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.