When the OU's Dr Ian Johnston took up a challenge from the BBC Radio 4 More or Less programme to calculate how tall can a Lego tower can get before the weight of it crushes the bottom brick, intrepid producer Ruth Alexander might have been surprised to find quite so much Lego at the OU...

The earliest OU Lego activity I came across goes back almost 20 years ago, to the time of the mechatronics course Designing Intelligent Machines. As part of a home experiment kit, students were provided with Lego bricks, some OU produced electronics, and I believe a ping pong ball (does anyone remember what the ping pong ball was for?!) so they could build their own desktop robot.

Almost a decade later, I was part of a small team that put together the Robotics and the Meaning of Life short course (T184 in OU jargon), which included an optional set of home experiment activities based on the Lego Mindstorms Robotics Invention System. Developing T184 meant that we had to play with do educational research around the use of Lego, and also spawned the OU's Robotics Outreach Group that delivered robotics outreach activities to schools across the UK over a five year period.

Revisiting Lego as part of the day job was certainly an eye opening experience. I'd had Lego as a child, though never Lego Technic (aka "technical Lego") but now I was supposed to be working with it. One of the first things I discovered was the geometrical beauty of it, in part through The Art of Lego Design, by Fred Martin, another educator active in promoting Lego based robotics:

"Most people realize that the LEGO brick is not based on a cubic form. The height of the brick is a larger measure than the length and width (assuming the normal viewpoint of studs on the top). But few people know the secret relationship between these dimensions: the vertical unit is precisely 6/5 times the horizontal ones. Put another way, a stack of ﬁve LEGO bricks is exactly equal in height as a six-stud LEGO beam is long."

If you also realise that Lego plates are 1/3 the height of the standard Lego block, the informed Lego inventor soon learns how to assemble Lego Technic structures that incorporate vertical and diagonal structures which provide mechanical strength. At the heart of it, is a geometrically inspired mathematics.

I also learned that Lego structures could be used to do multiplications, of speeds and forces, using gear trains. Simple gear trains achieve a multiplication effect in the following way: a large gear, whose teeth are meshed with a smaller gear, turns once; the smaller gear, with less teeth on its circumference, turns more than once. It rotates faster than the larger gear, though it can exert less rotational force ("torque"). This works the other way, too. The small gear turns once, and the large gear turns less than once, though it can exert a greater force. Things get more interesting when we move up to compound gears... Like this simple example:

Copyrighted image Credit: The Open University A Lego buggy

(Shh... don't tell anyone... but I managed to sneak out these course notes on gear trains...)

I never did quite manage to build mechanical computer though, unlike this example of a Lego difference engine...

As part of the T184 course materials, we also had to produce construction plans for the robot buggy that students would use for their programming exercises. One way to produce Lego building plans is to construct a model, photograph it, and then take it apart, photographing each step, and the piece(s) you have just removed from the model as you do so. Having captured the deconstruction of the model, reversing the order of the photographs produces the construction plans.

That was too easy though. Which is how I came to discover the world of CAD - Computer Aided Design. CAD packages? For Lego...? For sure - and they let us create images like the following, as well as construction plans:

Copyrighted image Credit: The Open University Lego gears

If we'd had time, or bumped the course up to a more traditional 30 point, 300 hour course from it's 10 point/100 hour allocation, who knows? We might even have included a unit on Lego-based computer-aided design.

(The package I used to use - MLCad - looks as if it's still around for Windows computers, with an alternative offering for Mac users. Check out the LDraw site for more details. I also notice there's now an "official" Lego CAD studio available for download too.)

Having built up a considerable amount of expertise in Lego robotics through developing T184, we didn't let it go to waste. TXR120 Engineering: An Active Introduction included a day long hands-on workshop, in which students took on the challenge of programming a robot to search an enclosed tunnel network for a lost teddy bear...

We also spent a lot of time in schools and at family learning events, running hands-on robotics sessions.

Whilst an updated version of T184 continues in the new course Technologies in practice, the Lego activities are no longer included. But fear not - Lego robotics still lives on, in part, in one other OU course: T885 Team Engineering. During the first residential weekend of that course, small teams of students spend a hectic couple of hours building a working model of a robotic amusement park, complete with autonomous robot buggies and automatically triggered amusements.

I'd like to think that if we had a bit longer - maybe a week or two - they could actually build an automated airplane factory...

Whilst the forces experienced by some of the Lego figures on the at times terrifying amusements built by the T885 student teams are often enough to shake some of the rides to pieces, they're not quite large enough to actually crush a Lego brick. I have seen Lego axles twisted and misshapen, though, as a result of some over-ambitious gearing schemes. I've never seen anyone crush a brick though. As to what sorts of forces you'd need to do that, here's Ian...