Circle packing, Origami, and RepRap

Eric Joisel's "Woman in Dress 2008"

Eric Joisel's "Woman in Dress 2008"

One of my interests outside MakerBot/RepRap is origami, the Japanese art of paper folding.  At it’s inception it was really only a hobby for the rich – the only ones who had access to such a luxury as paper.  Modern technical origami restricts one to only a single sheet of square paper transformed only through folding – no cuts, glue, tape, etc.

A lot of very interesting origami models have been developed over the years by some incredibly talented artists through a combination of experience and trial and error.  These kinds of models have so much personality they almost appear to be real – rather than mere squares of paper.  One of my favorite origami artists of this “genre” is Eric Joisel.  I still find it hard to believe his models, such as the “Woman in Dress 2008,” can really be made of just a single square of paper.

There’s been a movement in the last two decades to bring a more methodical and mathematical approach to design, sometimes with the assistance of a computer.  One of my favorite technical origami artists is Robert Lang).  His models tend to the more realistic, rather than representational (as with Joisel).  His insects, such as the stag beetle, are a prime example.

Lang has used his background in mathematics and origami to develop a giant collapsing/expandable lens – so that it could be transported to outer space and then deployed.  This allows a normal space craft to deploy a much larger lens than would otherwise be possible.

Robert Lang's "Stag Beetle BP, opus 477"

Robert Lang's "Stag Beetle BP, opus 477"

Unlike Josiel’s models which are typically totally unique and irreproducible by anyone (including Josiel!) Lang’s mathematically assisted models are usually carefully documented by diagrams or, increasingly frequently, crease patterns.  A crease pattern is what you would get if you totally unfolded a completed origami model.  Typically only the “major” structural folds are depicted in a crease pattern.

Brian Chan's "Attack of the Kracken"

Brian Chan's "Attack of the Kracken"

An interesting intersection between mathematics and origami is the problem of determining the most efficient manner of placing the most number of equally sized circle within the smallest possible area, called, “circle packing.”  The reason this is important to origami is that the center of each circle can be turned into an appendage.  Lang has developed a computer program that allows the creation of truly arbitrary proportions – any number of points with any kind of ratio of one appendage to another.

Brian Chan's crease pattern for "Attack of the Kraken"

Brian Chan's crease pattern for "Attack of the Kraken"

Even to someone who doesn’t have any experience with origami or the mathematics involved, the appearance of circles in crease patterns can start to make intuitive sense.  One of my all time favorite origami models is the “Attack of the Kraken” by Brian Chan.  (Check out the larger pictures of that model.  The entire thing is just one sheet of paper.  If you look closely you’ll see some of the tentacles are grabbing sailors!)  In addition to a picture of his final model he has also posted a picture of his crease pattern for that model, even labeling which parts of the model are derived from which regions of the sheet of paper.

I was reminded by all of this after reading Nophead’s recent post on circle packing as it relates to the optimal placement of resistors on a heated RepRap bed and reading Cory Doctorow’s Makers in which one of the characters is an avid origami folder.  As with RepRap, origami allows the production of complex models through an additive manipulation (layers with RepRap, folding with origami) of a simple material (plastic versus paper) in a methodical and repeatable process.

If you’re the least bit interested in origami, I’d highly recommend (in this order) Peter Engel’s “Origami from Angelfish to Zen,” a documentary on origami called “Between the Folds,” and Lang’s book “Origami Design Secrets.”  The Angelfish to Zen book is one of my favorite books for background on origami and a very accessible introduction to the hidden geometry  underlying even the most simple models (and real life too!).

Mendel FAIL

I can’t find my camera, so my camera phone will have to do. Here was my second attempt at printing Spacexula‘s Mendel production STL files.  Don’t even ask about the first attempt.

RepRap Mendel FAIL

RepRap Mendel FAIL

Spacexula offered some advice on how to fix this.  I have the Stretch feature turned on so that I can (hopefully) print better small circular features without the parts getting all globby.  He suggested turning Stretch off and just drilling out the holes if needs be.  Wise words from a man cranking out Mendel sets.

Unfortunately, I won’t have time to spent printing up parts until the weekend.  :/

These parts are not unusable.  Of the 13 parts on the sheet, I think five are probably perfectly serviceable.  The tall toothed gears are the most miserable parts – they are swayed and the teeth are basically intermittent bumps.  This has been one of my least successful completed prints in a long time.

Anyone want some Mendel parts?  Drop me a line.

March 21, 2010 | Comments Closed

Blender help?

Ball joint thing

Ball joint thing

I’ve designed a new part for printing on Bender1 .  Here’s a picture of the part.  I’m trying to see if I can print a working ball joint.  Obviously, it needs to consist of  breakaway multi-parts.

If this works I’d like to try using it as a component of a larger more complicated object.  However, Skeinforge throws a fit every time I try to skein it.  I’m uploading it here in case anyone can help me fix it.

Printable ball joint v5

  1. If you’re just tuning in, that’s the name of my MakerBot []

Peanut Butter Jar Mousetrap Insert

Peanut Butter Jar Mousetrap Insert

Peanut Butter Jar Mousetrap Insert

Here’s my entry in the Mouse Get! Challenge from Cathal Garvey.  I call it the “Peanut Butter Jar Mousetrap Insert.”

The idea is pretty simple.  Mice probably like peanut butter enough to squeeze into a small opening for a chance to eat it.  If the opening is difficult to wedge back open they might not be able to get back out.

So, buy a jar of peanut butter, eat most of it, leave some peanut butter at the bottom, cut out most of the top from the lid, print the “Peanut Butter Jar Mousetrap Insert“, put the insert with the pointy bits going inside, close the lid, prop it up somewhere so it doesn’t roll away, and wait for your peanut butter covered mouse!

Alternate alternate extruder controller mounting

Tony Buser’s post about his Alternative Extruder Controller Mounting reminded me that I’ve been meaning to show a better picture of my own setup.  I had blogged about it earlier, but not shown a good picture.

Side mounted extruder board, rotated motherboard

Side mounted extruder board, rotated motherboard

Here you can see where I’ve mounted the extruder board at the top left and how I’ve rotated the motherboard 90 degrees counter clockwise.  This gives me better access to the SD card slot.   If you don’t rotate the motherboard, the SD card slot is blocked by the extruder board.

Totally clear plastruder

Totally clear plastruder

Here you can see Leonardo Robot’s arm and how I’ve run the wires from the extruder motor and heater up to the board.

MakerBot + Bloom Box = Off the grid

Bloom Energy's Bloom Box

Bloom Energy's Bloom Box

You know, with a Bloom Box, a MakerBot, and enough plastic and time I could go completely off the grid.

Away from the things of man.

February 22, 2010 | Comments Closed

Patience grasshopper

Patience grasshopper, patience

Patience grasshopper, patience

Recent posts to the MakerBot Operators group show some people’s frustrations with this growing company. 1  Yes, they’re out of stock of electronics and other parts, but they’re also doing their best to crank out as many kits as possible.

Overall, I’d rather have them churning out robot kits than keeping spare parts in stock.  The plans for all of the electronics are open and free – you could have someone else fabricate them or build them yourself.  Still others have started up businesses selling lots of replacement parts and even upgrade kits.

We might be impatient for our kits, but they’re literally devoting their weekends and free time to getting these kits to us.  In fact, it’s their feverish dream to get a MakerBot kit into your hands.  You’re just not going to get this kind of devotion and service anywhere else.

I have one piece of advice if you’re waiting for your kit to arrive or replacement parts to be back in stock:  start designing stuff right now.  You already know what you want to build.  Just create a library of things you want to churn out.  Upload them to Thingiverse, get feedback modify, and improve them.  Heck, improve designs posted by others.

Your kit will be here before you know it and you’ll be happily (and woozily) sniffing ABS fumes too.  :)

  1. Photo courtesy of changhg []

Making Blocks II

Lego nubs and underbits

Lego nubs and underbits

My lego prints connect slightly better to other printed legos than real legos.  I suspect this is in part to the ridged texture to both parts.  This also makes me think that printing legos is a fool’s errand.

While lego nubs are circular, the parts they fit into touch the circular nubs tangentially.  For instance a nub fitting into a corner piece would be held in place by two straight sides and held against a circular tube.  The picture to the right shows the underside and nubby bits for several lego (lego compatible?) pieces.  This system probably works because of the exacting tolerances of real lego parts.  I’m guessing they tested the nub heights and contact points to find an optimal mix of most of the same criteria I have for an interconnecting building block system.

Without tighter printing tolerances, I don’t think three tangential points are going to be enough to hold printed parts together.  Thus, it may make sense to have taller nubs on printed parts.  Then again, the ridged nature of printed parts may allow them to better fit together without having taller nubs.

One benefit to having circular nubs is that you can make interesting components where pieces pivot.  But, this is more of a lego-hack than an actual useful feature.  I’m not as concerned about this particular usage because I could always design a printable pivoting part.

So, other than that one narrow usage, why circular nubs?  Why not circular nubs with circular holes?  Why not square nubs with square holes?  Or circular nubs with notches in them?

February 18, 2010 | Comments Closed