This is a project I wanted to make for a long time, thanks to my girlfriend who bought me a little book about Mathematics and music which I have in the car and kept reading constantly…
Only recently I have gathered enough knowledge, information and time to accomplish some complex wood work projects.
I decided to try to make my first DIY Harmonograph, a Victorian invention from 1844 that draws beautiful images based on musical tone relation such as chords, harmonics and overtones. Click here for a detailed explanation.
Following my obsession for harmonics, overtones and algorithmic music I plan to recreate old school devices as close as possible, to then create modern scaled down versions.
My V1 three pendulum harmonograph:
The first prototype seems to work quite alright, but because I wanted to make it somehow re-usable and non-permanent, there is a lot of friction and movement in the bearing system I´ve designed in order to connect the two moving arms which hold the pen.
Because of the oscillation of the pendulum and the fact that each arm pulls or pushes the other one depending on the initial force, the mechanism must allow for free movement in X and Y axis…
My solution was a small “joint” consisting in two bearings at 90 degree, inserted in a small square piece of wood.
Many things learned in this process, like using rubber bands to hold stuff together, using small wooden bids as temporary bearing…
I will post images here because is a neat trick that can be used in numerous projects but all this system clearly asks for an upgrade to a more stable and accurate device.
Another crucial element of the device is the Pen Holder. The pen must be perpendicular to the painting surface and be firmly attached to one of the arms. Some pens don’t draw if the angle created by the gimbal is too steep, it’s all a try an error experience untill you find the correct weights, pen and paper so the action has as little friction as possible. Remember that most of the energy is lost while the pen is in contact with the paper.
After some tests, I decided to add some minor improvements to the arms, to allow the change of different pen holder mechanisms, bearings vs magnets, counterweights and fine adjusting the height. For that I inserted a screw at the top of each arm/pendulum so different accessories can be installed.
Magnets are great for this kind of bearing, because there is no backlash and allows free movement in all directions. However, a magnet is only holding in one side, the other one repels, so once the angle is quite drastic, the joint weakens. The second issue is that you cannot use counterweights with magnets and we will see how this is essential in future posts.
It´s also extremely difficult to glue, because they move and you must be carefull to double check they are in the correct position or else will can end up with repealing joints instead of connections. The size of this magnets must be at least 8mm in diameter or bigger, I used 5mm at first and they are not strong enough.
A trick to glue them was sticking two together so you know the direction of the magnetic poles and leaving one of them inside the wood… but is tedious and you must make one at a time, making sure the connections are correctly placed and to avoid the spheres getting out of the drills.
Gimbal and Fulcrum:
One of the coolest parts of this design is the use of very simple bearings using only screws that rest in a pivot hole marked on a piece of metal. The friction here can be very low and allows for fine adjusting easily.
The point in which a pendulum oscillates, is called the fulcrum.
The gimbal uses a similar system but here the main Pendulum is resting on a washer which is resting on another two pivot points at the bottom, resulting in free movement in 2 dimensions. The bottom marks in the washer are done at 90 degrees compared to the top pivot holes…. each pair of resting screws allow movement in one axis.
The top of the gimbal will accommodate a 30 by 30cm platform, made of firm and flat 6mm thick MDF. The platform was reinforced using balsa wood along the edge and supports at 45º to the main pole. The system is held in place with a screw, so it can be taken apart. In the picture below you can see magnets being use to hold in place the sheet of paper.
Weights and frequencies:
Like Galileo discovered a while ago, the frequency of a Pendulum comes from the length of it and not the weight.
Another interesting fact is that the frequency of the oscillation keeps constant while only amplitude decades though time due to gravity. In a pendulum we can then change the frequency by modifying the height of the weight.
A series of 12 holes are drilled in each of the pendulums, forming a complete octave with its semitones. The holes allow for a small wooden dowel to fit in acting as a limit for the weights which then will allow different frequencies to be set by each pendulum. A washer is added to even the pressure of the weights.
Considering it has been a week project, with no real expectations of a good result, I’m extremely pleased by the first results. I see a lot of room for improvement and potential upgrades that will allow more control, repetition and outstanding images so this motivates me to carry on and see what can be done.
I will post now some scanned version of the most pleasing drawings I have made while fine tuning this first prototype.
Video of the first prototype in use:
Short video of the device in use, while listening to some relaxing ambient from my Aerial EP.
Hope you guys like it!
Muchísimas gracias por tu blog que está genial, y además por la ayuda sincera que prestas a aquellos que tenemos dudas de principiantes.
Sin duda una página muy recomendable y que me ha sido de muchísima ayuda.
Perdona el retraso en contestar porque se me ha debido pasar la notifiación. Muchísimas gracias por tus palabras, me alegra mucho ver que te ha sido de ayuda.