Hardware Reference
In-Depth Information
or on a desktop machine. here are almost a bewildering variety of Arduinos, but the vanilla
one at the time of writing is the Arduino Uno, so that is the one I suggest that you use.
Putting It Together
After you have all the components in place you can start to put them together. he irst thing to
do is to get the pendulums made. In my version of the harmonograph I have used four pendu-
lums that can be combined in a number of ways to produce the inal drawing. In place of the
complex arrangement of weights and counterbalances and gimbals used in conventional har-
monographs, you just want four simple pendulums of difering lengths. It is the ratio of the
pendulum's periods that gives the fundamental class of the pattern, and integer ratios look best.
So with that in mind I calculated some pendulum lengths to produce a fundamental frequency
of swing along with twice and three times swing harmonics. hese are set out in Table 16-1.
Table 16-1
Length of Pendulum for Various Harmonics
Harmonic
Normalise Length
Real Length
Fundamental
7.96
796 mm
2
1.91
191 mm
3
1
100 mm
he practical size of the third harmonic pendulum basically governed the size I needed for the
fundamental or longest pendulum. You can make the pendulums covering more harmonics if
you like, but you will see that they rapidly get quite big. For example, if you want to cover four
harmonics, with the shortest pendulum at 100 mm, then the longest pendulum needs to be
3180 mm. he mass of the pendulum does not afect the frequency of swing, but it will afect
how long it will swing. In efect it is the damping factor; in other words, the more the mass, the
longer it takes for the friction in the bearings to stop the swinging. Getting suicient mass into
short pendulums is tricky; it is easier for longer ones. In fact the equations assume that all the
mass of a pendulum is concentrated at the end of the rod or string. What happens in practice
with a distributed mass is that the efective length becomes the centre of mass of the pendulum.
his means in practice the pendulums have to be slightly longer than the theoretical length.
A trip around a national chain of DIY stores brought some rectangular metal tubing and solid
bar to my attention, and it looked as if that would do the job for the pendulums. So then I
had to design a frame to mount them on. For this I used 1 1/2" by 3/4" by 1/8" and 1 1/14"
by 1/2" by 1/8" aluminum channels, referred to as the
large channel
and
small channel,
respec-
tively. his has the great advantage that the small channel is a tight it inside the large one,
which makes the design a bit easier. I didn't ind that the DIY stores had this size in stock, so
I had to order it online. he idea is to make two U-shaped frames and bolt them together
with four lengths of aluminum channel. his is shown in Figures 16-4 and 16-5.
