geometry confusing - how is this angle not illegal?

[Jon22]

I'm trying to understand how the very shallow angle at the front of the 9493 X-wing is legal. It's step 14. I can't paste the images in, maybe I need more reputation points or something. I'm pasting what should be a permanent link to the images here. The right-hand side of the second image shows my recreated, simplified understanding of the situation: the geometry is equivalent to a 10-by-1 plate placed so it spans 10 studs in one direction, and half a stud in the other direction, and it's anchored to a pair of hinge plates. (I'm quite sure that despite the complicated connections along the axle in the front, the front of the X-wing is "in system" with the rest, it's just offset by one half-stud.)

The middle part of the second image shows a different angled situation that I do understand as legal: here the 10-by-1 plate spans 10 studs with an offset of 2 studs, and you can confirm it is legal because the diagonal of the plate measures square-root-of-101 studs (=10.0499 studs), and that is also the distance between the two fulcrums of the hinge plates.

But in the right-hand side, the situation with the much shallower angle looks illegal. When I calculate the distance between the fulcrum points of the hinge plates, it turns out to be square-root-of-100.25 studs, or 10.012 studs.

Is there a guideline for how much tolerance the TLG will allow for these kinds of "barely legal" connections? The geometry is not mathematically justified but it appears to be close enough that they didn't consider the bricks to be under too much stress to allow this in an official set.

Thank you for any help understanding this (and how to generalize it to other non-standard angles--this is neither a Pythagorean situation nor one involving the diagonal of a plate like the middle part of my recreated image, but something fuzzier, it seems)

[Mylenium]

I'm not clear why you even think it's an issue. The whole front part of the hinge construct merely slides along the central axle. It has no rigid connection to the central fuselage. Likewise, the sides of the hinge thingy can move freely. There is nothing here that would even warrant a discussion about illegal building techniques or whatever you are trying to see in those images. There may be some weird behavior actually building it due to tolerances causing some tension, but on an abstract engineering level everything should zero out and be stress-free connections.

Mylenium

[Peppermint_M]

5 hours ago, Jon22 said:

I can't paste the images in,

Have you tried getting the perma-link address and pasting it into the post?

Here it is for anyone wondering.

I can't see an issue on the technique, in fact it looks fine on the completed side? I have used something very similar in MOCs and there is no tension or damage for the parts.

[Jon22]

15 hours ago, Mylenium said:

I'm not clear why you even think it's an issue. The whole front part of the hinge construct merely slides along the central axle. It has no rigid connection to the central fuselage.

I don't doubt you are right that there is an explanation that makes it legal (because after all it feels fine in the hands, and TLG released it like this). But you are wrong that there is no rigid connection between the front part and the main fuselage. It is attached rigidly afterwards, you can see it in these two steps:

https://imgur.com/hdvsfr8

So the front part must remain in system with the back, and it cannot slide freely away to make room for the angle.

[EDIT: now I think you (Mylenium) meant something similar to what Lyichir meant below, that just the very front portion is able to slide along, and you are right about that. Sorry, I thought you meant the section that has the angled edges, the section with the blue jumper plates on top, was free to move.]

So, seeing the fact that the two parts are still in system with each other as in the "gridded" diagram on my first post, isn't it true that the geometry doesn't quite line up perfectly with such an angled piece? I'm assuming it's just okay because the tolerance of the bricks allows these not-perfect-but-close-enough constructions?

I'm not saying that it's not okay, or that it's "bad", or that you shouldn't use it, I just want to understand what makes it okay when it's not mathematically precise. Thank you.

Edited April 25, 2020 by Jon22
adding an explanation

[Lyichir]

1 hour ago, Jon22 said:

I don't doubt you are right that there is an explanation that makes it legal (because after all it feels fine in the hands, and TLG released it like this). But you are wrong that there is no rigid connection between the front part and the main fuselage. It is attached rigidly afterwards, you can see it in these two steps:

https://imgur.com/hdvsfr8

So the front part must remain in system with the back, and it cannot slide freely away to make room for the angle.

So, seeing the fact that the two parts are still in system with each other as in the "gridded" diagram on my first post, isn't it true that the geometry doesn't quite line up perfectly with such an angled piece? I'm assuming it's just okay because the tolerance of the bricks allows these not-perfect-but-close-enough constructions?

I'm not saying that it's not okay, or that it's "bad", or that you shouldn't use it, I just want to understand what makes it okay when it's not mathematically precise. Thank you.

It looks to me, looking at the full instruction sheet, like the frontmost section (the 2x3 section to which the hinges are attached, which is not secured to plates on either the top or bottom) still slides along the axle independently of the parts attached to the jumper plates. In other words, while that section remains centered thanks to the axle that attaches to the main body it can go "off-grid" along its length, by approximately a mere 0.06 modules. Thus, no stress on the parts nor any uncertainty in the geometry.

Just to help out, I went ahead and calculated the angle of the hinge. You will want it to be hinged to 177.141 degrees (with 0 degrees being the hinge in its "closed" state).

Edited April 25, 2020 by Lyichir

[Jon22]

6 hours ago, Lyichir said:

It looks to me, looking at the full instruction sheet, like the frontmost section (the 2x3 section to which the hinges are attached, which is not secured to plates on either the top or bottom) still slides along the axle independently of the parts attached to the jumper plates. In other words, while that section remains centered thanks to the axle that attaches to the main body it can go "off-grid" along its length, by approximately a mere 0.06 modules.

Ah, I see! So although the wedge plate added in step 23 is attached both to the main body and the angled section, keeping them in system with each other, and although the hinge plates at the front of the angled section are also attached to the front 2x3 section, that very front section is still able to get out of system enough, along the axle, to accomodate the extra length. Now I'm also wondering about the 1x2 white tiles either side of the front blue jumper plate. With the 3-degree angle that they must be angled at (thanks for calculating that!), shouldn't the inside front corners of the white 1x2 tiles impinge very slightly on the blue jumper plate? I'm guessing this tiny impingement is simply within tolerance, because I can't see how to get around it.

Thanks for looking at this.

[Lyichir]

43 minutes ago, Jon22 said:

Ah, I see! So although the wedge plate added in step 23 is attached both to the main body and the angled section, keeping them in system with each other, and although the hinge plates at the front of the angled section are also attached to the front 2x3 section, that very front section is still able to get out of system enough, along the axle, to accomodate the extra length. Now I'm also wondering about the 1x2 white tiles either side of the front blue jumper plate. With the 3-degree angle that they must be angled at (thanks for calculating that!), shouldn't the inside front corners of the white 1x2 tiles impinge very slightly on the blue jumper plate? I'm guessing this tiny impingement is simply within tolerance, because I can't see how to get around it.

Thanks for looking at this.

No, those tiles wouldn't collide with the jumper plate. Those hinges are at their widest in their fully extended position, so having them slightly hinged actually creates MORE space between them and the jumper. It would be a different story if the angled sections connected via their own studs, rather than those hinge plates, since that type of hinge plate angles along the "corner" where the two hinge sections meet, rather than centered on a rectangular part.

You also seem to be misunderstanding how the wedge plate attaches. It's not actually connected to the angled section at all, but rather to a long extended section between the two angled sections. This is why the tolerance of gaps between parts doesn't even come into play—the angled section are only connected via each other as well as via a central axle that merely keeps them centered without enforcing a rigid distance from the main body the way it would if the angled sections were connected via studs.

[Jon22]

4 hours ago, Lyichir said:

[smart stuff]

Thank you, your explanation was very good. I get it all now.