A Week of Successful Failures

This week I experimented with a new 'Marble' puzzle, using direct-modeling CAD programs CoCreate and ViaCAD to create the helical geometry.  Previously I'd built these puzzles using Alibre, but it had continually exhibited problems with the helical geometry near the origin.  That should be no surprise, I guess, because Alibre's method of defining geometry would yield undefined results for structures that intersect the axis of a helix.  Direct-modeling CAD probably won't have that problem because I can define the basic geometry first and then apply a coherent twist as a second operation.

But my first attempt didn't work quite right.  Although the STL mesh was superior quality to the ones Alibre had generated, the ends of the helix had a slightly different pitch than the middle.  The pieces would fit together, but it require excessive force to get past the section where the pitches were mismatched.  I'd just applied the "twist" transformation incorrectly.

I modeled the puzzle again, taking care to allow sufficient gaps between pieces and applying a consistent twist to the whole puzzle.  Now the curves were accurate so the pieces fit together smoothly, but the gaps were too large so the pieces wouldn't hold together snugly.

This was an experiment with two new CAD programs, so I decided to build a simpler two-piece dissection as a learning exercise.  I tried to compensate for the problems I'd encountered in the two previous samples.  This puzzle emerged with an inconsistent twist, just like the red one, so the curves didn't quite match.  Evidently I'd compensated in the wrong way.

Like the red one, the puzzle had to be forced past the mismatched curves.  But then the pieces were unpleasantly loose because the gaps were too large.  Again I had compensated incorrectly, so instead of avoiding the faults of the previous two samples this puzzle exhibited all the faults of both.  Even so, that's a good sign because it confirms that these issues can be properly managed...I just got careless somewhere.

In the meantime I had tried to build a new revision of my flat maze puzzle, but I ran into trouble while cleaning the model.  The outer layers had cleaned up nicely, just like the last two test models, but I was completely unable to clean the leftover material out of the middle layers.  It clung stubbornly in the grooves.

In my last revision of this model I'd brought the two surfaces closer together so their respective grooves overlapped.  That created continuous loops and circuits in the middle of the model, but these middle paths weren't completely accessible from either side...so the material couldn't be pulled out from either side.

In SDView I added an elaborate web of small peeling cuts inside the middle layers of the maze to isolate the material into pieces that could be pulled out from one side or the other.

But the layers didn't laminate together properly when I tried to build the model, so I canceled it halfway through because the plastic was starting to come apart.  The last three versions of this model had built okay (other than entrapped material in the last) so I'm not sure whether this was just bad luck or an indication of some other fault.  Maybe there are just too many cuts in the model, or maybe the cutting knife needs to be replaced.

Despite all these experimental failures, I think it was a very productive week!

More Cooksey Inspiration

Years ago I tried to devise a two-sided puzzle where the pieces would somehow interact between two mazes embossed on top-and-bottom surfaces, but I couldn't devise a suitable way to make the pieces interact.  This sketch sat untouched on my whiteboard for almost a decade.

A helpful inspiration came from Oskar's adaptation of Richard Cooksey's cylindrical maze puzzle.  Rather than trying to navigate mazes on both surfaces at the same time, I tried to design a puzzle that allowed the user to navigate one maze on one surface at a time, but switch between the two mazes strategically.

I built the first model in transparent material with a layer of red on one side to help visualize the maze.  A major mistake was immediately obvious: the horizontal and vertical components of the maze were inadvertently embossed on the wrong surfaces.  It might be possible to trace the maze with a pointer, but it couldn't be navigated with second part I'd envisioned for it.

So I revised the data and built another test model.  Since I'd recently obtained blue material, I incorporated a layer of blue on one side and red on the other.  The maze was correctly laid out this time: it didn't look right visually, but that's the point.  Now I needed the special accessory for navigating the two surfaces.

I needed a second piece with posts that navigated the two mazes, but with sufficient side clearances to allow those posts to travel the entire width of the maze.  That called for an extremely wide piece.

This second model works exactly as I'd hoped, which means the maze concept probably won't require any further revisions.  But it's not a whole puzzle yet.  It omits the critical features of the intended design, particularly an objective, because the model was simply intended to test critical features of the maze.

Classic 45 Vinyl

I 3D printed this imitation of a 45-RPM pop single by designing a simple disc with a long spiral groove.  When a model's geometry has small channels, narrower than 1mm, the SD300 cuts the outlines but doesn't apply Anti-Glue so the plastic stays in one piece unless the user forcibly tears it away.  That makes it possible to scribe cosmetic markings like a record groove or the text on my Cuburr puzzle.

The last time I tried to build this 45-RPM record model with ordinary black material, the resulting disc was too transparent.  The grooves were pretty, but the transparency ruined the effect.  To make the disc appear dark and opaque this time I sandwiched a layer of red material and a layer of blue material between the layers of black material.

The grooves look realistic enough to the eye, but they're too narrow to play back on an ordinary turntable.  I tried it, but the needle just skates across the surface.  So this 3D printed record is nothing more than a visual novelty.  The files can be downloaded from Thingiverse.

A Box for Guile

I've been trying to develop a puzzle that requires a box with very, very specific dimensions.  I couldn't find a ready-made box of the right size so I tried building it with laser-cut acrylic panels, but the box didn't have the right characteristics...and I lost access to the laser so I couldn't continue experimenting with it.

To build the box on the SD300 I designed a flat model with hinges that would reproduce the exact interior I needed when the wall panels were folded.

For stability I added a ridge along one edge that could engage tabs on the side walls.

When the panels are folded into the right shape there's a groove around the top rim of the box.

A separate plastic rim snaps into the groove, thereby completing the box.

The finished box matches the dimensions of my laser-cut prototype, but it adds the lid mechanism that was missing from the laser-cut model.  Now I can build as many as I need.

Rupee Puzzle, rev. 1

India recently adopted a currency symbol ₹ for their rupee, which elegantly combines elements of the Devanagari letter र with a Latin letter R.  I dissected the shape into a puzzle with carefully-disguised cuts like other, traditional letter-dissection puzzles.  My effort was concentrated on the complex shapes in the upper part of the Rupee symbol, but the lower part was somewhat hastily finished.

I built my first test model in one piece, but with built-in dividing lines.

After confirming that the overall shape was recognizable I snapped the pieces apart along the pre-cut dividing lines.

It might be very difficult to assemble such a complex shape, so I also built and tested a plastic frame that might be used as a template to help someone assemble the shape.  It's a successful proof-of-concept but I'm dissatisfied with the overall shape because it lacks angled serifs on the two bars and the lower leg ought to be connected differently.

In the future I will try to develop a better Rupee dissection that incorporates the aforementioned stylistic features.  In the meantime I decided to practice by re-creating traditional dissection puzzle of the letter T.  This basic puzzle has been around for a century or more, but it continues to stump people despite its apparent simplicity.  Since it's an old design I shared the STL files for the T puzzle as "public domain" at Thingiverse.

Rob's Puzzle Page has some interesting pictures of other dissected-letter puzzles here.

Nikola Tesla and Blue

Nikola Tesla proposed a Valvular Conduit in which fluid (or gas) flows freely in only one direction.  There are no moving parts, but reverse flow is impeded by inducing turbulence at the backward-facing junctions.

I expected it to be an ideal model to build in transparent material, thereby allowing the user to see inside, but I found my model just a bit too transparent.  Yes, I could see inside the model but it was hard to distinguish the channels from the walls.  Ordinarily I would resolve that by adding a layer of red material, which is strongly colored so it makes a good contrast.

But a friend had recently hooked me up with a carton of dark blue VisiJet LD material, which is 100% compatible with the SD300.  I hadn't tried it out yet, so this seemed like a good opportunity to test it.

I built another model of the conduit using transparent material as before, except this time I put in the blue material for just one layer.  When I removed the unused material the outline of the conduit emerged in sharp contrast.

The blue material makes the conduit walls stand out vividly.

Now it's easy to distinguish the channel even when looking through the fully assembled model.  Fluids can move easily through the conduit from left-to-right because the junctions converge without creating much turbulence, but right-to-left flow is impeded because the junctions divide the flow and force it back across its own path.