What's going wrong with my Lego geometry?

[mouseketeer]

I'm doing these mosaic-y backdrops, but something is going really wonky! I thought I had my Lego geometry correct (2 studes wide = 5 plate edges), and while this is working for the above (forest) mosaic, it's not working for the lower (castle) mosaic even though the numbers are the same. As you'll see the brown support is leaning out quite a bit (to the point that it's messing up another part of my model). What am I doing wrong here?

Here's a link to the images: https://imgur.com/a/QgFuqRK 

 

[MAB]

They should be exactly the same length, as 10 studs/bricks wide = 10x20 = 200 LDUs and 25 plates high = 8x25 = 200 LDUs.

However, you do need to make sure that you full squeeze the plates together for this to work. Are the tops of the plates all clean, as dirt can hold them apart.

[GregoryBrick]

That's a real puzzler! Two questions:

1. Are your vertical brown supports aligned properly? It looks like the ones at the top right of the castle mosaic are slightly rotated, which would push your blue/white/grey elements over the way they are shown.
2. Does the top row of blue plates fit properly along the bottom brown plate? Just to check.

Otherwise, beyond what others have said, all I can figure is that there is some sort of stacking error (the minute variations of those bricks are individually within tolerances but, by chance, this combination adds them up in this way?).

[NathanR]

Your geometry works perfectly in theory...

If you disassemble the top row of plates, and lay them out next to each other, do any appear to have different heights? There will be some variation, there always is, but it should be very slight.  I also notice  that the two blue plates either side of the extreme right battlement seem to have a slightly different colour to the rest - are you sure all parts are genuine Lego?

Also, the base of this mosaic seems to be made of 1x12 and 1x10 plates.  I usually find that these warp, the edges tend to curl up so columns of 1x1 bricks placed at each end bend inwards.  That might be affecting things here.

Oh, and one last thought - are any of the 1x1 bricks technic bricks? A 1x1 technic brick has the open hole mounted slightly higher than the stud of a 1x1 brick with stud on the side, so this could give a slight offset that would break the geometry.

[mouseketeer]

I'm glad I'm not missing some obvious error! 

I've definitely pushed all of the bricks as close together as possible, and laid them flat and pushed that way to make sure everything's fully aligned. Even though there is some colour discrepancy, they are all genuine Lego, new condition pieces. I swapped the brown plates around too to check if any had warped, but they seem fine.

I think it must just be the tolerances building up with these pieces. I separated the two lines that are horizontal, and it's only the bottom line (the one with the crenellations) that pushes out the brown column once they're disconnected. I might have to Bricklink some more medium blue and dark bley 1x1 plates and see if a different combination of bricks amounts to a different length. I guess normally this variation would barely be noticed, but the surrounding pieces I'm using just magnify it further. 

Thanks for the help everyone! :) 

[koalayummies]

7 minutes ago, mouseketeer said:

I think it must just be the tolerances building up with these pieces.

Yeah that could be it as I've seen this phenomenon discussed around here regarding Lego design team and engineers that scrutinize and approve official sets as 'tolerance accumulation'. I've seen it myself as well also regarding plate-thickness in SNOT construction like this and have had to swap plates for others or rotate them about their stud-axis to get better fitment. Let us know if you obtain better fitment and determine the suspect pieces.

[sheo]

My version:

As I can see from the photos, the horizontal stack of plates has the same width as the line of blue plates placed above, so the geometry is correct. If you look at the mentioned line, you will notice small gaps between plates which are intentionally added to all bricks to prevent friction. However, the base of the build consists of 4 stacked long plates which bend upwards. This bending displaces the left brown support and also pushes together 3 vertical stacks of plates and bricks negating the gaps between them. Therefore they seem to be shorter than the horizontal stack of plates. Try replacing the long plates at the bottom with several short ones (e.g. 4 studs long) and see if the problem persists.

[mouseketeer]

I gave it a shot but no luck! The bricks still misalign even with the brown frame completely removed.

[rodiziorobs]

I would say that definitely a tolerance issue, coupled with the specific bricks you are using.

The light blue (or whatever official name they have, @Aanchir could tell you) bricks, I have noticed, tend to be more prone to fiddly issues like this: differences in clutch from piece to piece, color variation, and--you guessed it--tolerances. The problems are not as bad as the early dark red bricks (circa 2005?) but noticeable in situations like this.

If you had to guess when your light blue bricks were made, when was it? The bunch I have from the Medieval Market Village are slightly different from newer bricks from the PAB, for example, and also varies from bricks to plates.

That's my guess as to why your forest mosaic works fine but not the castle one.

[sheo]

1 hour ago, mouseketeer said:

I gave it a shot but no luck! The bricks still misalign even with the brown frame completely removed.

Here is a comparison of your build and a build with a base consisting of short plates (I also used plates 1x4 with 2 studs):

By the way, in both of your builds the top side of the frame is bending as well.

 

[mouseketeer]

Hmm that's really interesting - I'm having trouble replicating it though with my pieces. I've taken off the brown border completely, stood the two sections on their edges against the table and the bricks are still overhanging.

[sheo]

1 hour ago, mouseketeer said:

Hmm that's really interesting - I'm having trouble replicating it though with my pieces. I've taken off the brown border completely, stood the two sections on their edges against the table and the bricks are still overhanging.

If you mean that you are putting 3 vertical sections freely side by side then of course they will be shorter that the horizontal stack of plates because you are eliminating the gaps between sections. And if are still having two stacked 8 10 stud long plates at the bottom, then the bending should be still present.

Edited May 18, 2018 by sheo

[ReplicaOfLife]

Definitely a tolerance issue.

Also note that bin the forest mosaic, everythink is built sideways except for the frame, while in the castle mosaic, the upper half is built sideways, while the lower half is build right side up. My guess is that this doesn't boil down to the color of the pieces, but is just a general poblem with regular tolerances wotrkinbg against each other.

Possibly five plates are closer in height to the theoretical width of two studs, but a two stud wide plate/brick is actually slightly narrower than it should be to make it easier for them to connect. So when put next to each other like this, the stacked plates are wider than the plates placed next to each other.

Edited May 18, 2018 by RogerSmith

[mouseketeer]

28 minutes ago, sheo said:

If you mean that you are putting 3 vertical sections freely side by side then of course they will be shorter that the horizontal stack of plates because you are eliminating the gaps between sections. And if are still having two stacked 8 stud long plates at the bottom, then the bending should be still present.

Bit of trouble parsing that, haha - I mean that I've taken the sideways-studs section (with the crenellations) and placed it alongside the 7-plates-hide vertical-studs section (with the castle), to exclude both the 1x10 white plates and the 1x12 brown plates which can be subject to warping, but even without them the sideways-studs section is longer than the vertical-studs section. I'm going to put this down to something that works in theory, but in practice goes a bit wonky!

[sheo]

24 minutes ago, mouseketeer said:

I've taken the sideways-studs section (with the crenellations) and placed it alongside the 7-plates-hide vertical-studs section (with the castle), to exclude both the 1x10 white plates and the 1x12 brown plates which can be subject to warping, but even without them the sideways-studs section is longer than the vertical-studs section.

That's because you eliminated the gaps between vertically oriented sections when you put them freely side by side.

[mouseketeer]

Ohh, I get what you mean! So I redid it with the vertical section on three 1x4 plates (which were then on two 1x4 plates to secure them), and while the gap isn't as pronounced, it is still there, which then gets magnified because of the 1x1 column. It does seem to be a combination of bending 1x plates and the tolerances.