# LEGO Structure With Equilibrium Point

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## Introduction: LEGO Structure With Equilibrium Point

LEGO is used for children’s fun or even to show application of engineer, physics or simple math concepts. A LEGO structure with distributed base points is an easy task. If you eliminate the most of the points will be difficult to get mass equilibrium. Then you will need tools to verify the work previously. With mathematic it is possible to validate the development of an irregular structure with assurance that it will not fall.

### Supplies:

The basic material are LEGO bricks. To verify the structure we use a spreadsheet but you can made by hand.

### Teacher Notes

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## Step 1: The Matrix

In the spreadsheet define the size of the field used in the structure - width and height. It is a matrix that define one brick of LEGO with 1x1 in every element. Format the elements (cells) for better presentation as you wish.

Note: You can replace the spreadsheet by a squared paper. In this case reserve the four lines at the bottom for assessment.

## Step 2: The Sketch

In the bottom of the field we will put only one brick to support the entire structure – base or balance point. Choose a position in the central region. This is the first brick. For every brick in the structure assign 1 in the cell. To improve the visual change the cell color. From now on connect another bricks in the structure. Do not create another base point that touch the floor.

Note: If you have finite number of bricks is better to assess them first.

Note: The main type used is 1x2 size. Try to use only one size type in entire structure. Respect the mass distribution that is important. The easy way to achieve is to use the same type of brick.

## Step 3: The Validation

With the completed structure let's validate it. Sum the ones in each (vertical) column. Put the value in the first row below the matrix. Count the distance from balance point to each column. Put the value in the second row. In the third row multiply the distance by the sum. In the left side of the balance point sum the resultant values. Put the value on the left. Make the same for the right side. If the left value equals the right value it works - is stable. If not you can review the structure and some calculus.

## Step 4: The Build

From the sketch build the real structure. In order to facilitate, build lying down. When you finish lift up the structure.

Note: Take care during assembly, the plug-in errors can bow the structure that will collapse.

Note: The main type used is 1x2 size. Try to use only one size type in entire structure. Respect the mass distribution that is important. The easy way to achieve is to use the same type of brick.

## Step 5: Conclusion

The pictures show my results with two different structures. That both remains stand and static. Create yourself another structure, but if you follow the steps it will work.

Curious people want to know more about concepts used here. They are from physic the equilibrium point or center of mass, and the mathematical tool are the matrices. The theory details can be found in Wikipedia.

That's all folks!

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## 2 Discussions

You can make use of excel formulas to automatically calculate realtime on change in blocks.
Here is a sample in case somebody wants it.
(Not just for automation but in general to try the equilibrium method.)
ODF Format: https://jmp.sh/ZZF9RGb
XLS Format: https://jmp.sh/PmsLVoa

Very good. It enriches the main text.