LEGO MINDSTORMS robotics

Raphael, Apr 6, 2015

This collection of worksheets and animations explains some of the math and mechanics concepts behind LEGO Technic elements (gears, levers) and LEGO MINDSTORMS (NXT/EV3) robotics.

Table of Contents

  1. Introduction
    1. Introduction to the EV3
  2. Constructing with beams
    1. LEGO rectangle or parallelogram
  3. Turning a wheel
    1. Rotation of a small wheel
    2. Rotation of a big wheel
    3. The rotation of a wheel - cycloid
  4. Gearing up/down
    1. Two gears
    2. Small gear turning a large gear
    3. Gearing up
    4. Gearing down
    5. Simple LEGO gear train
    6. Double LEGO gear train
  5. Motors
    1. LEGO motor with beam
  6. Moving the robot
    1. Advancing in a straight line
    2. Robot moving on a circle
    3. FLL 2007 - Power Puzzle
    4. Robot moving by button control
    5. Two robots at constant speed
    6. Turning more or less

1.

Introduction

  • 1. Introduction to the EV3

1.1.

Introduction to the EV3

The ideal tool to teach MINT disciplines
The LEGO MINDSTORMS EV3 robot is very popular in education. It is ideal to teach the MINT disciplines:[br]- Mathematics[br]- Informatics[br]- Natural sciences[br]- Technology[br][br]The LEGO MINDSTORMS EV3 Education kit consists of a an intelligent and programmable brick, 3 motors and multiple sensors which allow to build robots or other interactive machines. They can be programmed with an intuitive graphical language.
The LEGO MINDSTORMS EV3 robot
– Raphael

2.

Constructing with beams

The LEGO Technic beams are the main elements of construction. They come in odd length from 3 to 15. The advantage of an odd length is to have a central hole which allows do balance the beam. Beams are connected with connectors which can be with or without friction.

  • 1. LEGO rectangle or parallelogram

2.1.

LEGO rectangle or parallelogram

A quadrilateral with opposing equal-length sides is either a parallelogram or a rectangle, depending on the angle.
What is the opposite angle?
– Raphael

3.

Turning a wheel

  • 1. Rotation of a small wheel
  • 2. Rotation of a big wheel
  • 3. The rotation of a wheel - cycloid

3.1.

Rotation of a small wheel

The rotation of a wheel on a ground surface is the combination of a rotation and a translation.

How far does the wheel move? What happens if you change the radius?
– Raphael

3.2.

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3.3.

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4.

Gearing up/down

  • 1. Two gears
  • 2. Small gear turning a large gear
  • 3. Gearing up
  • 4. Gearing down
  • 5. Simple LEGO gear train
  • 6. Double LEGO gear train

4.1.

Two gears

Use the slider to change the radius of the second gear. How does the speed and the turning angle of the second gear change?
– Raphael

4.2.

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4.3.

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4.4.

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4.5.

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4.6.

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5.

Motors

  • 1. LEGO motor with beam

5.1.

LEGO motor with beam

The motor moves with increments of 30°. You can stop the animation and move the slider manually. You can change the length of the beam from 3 to 15, in increments of 2.

How many times does the beam stop?
– Raphael

6.

Moving the robot

  • 1. Advancing in a straight line
  • 2. Robot moving on a circle
  • 3. FLL 2007 - Power Puzzle
  • 4. Robot moving by button control
  • 5. Two robots at constant speed
  • 6. Turning more or less

6.1.

Advancing in a straight line

For each rotation of the wheel the robot advances by de circumference of the wheel which is 2*π*R.

How far does the robot move for 1, 2 and 3 rotations of the wheel?
– Raphael

6.2.

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6.3.

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6.4.

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6.5.

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6.6.

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