Design

I used a combination of angle, channel and T section aluminium to construct the support. These were bolted together with M3 bolts to form a ridged construction, utilising cross braced pieces. I used xx mm thick aluminium and it might have been better if I had used thicker material because the final construction was not as ridged as I hoped. However, the twisting of the supporting structure did add another variable into the mix and produced some interesting effects so I will not rush to reconstruct it. The pendulum itself was a simple piece of channel aluminium with the walls at the end filed flat so I could glue a magnet to the end.

Next came the sensors, the reed switches are small glass tubes with wires coming out of the end. I cut up a small piece of strip board for each one, this was sufficient to also mount a surface mount resistor and LED on it. By arranging the reed switch to pull down to ground, I could get the LED to light when the switch was closed. The LED and it's current limiting resistor also acts as a pull up for the input, two for the price of one!

As this was going to be a music generator I decided to design it with a MIDI output, that way I could either feed it back into a computer for further processing or connect it directly to a MIDI sound module.

Next, as I wanted to make this a stand alone system I built a stand alone Arduino, however you can also use a regular Arduino if you want. I also used a 16 input port expander to give me 16 switches, however if you want to omit this port expander you can do an make a much simpler circuit. The schematic for all three variations can be downloaded here Pendulum_Schematics.zip so you an build what ever variant you like. Below is the schematic of the simplest Arduino only configuration. Finally there is an RGB LED used to add a bit of colour to the system when it is running, again this is optional as the system doesn't rely on it. The software is downloadable here Pendulum_soft.zip

Construction

Chaotic Pendulum

A pendulum is one of the most regular things in physics, it was one of the first things studied when Newtonian Physics was being invented. Legend has it that Galileo timed the swinging of a lamp in a Church with his pulse and found that the period was totally independent of the amplitude. That is the time it took to swing back and fro was the same irrespective of if it was swinging through a large or small arc. We now know that is not strictly true but to a first approximation it is. The pendulum was the basis of most clocks and time pieces for centuries and,, with the right care and attention, can be accurate to a second per week.

So what's with the title? Chaos does not fit very well in all this regularity. Well it turns out that a pendulum, of the right sort, is a very good model for chaotic behaviour. This is when slight disturbances in forces acting on a pendulum accumulate over many swings to produce a path this is difficult if not impossible to predict. To perform this trick we need two changes to a regular time keeping pendulum. First we need to make it swing in two dimensions or degrees of freedom, and second we need to subject it to small disturbing forces as it swings. And as a demonstration of this irregular motion why not let it play a tune and so I give you the chaotic Pendulum.

In Exhibition

At the Maker Faire (Newcastle 2010) people were mesmerised by the pendulum watching it intensely for minuets. Most reported it as a most relaxing experience, that despite all the noise going on around them.

If you watch the video you will see the pendulum appear to lock into a repetitive pattern, only to slowly develop. A typical sequence is where it alternates between two notes, then a third creeps in, and a fourth only to die down again. It is a project that has a lot of life in it and offers the chance for you to put in your own variations.

Concept

The concept is simple, a bar is suspended by a thin thread, it has a magnet at the end. It swings over a surface where at certain locations there are small magnetic switches known as reed switches. These are mechanical switches that close in the presence of a magnetic field. The minute energy that is needed to close the switch comes from the momentum of the swinging bar. Each time a switch is triggered a small amount of mechanical energy is removed from the swinging and the previous regular path is deviated slightly. This happens each swing and, depending on the number of sensors, at various parts of the swing. The result is an ever developing path and consequently a slowly changing triggering of the reed switches. The last stage in the process is to make each of these switches trigger a note, and also as a final flourish, light an LED.

Reed switches have quite a shot range, only a few millimetres, and I wanted to place them all over the surface. To make sure that the magnet did not fowl the switch at the centre of the swing and yet was sufficiently close to trigger the switch at the extreme end of the swing I needed a long bar. This was so the radius change was kept to a few millimetres over the full swing. I calculated that to do this I needed a pendulum bar of at least a meter, but basically the longer the better. So the first thing to make was the pendulum bar and it's support.

Construction

Construction is very much of a personal choice, the photographs show what I did when I made the full stand alone system, using a real Arduino board would be a lot simpler. Basically I constructed a small styrene box to hold the processor and I used it's translucent properties to make it glow with the RGB LED. I pre drilled the sides with holes to take the sensor wires which I made by twisting together three strands of very thin insulated wire. I placed the sensors in a semi regular pattern over the board and stuck them down along with the connecting wires with silicon sealant. You can see from the picture I actually move one of the sensors to bring it into play a bit more.

Operation

The sensors on the extremities don't get triggered all that often and you may want to use that to add a bit of variety. There is a mapping of sensor to note, that is what note each sensor triggers. I used one of these outer sensors to change that mapping and I reflected that mapping in the colours produced by the RGB LEDs. I made the LED change between two colours when each note was triggered. The actual colours that were used depended on the mapping in use at the time. Hence every time the mapping changed so did the two colours produced from the LED. If you examine the software, that is downloadable here, you will see this mapping is achieved by simply using a multi dimensional array used as a look up table.

There are lots of other variations you could play with this system. Sensors could trigger not notes but samples or loops, or you can get effects like a vocoder with the pendulum action changing the parameters.