Lego Geometry Gus Jansson NWBrickCon – October 5, 2002

Why Study Lego Geometry? Avoid trial and error approach to making parts fit Determine exact distance between points on a diagonal Design intricate structures in your head when you don’t have access to your bricks

The Lego Unit (L) 4L 2L ?

The Height Of A Brick 4L 2L 1.2L

Plate Height Plate height is 1/3 of Brick Height. 1.2L / 3 = 0.4L

The Beam Stack a b 0.4L a b a + b = 1.2L b + 0.4L + 0.4L + a = 2.0L

What about a and b? a = 0.5 b = 0.7

Stud Size? Distance between studs is 0.4L

Gap between studs = 0.4L 1L 0.2L 0.6L

90° Bracket

2L 0.4L

90° Bracket 1.2L 0.4L 2.0L 0.4L 2L 2.4L

90° Bracket

1x1 Headlight Brick

1L 0.8L 0.2L

1x1 Headlight Brick 0.8L1.2L1L

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 2L 3L 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 1.0L1.5L 0.75L 0.75L gap

Diagonals One way to fit hard combinations Use Pythagorean Theorem to measure distance on diagonal

Diagonals 1L 2L

Diagonals 1.5L L = 2.25L

Diagonals 0.5L 0.4L 1L 0.5L 1.0L

Diagonals

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

UNDONE: 1Good ways to mount motors 2Light sensor mounting 3Light sensor shrouding(like Alegomazer) 4Good techniques for angles like Alegomazer light sensor block 5Circular exercise