When building some technic MOC, I find that switching orientation is a part that is time consuming and very ad-hoc. Switching orientation is the equivalent of SNOT (Studs Not On Top) for technic build (I don’t know of a more official term). I usually end up randomly trying the connector du jour until getting something that works. It’s now time for a more rigorous approach.
One of the greatest books about lego technics (The Unofficial LEGO Technic Builder’s Guide) does contain a wonderful amount of information, but not much about studless orientations connections. It’s probably too evident for builder with this amount of experience.
How many orientations are there?
Before figuring out the connections, we need to figure out how many relative position we have. Let’s consider the relative position of 2 studless technic beams, we will have the beam of reference in red and the one we’d like to attach in black.
Since we are ignoring translations for now, we can enumerate this in term of rotations. In 3D we can code rotations using Euler angles. There are many choices in term of conventions, here we’re going to stick with the closest to some modeling software like stud.io. In stud.io, you can rotate around the Y axis using up/down and around the Z axis using left/right. The rotation are extrinsic: they use the scene axis, not the brick axis. With this, we chose to use Euler extrinsic rotations given as z-y-z.
Taking into account the symmetry of the beams and given that we’re only interested in perpendicular constructs, we have 8 possible rotations:
However, of these 8 rotations, we can eliminate a few of them
|just a rotation around z, it’s the same as|
|this is a rotation around z of , for beam this the same as|
Note the color here, this is to highlight that this is equivalent to the .
That’s a rotation around the X axis.
After that, we are left with:
So we have 5 possible relative orientations. Now, we can start enumerating different way to connect those. I’ve been trying to give them some names, but those are not the best…
That’s the most basic one, and usually it’s not a problem to set up this one.
This one is very useful to provide strength: for example to prevent several parallel beams from separating.
The next connection can be found on the Mine Loader (42049) it’s pretty useful to serve as guide for axles, but not too strong for torsion.
Basic connection to build any linkage:
If you don’t need the mobility, it’s better to use the L-shape pieces:
I think that’s a good start: let’s see in practice how much it helps. I’ll definitely be adding some more combination here as I discover them around.