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## Meshing Lego gears |

After a year or so, I finally found some time to finish a "meshing computer" that I had started using Hypercard. This application is now available (see end of page).

Making Lego gears mesh is not trivial: one has a limited choice of bricks to build the assemblage that will provide the bearing holes at the right distance. If the distance between axles is too large, the wheels will not or loosely mesh, if it is too small there will be forces on the axles or the wheels will not fit at all.

The question often posed is: given I want a certain transmission ratio, which gears should I select and how do I position the bearing bricks for a satisfactory running pair of gear wheels?

Here is an example: take a normal 24-teeth gear and a 40-teeth one. They mesh very well when put in the same technics beam:

But there are other arrangements too, such as this one:

a 24x40 transmission (ratio: 1.6666) | a possible brick layout for it. |

To say the least: this is not obvious! The horizontal distance between the axles is 2.5 knobs (2.5x8mm) and the vertical one is two beams and two plates (2x9.6 + 2x3.2mm).

It would be nice to have a tool to display the possible arrangements, and that is what the meshing computer does.

The grid of axle positions has a normal pitch of 8mm horizontally and 9.6 vertically.

By inserting plates vertical distances of nx3.2mm (n>2) can be obtained.

Horizontal distances of mx4mm (m>1) can be made using the special brick of 8mm with one central hole. There is also a special vertical brick allowing a vertical pitch of 1.6mm.

Effectively then, the grid of axle positions has a pitch of 4mm horizontally and 1.6 vertically.

The distance between any two points in this grid can be computed using Pythagoras's theorem.

A choice of two gears imposes a distance between the axles that is related to the sum of the radii of the gears:

There are quite a few important considerations, but the main work the program does is to find the positions that give a satisfactory transmission for any pair of gear wheels.

You can download the application for free: Mac OS X — Windows.