OK…so it has been a couple of weeks since my last post here: In part, I have been distracted reviewing the new LEGO Stationery line for New Elementary.  You should go over there and have a read of it sometime.  I’ll still be here when you come back.

This post was inspired while considering ‘What sets the MOCs that make me stop and say “Wow “apart from the others?’ – especially as a landscape inspired model.  There is no doubt that, for me, some of the most eye-catching constructions out there occur when the strict 90 degree world of LEGO is able to be overcome.  This ‘going off grid’ can be achieved at multiple levels: using a turntable base and octagonal plate to turn the action 45 degrees; using hinges such as might otherwise be used to open a playset building.  The problem with some of these techniques is that they do not easily clutch to the underlying plate.

So let’s look at a technique that I saw used by James Pegrum in Bricks Magazine earlier this year Issue 10, and also issue 6.

This will involve some geometry (sorry).  Let us consider a 2 x 4 lego plate, on a base plate. Next, place a single stud under opposite corners. Considering the intervals, this forms the hypotenuse of a triangle, with opposite and adjacent sides measuring 1
step and 3 steps respectively. The distance between these connection points is the same as the distance between the other two corners of the 2×4 plate, and so you can rotate that plate until those corners meet the studs.

Tan(The angle of the offset)  = opposite/adjacent

=1/3

inverse tan (1/3) = 18.5 degrees

But this only accounts for half the rotation we see…(do this with 1 x 1 and we get an angle of 45, but rotation is actually 90) – not only does the offset rotate up from the baseline, it also rotates down. So in this case =37 °.

SO angle of rotation = 2 x inverse tan(opposite/adjacent)

Here are a few examples:

Now, if you wish, you can carry this exercise out to an unreasonable extreme.  Here are the placements for the examples above, and the closest approximations I could find to ‘even 10’ degree angles.  Lego does make this a little challenging.  At least these ratios will be achievable within the scale of most MOCs…

Did this technique change my life?  Probably not. Will I employ it in the next 12 months? Almost certainly. I appreciated the fact that it made me pull out some trigonometry just at the time my kids are starting to learn about it, and helping the cogs in my head to turn  again.

Do you have a favourite way of going off the grid ( that doesn’t involve a bunker, solar panels, bow and arrow and a vegetable patch?)

Why not comment below.
Play well.