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Showing posts with label angles. Show all posts
Showing posts with label angles. Show all posts

LEGO Techniques - A Frames

Happy New Year!  With a new year comes new parts and I've got a small slew of part based technique posts planned.  We'll start off the year where everything else starts off, at the very beginning.  With the alphabet that's with the letter 'A'.

A is for A-frame.

Thanks to the keen eyed Caperberry and the trigger finger of BrickOwl, this part was brought to my attention before release of any sets featuring it.  I had to obtain a few for my angling pleasure.

It's a very odd part.  It's like a fixed 1x4-1x4 plate hinge.  With struts in the middle.  And no hinge knob.  And it's at exactly 45°.  While 45° makes a lot of sense, I sincerely hope that a similar 60° plate is in TLG's future.

My first thought was to connect 8 of them together.  Sounds legit, right?  The result is a very fine crosshair, spider web, or basis for an octagonal SHIP component.

Overlapped A's
Adjacent A's
There's also the possibility of reversing them.  I remember how cool I felt when in third grade I was the first kid who had learned to draw an 8 pointed star without lifting my pencil from the paper.  I taught my buddies and we created a secret society out of being able to draw octo-points.  There's a lot of geometric potential here.  Paging Katie Walker...

The inherent problem with 45° is that the hypoteneuse will never be an even number.  Thankfully we don't have to go TOO far before we get within a relatively acceptable tolerance.  With 5 stud legs you can force a 7 stud hypoteneuse.  To wit, 5² + 5² = 25 + 25 = 50.  √50 = 7.071.  Pretty close tolerance at 1%.  Theoretically you could do legs of 10 studs.  But while the tolerance is still 1%, that's about 1/7 of a stud in distance or near 1mm.  Another sweet spot (known to roof framers for creating hips) is that 12² + 12² = 144 + 144 = 288.  √288 = 16.97.  This is even closer at 0.1% off, or about 1/34 of a stud.  That's 1/4 of 1mm; hardly even noticeable!  Other variations are possible though the size of your built up brace is going to get very large.

You might also stagger them to get a nice little spacing effect.  Mathematically speaking there should be space enough for a sideways tile.  Practically speaking, there is.

Then I wondered what could result if they were connected in 3-D.  I get a little lost with 3-D angles myself.  Advanced Trig was not my best subject.  Mostly I go off of trial and error with a pinch of gut feeling.  Nonetheless, I was able to make a nice little stand for half of Bespin.

These parts may not be earth shattering in the job they can do, but they certainly offer a lot of stability not seen in parts like plate hinges.  I can see this being the next big thing in 2014.  Not always a featured part, but a highly utilized structural part.  If you'd like to play around with a few, I've got 16 shiny new ones available for sale in my store.  Make an offer on multiples.

LEGO Techniques - On Angles

If you don't follow Caperberry's New Elementary, you should.  He posts about new elements that are being released.  Of special interest are the new molds or designs.  He recently highlighted the new A-frame plate that will be in the upcoming Ninjago sets.  This piece will allow for a rigid 45° angle without the hinge pivot that would otherwise get in the way.  We've got a smattering of rigid 30° connections, but very little that is adequate at 45°.  This will be a fun new piece.

The 1x2-1x2 plate and brick hinges have a distinct advantage though.  They can be made to swivel in any angle from 0 to 180°.  But for their multi-lingual advantage, they suffer one problem.  The pivot can often get in the way structurally or aesthetically.  And not just on one side but on both sides of the hinge.  On small builds, there's not much to do about it.

But there is a way to lock plates together and achieve angles.  A while ago I posted some brick built solutions for an equilateral triangle.  I'm going to open up that can of worms (Pandora's box?) and look at some of the other simple ways to create brick built angles.

The premise is this; touch two 1x8 plates at their corners.  Then take a 1x3 plate and attach at each set of points going out.  By the time you get to stud 7 and 8, there's not much difference in the created angle.  The result is the same as using a plate hinge, just without the pivot.  The problem with this construct is that the two studs closest to the origin are still a touch more than 2 studs wide.  So it cannot effectively be connected.  The better solution would be to use 1x8 technic plates.  These should be a staple of any MOCers collection anyway.

Since a system and technic 1x8 would be so close in angle, I chose not to feature both.  You can see though how to achieve some different angles with this technique.  But notice how quickly the angles drop at first before tapering to a slow crawl.  This is a good visual example of a hyperbola.  If you were setting out to create a circle, the only useful one would be the last one.  The rest of them don't evenly divide into 360°.  If you've seen my slope and wedge charts, you can see how these might be useful in conjunction with those pieces.

Of course there are many more uses to these than making large circles.  I imagine wings or gangways with jogs in them.  There are a plethora of other options as well.  You could run this exercise with a 1x4 plate instead of a 1x3 as the spacer.  Or you could lock the 1x3 plate on the number 1 studs and use a 1x4 for the angler.  Or a 1x6.  Or do all that further out on a 1x12.  I suppose someone could create a whole matrix of possibilities, or possibly a little GUI script that will calculate it all out for you.

Let me know when you're done with that, Ace.  I'm headed to bed.