The Geometry Of Legos - Roboplex

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Required Stuff Please do not wander the building. Rest Rooms Location. Food and Drink. Cell phones2

WARNINGCHOKING HAZARD – Do NOT put LEGO blocksor pieces in you mouth for any reason. Not only isit gross, they just don’t taste good. Also no LEGO pieces in your nose, ears, eyes or anywhere elsethey don’t belong.3

Introduction Annual production of Lego bricks averages approximately36 billion per year, or about 1140 elements per second. Since 1958, more than 400 billion Lego pieces have beenproduced, or 86 for every person in the world! There are roughly 4,200 different Lego elements in 58different colors.Same piece, many different namesSame piece, many different colors4

Hands-on Exercises Parts ListQtyItemP/N8Friction Peg41217153Beam 11M2QtyItemP/N2Axle 5M421163945628052Double cross block4121667Peg 3M4514553124z gear45145582Beam 5M414213518z gear601245123x5 90 beam45850401Axle 3M42118152Beam 7M44959351Axle 4M3705262Cross Axle 2M41428651Bionicle eye41739412Technic Cross Block 2x141404301Half bushing42396012Technic Cross Block 2x241628571Bushing42271553Non-friction pegs42118075

LEGO Mindstorms EV3 kitThe LEGO Technic elements in theMindstorms sets are: Electronicelements Beams Pegsand axle pegs Axlesand connectors Gears Wheels Decorativeelements Miscellaneouselements6

Electronic elements Intelligent Brick Drive motors Touch sensor Color sensor Ultrasonic sensor Gyroscope Connector cables7

Intelligent Bricks History EV3 Educational releasedAugust 1, 2013 Commercial releasedSeptember 1, 2013NXT Released 2006RCX(Robotic Command eXplorers) Released 19988

Sensors6008472: EV3 Touch Sensors (2) 6008919: EV3 Color Sensor 6008916: Gyro 6008924: Ultrasonic Sensor 9

Drive Motors 6009430: EV3 drive motor 6008577: Medium motor10

Beams Straight beams Angular beams Frames Thin beams Links11

Beams - Straight Beams are measured by counting the number of holes. Beamscome in odd numbers when counting the holes, withone exception. Beamsstart with15 holes and go down in size by two holes tothe 3 hole beam and include one even-numbered beamwith 2 holes. The number of holes corresponds to the length of thebeam in Fundamental LEGO Units or Modules (1M is8mm).12

Beams - Straight 3M Beam 5M Beam 7M Beam 9M Beam 11M Beam 13M Beam 15M Beam13

Tip for determining beam size. To quickly determine the size of the longerbeams: place a finger on the middle hole of thebeam, then you can quickly count how manyholes are on one side, double it, and add one.1234514

Specialty beams 6008527: Horizontal to Vertical Beam 90 Degrees 6006140: Beam 1X2 with Cross And Hole 4538007: Cross Block 3X215

Pegs and Axle Pegs Pegs are like the nails, screws, and bolts of LEGO Mindstorms , they hold things together. Pegs fit in the beam holes. Two primary groups of pegs: Friction Non-Friction16

Pegs and Axle Pegs – Friction 4121715: Connector Peg with Friction 4140806: 2M Friction Snap with Cross Hole 4514553: 3M Connector Peg with Friction 4206482: Connector with Friction Cross axle 4184169: Ball With Friction Snap*4121715414080145145534206482418416917

Pegs and Axle Pegs – Non-friction 4211807: Connector peg 4514554: 3M Connector peg 4666579: Connector peg Cross Axle412171541408014184169420648218

Identifying friction and non-friction pegs Friction pegs have ridges that help to create frictionwith the beams. Non-Friction pegs are smooth.19

Beams and “snap” combinations 4225033: Beam 3M with 4 Snaps 4296059: Angular Beam 90 with 4 Snaps20

Using Beams and Pegs Hands-on activity21

Extending Beams Using two black pegs withfriction connect two beamsusing the two end holes ofeach beam. Test: Holding the ends of theextended beam gently flexit. Result: The beam isstraight but still has someflex.22

Extending Beams Using the same two blackpegs with friction, overlapthe beams five holes. Test: Holding the ends of theextended beam gently flexit. Result: Structure is morerigid.Note: Adding additional black pegs will hold the beams togetherbetter, but not required for strength.23

Increasing Strength by Making WiderUsing two 3M blue pegs withfriction, overlap the beamsfive holes. Then add anadditional beam on the pegsextending. Result: A more ridgedstructure. Note: Alternate the direction of the 3M blue peg ridgeto reduce separation. Peg ridge can be used to helpin keeping pegs in place on removable attachments.24

Angular beamsAn angular beam with threeholes before and seven holesafter the bend is a 3x7 angularbeam. 3x5 90º angular beam has holesat both ends. 2x4 90º angular beam has a holeat one end and cross hole at theother. All other angular beams havecross holes at the ends. 25

Angular beams 4141270: Angular Beam 4X2 90 4211713: Angular Beam 3X5 90 (Med. Grey) / 4585040(White) 4211624: Angular Beam 3X7 4509912: Angular Beam 4X426

Angular beams 4495412: Double Angular Beam 3X7 4112282: Technic Angular Beam 4X6 4552347: T-Beam 3X3 with Hole27

Angular combinations28

Frames Frames are referred to based on their shape: Oframe HframeFrames add strength to structures.4539880: Beam Frame 5X74539880: Beam Frame 5X729

Thin beams Are half the width of a normal beam. Useful for adding functions or styling to yourrobots.6009019: Triangle4142236: Lever 1X4,Without Notch4112287: TechnicLever 3X3M, 90*4503417: Technic 5MHalf Beam*30

Structural frames Hands-on activity31

Make a Structural Frame Using two 11M beams, two 5Mbeam, and four black pegs,make a structural frame asshown.32

Strength Test of Structural Frame Hold the bottom and presson one side of the frame. What happens to theframe?HOLD33

Adding Strength to the Structural Frame Using two 11M beams, two 3X590 angular beams, and sixblack pegs, make a structuralframe as shown. Hold the bottom and press onone side of the frame. What happens to the framethis time?34

Reinforcing with angles A beam angled betweenthe two beams will alsoimprove the structuralstrength.35

Axles and connectors Axles Bushings Cross blocks36

Axles Length is same as a Lego brick, the smallest is called a2M axle (with groove) andcommonly red or black. Theodd number axles aretypically grey (3, 5, 7M axle). Theeven number axles aretypically black (4, 6, 8M axle).37

Specialty Axles Axle with end stop Cross axle with end stop Cross axle with end knob4263624: 5.5MDouble Cross Axle4560177: Cross Axle4M With End Stop4499858: Cross Axle8M With End Stop6031821: Cross Axle3M with End Knob38

Bushings 4239601: Half Bushing for Cross Axle 4211622: Bushing for Cross Axle 4560175: Double Bushing 3MBushings can be used as spacers to prevent tires fromhitting beams or other structures.39

Cross blocks 4173668 - Cross Block 90 4121667 - Double Cross Block 4140430 - Technic Cross Block 2X1 (Mickey) 4162857 - Technic Cross Block Fork 2X2 (Minnie) 4210857 - Technic Cross Block 90, 2X340

Cross blocks combinations Using this cross block combinationallows mounting two beams at aright angle.41

Cross blocks combinations This cross block combination allows two beams to bemounted smooth sides together.42

Cross block combinations This combination of cross blocks also allows mountingtwo beams at a right angle.43

Tip for removing small cross axleconnector Use long axle to push small axle through.601172 BrickSeparator44

Cross blocks Hands-on activity45

Cross blocks: Hands-on parts needed 7M beams (2) Technic Cross Block2X1 (Mickey) (2) Technic Cross BlockFork 2X2 (Minnie) (2) Black peg withFriction (8) 2M Cross Axle withGroove (2)46

Cross block building instructions Align Technic Cross Block 2X1 (Mickey)with Technic Cross Block Fork 2X2(Minnie). Insert 2M Cross Axle with Groove. Repeat to make a second crossblock assembly.47

Cross block building instructions Insert four black pegs into the crossblock assembly. Repeat on second cross blockassembly.48

Cross blocks building Instructions Place two 7M beamson cross blocks.49

Bracing LEGO pieces are designed to separate when pulled.When intentional it is called disassembly. Sometimes assemblies pull apart unintentionally simplysitting there or while operating. This is called structuralfailure. One solution is bracing. Bracing can add strength with minimum weightincrease.50

Additional cross blocks 4210857: Cross Block 3M 4502595: 3-Branch Cross Axle Cross Hole 4538007: Cross Block 3X251

Bracing – Sample 1 Bracing uses combinations ofLEGO part at right angles.52

Bracing – Sample 2Step 1Step 253

Bracing – Sample 2Step 354

Bracing Hands-on activity55

Bracing: Hands-on parts needed 11M beams (3 ea.) 5M beam (1 ea.) Double cross block (2 ea.) 5M axle (2 ea.) Black peg with friction (2 ea.)56

Bracing: Hands-onStep 1Step 2Step 357

Axle connectors4107085: Angle Element, 0 Degrees [1] 4107783: Angle Element, 180 Degrees [2] 4107767: Angle Element, 90 Degrees [6] 4513174: Cross Axle, Extension, 2M 4526985: Tube W/Double Ø4.85 58

Gears Gears are rotating parts with teeth thatmesh with other parts with teeth. LEGO gears are identified by the numberof teeth followed by a “z”. Most gears are 1M thickCombination Reference:

Gears 6012451 - Gear Wheel 8z 4177431 - Double Conical Wheel 12z 4640536 - Gear Wheel 16z 4514558 - Gear Wheel 24z 4285634 - Gear Wheel 40z60

Gears 4565452 - Conical Wheel 12z 4640536 - Gear Wheel 16z 4177430 - Double Conical Wheel 20z 1M 4211510 - Worm gear 4255563 - Double Conical Wheel 36z61

Gear mbinationUnknownCombination62

Gear combinations24z to 24z (1:1)20z to 24z (5:6) to 8z (3:1)63

Gears Hands-on activity64

Gears: Hands-on parts needed 24z gear 8z gear 3m axle 4m axle 5m axle Double Cross Block Bionicle Eye Half-bushing bushing65

Gears: Building instructions Insert 4M axle into the 24z gear. Insert the gear assembly throughthe fourth hole in the beam. Install bushing on the axle. Install double cross block on theaxle behind the bushing. Insert the 3M axle into the otherend of the double cross block.66

Gears: Building instructionsInsert the 5M axle into the 8zgear. Insert the gear assembly intothe second hole in thebeam. Install the half-bushing ontothe other side of the 5Maxle. Install the orange bionicleeye on the other end. FRONTBACK67

Gear: Testing Turn the crankslowly one rotationand count thenumber of rotationof the bionicle eye.How many turns did the bionicleeye make?68

Gears: Motion Transfer How can you achievelinear motion?69

Motion Transfer Hands-on activity70

Motion Transfer: Building instructions Place 5M axle in 24zgear. Insert gear into fifth holein an 11M beam. Insert gray non-fractionpeg into hole on gear.71

Motion Transfer: Building instructions Insert gray non-frictionpeg in last hole on 11Mbeam.Insert 11M beam (red)second hole on graypeg.Insert gray non-frictionpeg in last hole of 7Mbeam.Insert 7M beam (yellow)on gray non-friction pegson gear and 7M beam(red).72

Motion Transfer: Building instructions Insert bushing on 5Maxle on the oppositeside of 11M beam. Insert double crossblock on 5M axle. Insert second 5M axleinto double cross block.73

Motion Transfer: Testing Rotate the handle(5M axle). What happens tothe forward (red)11M beam?74

Linear Motion with a motor Adding a motor to drivelinear motion is simple. The 24z gear and drivemotor both have threeholes.75

Gears: Using worm gears Worm gears can be usedto create linear motiontoo. This Forklift attachmentis one example. Rotating the gear causesthe forklift arms to travel upand down. Notice that the 8z geardoes not rotate.76

Caster 6023956: LEGO Steel Ball 4610380: Power Joint 77

Wheels (Tyres), Rims, and Tracks The LEGO Group is one of the world’s largest tyremanufacturers.6035364: Tyre LowWide 56 X 284634091: Rim Wide43.2 X 26 with6 Holes6014648: TrackElement, 5X1.54582792:Sprocket, Ø 40,778

Simple Wheel MatchingAssembly the two wheels onan axle with a bushing in themiddle. Align the bushing with theline on a slight slope with theaxle at 90 to the line. Let the wheel assembly rolldown the slope and watch ifthe bushing moves off theline. 79

Miscellaneous 4652236 Upper Part For Turntable 28z4587275: Wedge-Belt Wheel Ø246028041: Tyre For Wedge-Belt Wheel417394:1Bionicle Eye4563044: 2X1X3 Steering Knuckle Arm80

Decorative elements Are just that. Have beenused for a number ofthings.4566251 LeftPanel 3X54566249 RightPanel 3X54541326 LeftPanel 5X114566249 RightPanel 3X581

How many? Take six eight-stud LEGO bricks (2x4) –how many ways can they be combined? Withthe aid of computers, the exactnumber of combinations has beencalculated as 915,103,765! Just so you know, two eight-stud LEGObricks can be combined in 24 differentways and three eight-stud LEGO bricks in1,060 ways.82

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Sep 27, 2015 · Beams - Straight Beams are measured by counting the number of holes. Beams come in odd numbers when counting the holes, with one exception. Beams start with15 holes and go down in size by two holes to the 3 hole beam and include one even-numbered beam with 2 holes. The number of holes corresponds to the length

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