# Lego Technic Pi Day Machine

Here I present a Pi Day special Lego Technic machine that produces a gearing ratio of Pi/8 using a 56mm wheel driving a 13x13 square wheel.

The correctness of the ratio is confirmed by matching it with output of a 2 differential gearing system that produces a ratio of 355/904 also approximating pi/8 to 7 significant figures.

# More to explore

### Gearing Ratio Calculator Tool Help

## Lego Technic Gearing Ratio Calculator Tool

Here I present my new Lego Technic Gearing Ratio Calculator tool. This tool allows you to upload your Lego Technic .ldr (Lego Draw) file and it will simulate the gearing system and visualize it as well as showing the gearing ratios relative to the input component.

The tool can be accessed...read more

## New Flat 12/20 Gear Friction

The Lego Technic set 42140 App-Controlled Transformation Vehicle introduces two new gears - a flat version of the 12 tooth bevel gear and a flat version of the 20 tooth bevel gear. These gears are designed to have less friction.

In this video I measure the difference in gearing efficiency...read more

## Measuring Gearbox Efficiency

This video describes a method for measuring the efficiency of a gearbox using the Lego Technic Powered Up hub. Gearbox efficiency is defined as the ratio of the output power to the input power and here I show how to measure each of these values to allow you to calculate the overall efficiency.read more

## Lego Technic Binary Expansion of Pi

This Pi Day video demonstrates how to approximate a gearing ratio of Pi by representing Pi as a binary number and using differentials arranged in a chain formation to create the binary representation. Each differential implements 1 binary digit. If the binary digit is zero the differential can be...read more

## PI Day Lego Technic MOC using two lego differentials

Here I present a PI Day special Lego Technic MOC that produces a gearing ratio of the match constant PI to 6 decimal places. This is using two differentials to produce a gearing ratio of 355 to 113. Celebrate PI day 2020.

More details of how to design two differential Lego Technic gearing...read more

## How to use a Lego Technic differential for creating prime gear ratios for MOCs. Part 1

Here I discuss techniques for creating prime number gear ratios such as 17:1, 19:1, 23:1, and 53:1 using a Lego Technic differential. Learn the mathematical relationship between the gear to create your own MOC desired ratios. Use this lego differential tutorial to design your own lego gear ratios...read more

## How to measure a Lego Technic Crane's Efficiency. The results surprised me!

Here I demonstrate how to measure the efficiency of a Lego Technic MOC crane using basic physics. Efficiency is the ratio of the useful energy output (the potential energy put added to the weight) the to the input energy (power source power). The efficiency curve is interesting and does not look ...read more

### How do you make a 1:N gearing ratio?

## Lego Technic Powered Up 3 Speed Automatic gearbox 2

This video presents a revised version of an earlier Lego Technic Powered Up 3 speed automatic gearbox. The previous gearbox used a differential for torque measurement and used a powered up large motor to convert the differential rotation into a torque measurement.

However as it turns out ...read more