for 96 weeks; the proportional amount of creosote fed to the rats would be 6.6 kilograms for a 25-kg kid. I think the amount of creosote you could plausibly absorb from Heckballs is about four or five orders of magnitude lower than that.
But I also plan to air them out for a period of time in order to reduce creosote levels, both for the smell and to prevent itching.
The 800-micron-wide breakable tabs on the parts were enough to keep the sheet from falling apart during fabrication; none of them got cut by the laser. But they broke apart easily by hand, unlike yesterday’s 1mm tabs.
An unexpected benefit of reduced outside divot size is that the resulting knobs on the ends of the scraps no longer easily slip through the divot holes, so now if you turn the scrap pieces sideways, you can slide them into the slits and hang them there.
Try the nonflat-slit-bottom thing suggested by the engineer at Max58.
Slit the scrap squares to make them connectable.
Taper the beam ends.
Write a predictive cost model.
Add snap joints or at least bent slits to make the fit consistent.
Add engraved JECVALZ logos.
Take more photos.