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LDraw units are defined so that a simple 1x1 brick has a side of 20 ldu and a height of 24 ldu.

Using simple building techniques, it's easy to create 2 ldu offset, as illustrated in this picture, where the gap between the two red bricks is 2 ldu wide:

2 ldu offset

Of course, it's also possible to build any kind of offset, including 1 ldu, using continuous techniques such as parts gliding on axles, as illustrated in this picture:

1 ldu offset, continuous

But is it possible to build an exact 1 ldu gap without this kind of cheap trick?

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I don't have an answer, but I do know this: the dimensions of basic bricks are multiples of 2 ldu. That means that any rectangular arrangement of bricks can't possibly have a gap of 1 (or any other odd number) ldu. Any solution to this problem will, therefore, involve bricks with odd dimensions or bricks placed at an angle (i.e. some kind of SNIR technique). –  Kramii Nov 23 '11 at 22:32
    
Good thinking, but SNIR is not what I have in mind here, no angles other than 90° are required. –  Joubarc Nov 24 '11 at 5:37
    
Perhaps we could use the fact that bricks are not exactly 20 ldu wide: they are actually 0.25 ldu short at each end (which means that an ordinary lego wall has gaps of 0.5 ldu between the bricks)? Or that the studs on system bricks are approximately 0.25 ldu lower thatn the holes on technic bricks? –  Kramii Nov 24 '11 at 10:02
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Yay, one more "don't-care-to-explain" downvote. Gotto love these. –  Joubarc Nov 28 '11 at 7:39
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From my experiments, I found that a 1 ldu offset is perfect for holding a piece of thick paper. So it does have its uses. –  Kramii Nov 28 '11 at 13:53

4 Answers 4

This is a very very silly solution, but it should be possible with gears.

Get the ratio correct and you'll be at 1/4 rotation per 1ldu. Then slide in one of these: , lock the axel and you're capable of any ldu spacing.

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Sounds ingenious, but I'm not entirely convinced. It's nearly like a continuous solution (I'm looking for a solution with pure stud connections), and the calculations must be horrible. –  Joubarc Nov 25 '11 at 5:04

LDUs are synthetic units for LDraw, a lego design software.

(I am personally convinced that the correct answer to your question is that there is no way to create a 1 LDU gap and that we are very fortunate to have the Erling brick to create a 2LDU gap.)

If you look at the 2 links provided, you'll see that both the Erling and the standard lego brick dimensions only have even values. There is no way to end up with an odd number in these conditions.

If there is a solution, it must involve a brick that has an odd dimension in some direction.

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Your last statement is right on the spot, and there is one such element. (Also, note that for a 2 ldu gap, the erling brick alone isn't enough as it only has dimensions that are multiples of four. That's why you need a half-brick (10 ldu) offset too, which is what the jumpers are for in my picture) –  Joubarc Nov 28 '11 at 8:19
    
wow a bounty! thanks! –  jfyelle Nov 30 '11 at 1:35
    
Don't thank me, it's all automatic. You got half of the bounty award because your answer was the most upvoted since the bounty started. Well, you were halfway there, so it makes sense :-) –  Joubarc Nov 30 '11 at 7:30
up vote 10 down vote accepted

(Note: my HDD crashed recently and until I get that fixed I can't really make LDraw images. I did create one for this beforehand, but it's on the same HDD.)

As jfyelle said the solution consists of using one LEGO element which has an odd ldu dimension somewhere. There is such an element, which isn't even new or particularly rare, that is, the Fence 1 x 4 x 2:

Fence 1 x 4 x 2

The centre part has a thickness of 6 ldu, which means that there are 7 ldu on each side. So if you add a 2x4 plate in it, the thickness of the plate (8 ldu) means that it will stick out by exactly one ldu. If your fence is one red brick, just put a 1x4 brick and a 1x4 brick with for knobs on the other to connect to the plate. Your two red bricks should then be 1 ldu apart.

I did learn that trick from Didier Enjary in his excellent Advanced Building Techniques Guide which is well worth reading. That document contains a whole chapter on offsetting, but curiously the 1 ldu offset isn't listed explicitly; rather, the fence element and its 7 ldu offset is mentioned casually in the SNOT section.

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Full credits and my thanks go to Didier Enjary. I tried to have him come and answer himself, but he declined. Note that he also thinks the practical usefulness of the this is very limited. –  Joubarc Nov 28 '11 at 13:29
    
That was a hard question :) –  jfyelle Nov 28 '11 at 13:37
    
It's even harder to judge the difficulty of a question when you already know the answer. –  Joubarc Nov 28 '11 at 13:39
    
Well, I was impressed I could came up with the principle. I'm away on a business trip however and couldn't really afford to browse the bricks for a solution. I'm sure I would have dismissed the puny fence. By the way, for your crash, get yourself a standalone solid state hard drive and use syncback to backup your stuff. –  jfyelle Nov 28 '11 at 13:47
    
@Joubarc: That's truly brilliant! Many thanks for the posing this entertaining little puzzle. It's been bothering me for days. Now I'm kicking myself. The first time I ever came across SNOT it used these very same fences! –  Kramii Nov 28 '11 at 13:50

There is another piece with an odd LDU dimension: the 1x1 bracket is 3 LDU thick. Paired with an Erling brick, which has a 4 LDU offset built in, it's a very compact way to create a 1-LDU offset, like psiaki has done here:

1 LDU steps by Psiaki

Then it's just a matter of translating the offset into a gap between bricks using standard bracket pieces like I have done here:

1 LDU gap enter image description here

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nice one, I didn't know about the 3 ldu bracket –  Joubarc Mar 18 '13 at 20:32

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