mrob.com Common Glossary

LATS LEGO Approximate Tooth Spacing The spacing of teeth on a linear gear element such as piece 3743. This is 2/5 of a LSS, or 3.1944±0.0008 mm. As the name implies, it is an approximation to the "ideal" spacing which is LITS. Conveniently it is exactly the same as LPH.

LBH LEGO Brick Height The height of a normal LEGO® brick, not including the bumps on top. By definition, 1 LBH = 1.2 LSS. Therefore, 1 LBH = 9.5832±0.0024 mm.

LDU LDraw Unit A unit used in the CAD/CAM program LDraw for creating 3D models of LEGO constructions. (LDraw is a popular alternative to the official LEGO design software.) The LDraw unit 1/20 of an LSS, and it also evenly divides the LBH and LPH. One LDU = 1/20 LSS = 0.3993±0.0001 mm.

LGDU LEGO Gear Distance Unit The distance two LEGO® gears have to be to mesh well, divided by the total number of teeth. (For example, two 8-tooth gears have a total of 16 teeth, and they have to be 16 LGDU apart to mesh well.) By design, 16 LGDU = 1 LSS. Therefore, 1.0 LGDU = 0.499125±0.000125 mm¹.

LITS LEGO Ideal Tooth Spacing The spacing of teeth around the circumference of a LEGO® gear. The standard engineering term is circular pitch. Ideally it would be 2 π times the LGDU, or about 3.1361±0.0007854 mm. The linear gear rack element, piece 3743 has 10 teeth; its length is 4 LSS = 31.944 mm long, which is a close approximation of 10 LITS = 31.361 mm. Other parts like the worm gear take advantage of the same close approximation.

LPH LEGO Plate Height The height of a LEGO® "plate" (such as piece 3020), which is one third of the height of a normal LEGO® brick, not including the bumps on top. By definition, 3 LPH = 1 LBH. Therefore, 1 LPH = 3.1944±0.0008 mm.

LSS LEGO Stud Spacing The horizontal spacing between adjacent "bumps" on a LEGO® brick. Experimental measurement of carefully constructed long "walls" of long bricks shows that the LSS is 7.986±0.002 mm.

Sources

I measured the LSS using carefully constructed long "walls" of Technic bricks:

measuring the LSS

For example, measuring a length of 112 studs with the meter-stick pictured, I get 895 millimeters (to within ± 0.2 mm), which is clearly about 1 mm less than the length you'd expect if the LSS were exactly 8 mm.

Here is my original LUGNET posting from 1999, describing my measurement of the stud pitch:

Subject: [Building FAQ] What are the dimensions and aspect ratios of LEGO(r) bricks? Author: Robert Munafo Newsgroups: lugnet.faq Date: Thu, 22 Jul 1999 22:30:22 GMT From: Robert Munafo <MUNAFO@GCCTECH.stopspammersCOM> I have added the Metric and Imperial dimensions to the previous discussion of ratios. [...] The actual dimension (rather than the ratios) can be determined by carefully measuring a properly constructed "wall" of bricks. Vertical dimensions are prone to error caused by sloppy stacking, but long horizontal walls constructed from two or more layers of overlapping bricks are not prone to such error. A wall of this type built from Technic beams made in the late 1990's shows that the stud pitch distance is 7.986 millimeters, plus or minus 2 microns, when the parts are at 25 degrees centigrade (77 degrees Farenheit). It is also worthwhile to note that LEGO bricks are always made a little smaller than this dimension would suggest. For example, the length of a 2x4 brick is a little less than 4 times 7.986 millimeters. The length is diminished slightly so that there will be a small gap when bricks are stacked next to each other. This gap allows for dust, marred surfaces and other imperfections. If the gap were not there the bricks would tend to push each other apart and the overall construction would be less strong. Using the ratios above and converting to imperial measurements yields the following figures for all three dimensions: Brick height 9.582 mm 0.37724 in Plate height 3.194 mm 0.12575 in Stud pitch 7.985 mm 0.31437 in The following popular approximations are often used. Note that the Imperial approximations are each about 1 percent smaller than the corresponding S.I. (Metric) approximation: S.I. Imperial Brick height 9.6 mm = 48/5 mm 0.375 in = 3/8 in Plate height 3.2 mm = 16/5 mm 0.125 in = 1/8 in Stud pitch 8.0 mm 0.3125 in = 5/16 in

Second posting:

Subject: Conversion between LDU, inches and millimeters Author: Robert Munafo Newsgroups: lugnet.faq Date: Tue, 24 Aug 1999 23:13:12 GMT From: "Robert Munafo" <munafo@gcctechNO.SPAMcom> In lugnet.faq, Jeremy Sproat writes: > Adam, do you have an inch <-> LDU conversion constant as well? Conversion constants are much more relevant to the stud pitch than the brick height or width, because brick heights and widths are subject to the error caused by the fact that LEGO always designs elements so there will be tiny gaps when assembled, to make them fit better even when marred or dirty. The stud pitch in LDU is given by Steve Bliss's section of the FAQ answer, which says that the stud pitch is 20 LDU (LDraw units). That's an exact figure, because of the LDU's role as a way to make it easier to position pieces at integral stud-positions when you're building a model in LDraw. The stud pitch in the physical world is (from my section of the FAQ answer) 7.986 millimeters plus or minus 2 microns. Expressed as a percentage the error is 0.025 of a percent (or 1 in 4000). The inch to millimeter conversion is (by international standard) exactly 25.4 millimeters to an inch. That is also an exact figure (by international agreement). When you do the math, you get the following conversion factors, each with its corresponding error term: 1 LDU = 0.3993 +-0.0001 millimeters 1 millimeter = 2.5043 +- 0.0006 LDU 1 LDU = 0.015720 +- 0.000004 inches 1 inch = 63.611 +- 0.016 LDU - Robert Munafo http://www.mrob.com/ LEGO: TC+++(8480) SW++ #+ S-- LS++ Hsp M+ A@ LM++ YB64m IC13

1 : Yes, that's right, we know the LGDU to within 125 nanometers.

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The graph paper in my newer photos is ruled at a specing of 1 LSS, which is about 7.99 mm.

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