1. Lego Geometry Gus Jansson NWBrickCon – October 5, 2002

2. 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

3. The Lego Unit (L) 4L 2L ?

4. The Height Of A Brick 4L 2L 1.2L

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

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

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

9. Stud Size? Distance between studs is 0.4L

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

11. 90° Bracket

12. 2L 0.4L

13. 90° Bracket 1.2L 0.4L 2.0L 0.4L 2L 2.4L

14. 90° Bracket

15. 1x1 Headlight Brick

16. 1L 0.8L 0.2L

17. 1x1 Headlight Brick 0.8L1.2L1L

18. 1x1 Headlight Brick

19. Gears: Radius and Teeth 1L Radius of 8-tooth gear: 0.5L Circumference is linear to radius Formula:t = 16r or r = t/16

20. Gears: Radius and Teeth 2L 3L 16 tooth gear – radius is 1L 24 tooth gear – radius is 1.5L

21. 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

22. Gears: Making them fit Easy to Fit Combinations:

23. Gears: Making them fit Harder to Fit Combinations:

24. Gears: Making them fit 1.5L

25. Gears: Making them fit 1.0L1.5L 0.75L 0.75L gap

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

27. Diagonals 1L 2L

28. Diagonals 1.5L + 0.75L = 2.25L

29. Diagonals 0.5L 0.4L 1L 0.5L 1.0L

30. Diagonals

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

34. 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