# 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 systems is shown in my Differentials part 3 video.

# More to explore

## 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 355/9...read more

### 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

## 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

## 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

### What is a gearing ratio?

## 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

## Lego Technic 1,000,000,000 to one gearing MOC

This Lego Technic MOC has over a billion to 1 gearing ratio. It is designed to resemble an architectural tower structure. I measure the input speed of over 3000 RPM using a digital tachometer and calculate the rate of rotation of the tower top to be about 222 days per rotation.

...read more## How to use a Lego Technic Differential for your MOC Part 2: Computer Generated Solutions

In this video I present optimal computer generated solutions for designing 1:N (N=prime) ratios using a single Lego Technic differential. Insights and ideas are shown for implementing the 1:N designs in practice using Lego Technic liftarms with an example 421:1 gear ratio device. All the possible...read more