Lego Geometry

Gus JanssonNWBrickCon – October 5, 2002

Why Study Lego Geometry?

Avoid trial and error approach to making parts fitDetermine exact distance between points on a diagonalDesign intricate structures in your head when you don’t have access to your bricks

The Lego Unit (L)

4L2L

?

The Height Of A Brick

4L2L

1.2L

Plate Height

Plate height is 1/3 of Brick Height.

1.2L / 3 = 0.4L

The Beam Stack

a

b

0.4L

0.4La

b

a + b = 1.2Lb + 0.4L + 0.4L + a = 2.0L

What about a and b?

a = 0.5b = 0.7

Stud Size?

Distance between studs is 0.4L

Gap between studs = 0.4L

1L

0.2L0.2L

0.6L

90° Bracket

90° Bracket

2L

2L

0.4L

0.4L

90° Bracket

1.2L0.4L 0.4L

2.0L

0.4L

2L 2.4L

90° Bracket

1x1 Headlight Brick

1x1 Headlight Brick

1L

1L

0.8L

0.2L

1x1 Headlight Brick

0.8L 1.2L 1L

1x1 Headlight Brick

Gears: Radius and Teeth

1L

Radius of 8-tooth gear: 0.5L

Circumference is linear to radius

Formula: t = 16r or r = t/16

Gears: Radius and Teeth

2L3L

16 tooth gear – radius is 1L

24 tooth gear – radius is 1.5L

Gears: Double Bevel

12 tooth – radius is 0.75L

20 tooth – radius is 1.25L

New gear with Spybot set:

36 tooth – radius is 2.25L

Gears: Making them fit

Easy to Fit Combinations:

Gears: Making them fit

Harder to Fit Combinations:

Gears: Making them fit

1.5L

Gears: Making them fit

1.0L 1.5L 1.5L 0.75L

0.75L gap

Diagonals

One way to fit hard combinations

Use Pythagorean Theorem to measure distance on diagonal

22 bad

Diagonals

1L

2L

236.221 22

Diagonals

1.5L + 0.75L = 2.25L

Diagonals0.5L

0.4L1L

0.5L1.0L

965.19.15.0 22

Diagonals

Diagonals

Diagonals

992.37.35.1 22

Diagonals Chart

Full Chart available on Brickshelf.com. Search for member Gjansson and look under Lego Geometry.

UNDONE:

1 Good ways to mount motors

2 Light sensor mounting

3 Light sensor shrouding(like Alegomazer)

4 Good techniques for angles like Alegomazer light sensor block

5 Circular exercise