Building the Best Harmonograph

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\title{Building the worlds best harmonograph}
\author{Maker0}

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\begin{abstract}
The harmonograph is a complex drawing machine, with complex interactions between multiple pendulums, producing twisting twining beats. Underlying symphonies in drawn lines, with emergent patterns. Lets look at what the harmonograph is, how it works, and how you can build your very own, with materials you probably already have.
\end{abstract}

\section{History}
A harmonograph is a mechanical apparatus that employs pendulums to create a geometric image. The drawings it creates are called Lissajous curves. The harmonograph was invented in 1844 by Hugh Blackburn, a professor of mathematics at the University of Glasgow.
\section{Functionality}
Harmonographs can have many pendulums and axes interacting, but every version of harmonograph suffers from the same constraints: force, and overcoming drag. Traditional harmonographs use mass and leverage to overcome drag placed on a pen. This makes traditional harmonographs cumbersome, heavy, a little bit hazardous. Everything from construction cost, to run time, to image quality is effected by the amount of drag which must be overcome to produce motion. \\ \\We want to make the worlds best harmonograph, which I assume means, light, small, and safe to operate. Maybe the whole thing can fit in my backpack, or pocket? The thing that makes harmonographs not work is drag,
so how do we get rid of drag? The sources of drag are mainly from the pen dragging across the drawing surface.
Other forms of drag occur, from mechanical friction in things like fulcrums, bearings pivots, motors, having poorly designed pendulums, wind resistance, or obstructions in path of the pendulums. \\
If we get rid of pen drag, the size and mass of the machine can be greatly reduced. In wondering how to do this, I was playing with a drawing tablet. I noticed the stylus did not actually need to
touch the surface of the tablet to send the draw signal. The stylus, which works like a antenna, between the tablet acting like a transceiver which gets a stronger signal with the nib fully inserted.
With tape, or an elastic band suppressing the nib, the pen can operate about an inch away from the drawing tablet surface. This solves the primary constraint,of pen drag.
\section{Construction}
\textbf{Material needs}: magnets with a fastener, lightweight metal plate, string. other fasteners and or tape are optional.
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\textbf{Optional material}: a usb switch can make stopping the drawing process easy.
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\textbf{Software}:Your choice for software. I use myPaint, a free, and open source drawing program that works well with drawing tablets. Many other options exist.
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\textbf{Tool needs}: A drill, scissors or something to cut string with.\\
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 Core requirements are that the plate is suspended by strings, and that the stylus is suspended above the drawing tablet via the plate.  \\

 To begin, locate a place where you wish to suspend this harmonograph. It should be sturdy enough to withstand supporting the total mass of the system. between 0.5 to 5 Lbs.
 Next, determine the total length of string needed for each pendulum. Pendulum length determines both the speed of drawing, and travel of the stylus. This figure is the desired distance of travel with enough extra material to be able to secure the string to the magnets or some other supporting means. Tie one end of the string to the a magnet. Repeat this step as necessary, for the total number of pendulums you wish to have. in your metal plate, drill a hole sufficient to insert the stylus for your drawing tablet. Cork it with tape if necessary. Suspend the pendulum magnets, affix the magnets to the plate with the stylus in it. Situate the stylus above the drawing tablet. Plug the drawing tablet into your USB power switch. Open your drawing software of choice, and configure the software to draw lines. Give the harmonograph a gentle tap, and switch on the tablet feed. You should observe a pattern emerging. Switch off the tablet feed when you feel the drawing is complete.


\section{Operation}
Once your harmonograph is suspended, and your drawing tablet is in place beneath the stylus, you can give the harmonograph a gentle push. harmonic motion should immediately ensue. You can watch this motion for as long as you like. An efficient design will run for a very long time. An inefficient design may cease almost immediately. You can experiment, changing pendulum lengths, angles, positions, orientations, mass, distance from the detector (drawing tablet) and so on. Subtle changes may have vastly different emergent patterns.
\section{Annex of variations}
There are many ways to make this type of harmonograph. You can use inter woven strings in many patterns to create unique motions and interactions, use as few, or as many pendulums as you want. The use of magnets and a metal plate is what I found to be the easiest materials to procure, modify, and interact with. Many other possibilities exist, I have made similar, functional harmonographs with wood, cardboard, electrical boxes, plastic plates, and other materials. The primary issue I had with other construction methods was in changing the pendulum length and position. Using magnets made that process exceptionally easy to change.  \\
Adding mass, to the harmonograph can also extend operational time, or add emphasis to minute waves.

\section{Conclusion}Building the worlds best harmonograph is entirely subjective, but I hope readers can see the
benefits of building a harmonograph in this way. \\ Many possibilities exist for the construction of the harmonograph. tying strings to a plate, with the opposite ends secured to some other support
is feasible, although may not be as easily adjusted. The method of using magnets on a metal plate has been simple for my uses. This type of harmonograph is both highly configurable, and simple to construct. Users can enjoy learning about chaotic and periodic motion, while drawing pretty pictures. Most importantly, have fun!

Other variations: motors may be added to the pendulums to add a self-starting functionality. Use of other energy inputs can also be used to change the operation of the harmonograph in various ways.

\section{Glossary}
\textbf{Pendulum:} a weight hung from a fixed point so that it can swing freely backward and forward.\\
\textbf{Lissajous curves:} a family of curves described by the parametric equations. Common examples include circles, parabolas, and ellipses.

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