This Instructable shows how to first create a 3 pendulum harmonograph, and then use its mechanical drawing capability to create long exposure photographs of light harmonograms.
A little bit about a harmonograph can be found here:
In short it uses the physics of several pendulums to control where a drawing point is in space. In a 3 pendulum harmonograph two pendulums control the position of a pen. The third pendulum is used to rotate the drawing surface. The relation between these three pendulums creates the varying patters one can draw. These patterns depend on the amplitude of the swing of pendulum, the phase of the swing of the pendulums to one another, as well as the frequency at which the pendulums swing back and forth. Another variable is the direction in which these pendulums swing. In this instructuable, we will show you how to create a single dimension pendulum and a two dimensional pendulum to achieve various pendulum movements.
On the history, theory, and what these cool patterns represent:
The the invention of the harmonograph is thanks to Professor Blackburn in 1844. Towards the end of the 19th century people loved these things. They could often be found at soirees and dinner parties; everyone gathering around to watch as the beautiful patterns emerged.
Physically the pendulums represent wave forms, which could be thought as in this scenario super slow sound waves. Like sound waves the motion of the pendulums can relate to each other in different ways creating harmony with one another. In the harmonograph the pendulum's frequency is changed by raising or lowering the weights at the end of each pendulum. Depending on the relation ship between how quickly each pendulum swings back and forth different patterns will emerge. More on pendulum swing and how this relates to the ratios of music theory can be found in other resources such as in the book Harmonograph, A visual Guide to The Mathematics of Music, by Anthony Ashton.
Before we get started, we'd like to give some credit to the people who have provided tutorials which helped us greatly in creating our own harmonograph and be able to convert it to be able to capture long exposure light harmonograms. Like most recipes, we've taken what we love about several and then added our own spices to make it our own. Please expand on this further and share with us your personal evolutions!
The first is Karl Sims, who's documentation can be found all over the web when trying to figure out how to build one of these machines.
Another is Wayne Schmidt. His version adds the capability to allow the pen/arm pendulums to swing in 2 dimensions.
If you're looking for some inspiration, turn to Desmond Paul Henry who's taken this aesthetic and technique to profound levels.
Step 1: Parts and Materials
*Note the dimensions given for the materials below are specific to our design and what we found worked with our camera we selected for the long exposure photography. Feel free to change the dimensions to work with your design.
What you'll need to build the Harmonograph:
- Table Top: 1x 3/4" thick material like MDF or ply-wood cut to 33"x33"
- Legs: 8x 3/4" thick material like MDF or ply-wood cut to 4"x33-1/2"
- Pendulums: 4x 3/4" thick dowels, 2x cut to 45" long (for the pen pendulums), 1x cut to 34" long (for the camera plate pendulum, 1x cut to 42-1/2" long (for the drawing plate pendulum)
- Arms: 2x 1"x1"x24" long pieces of balsa wood, these will be cut down to the appropriate length later, we can start at 24"
- Drawing Plate: 1/4" thick by 9" x 13" piece of MDF
- Acrylic Base: 4x 3/4" x 2" x 9-1/2" MDF pieces (for vase verticals), and 4x 3/4" x 2" x 14" MDF pieces (for base horizontals)
- Clear Acrylic - 1/4" thick by 14"x24"
- Pendulum supports: 3x 2"x2"x1/4" thick squares MDF or other similar rigid material
- Mending Plates; 6x 3" long x 3/4" wide
- Washers: 3x 2" outer diameter with 1" inner diameter
- Clamps; 5x Clamps. We've seen other people use alligator clamps to hold up the weights,
- 12x 6-32 x 3/4" Phillips Pan Head Screws
- 18x 6-32 nuts
- 9x 1-1/4" Finishing Nails
- 8x 2" x 2" L-brackets
- Box of 1-1/4" Dry wall screws
- Box of 1/2" wood screws
- Weights: 12x 1-1/4 lb weights. You may use other weight amounts, we found getting up to around 5 lbs was a good range
- 4 high-pull magnets
- A rubber band
What you'll need for the light Photography:
(Note that this is specific to our method of creating a color changing LED. Conveniently we had these materials around the studio as we use them all the time for other light art projects. There are more simplified ways of creating a color changing LED. A tutorial for which can be found here)
- Computer: We are using a mac book pro
- Software: Resolume, and Madmapper, demos can be found for both of these programs on their websites.
- Entecc Pro USB to DMX converter
- USB A to B cable
- DMX LED Decoder such as this one
- AC to DC 12V Power supply such as this one
- A standard AC power cable to power the power supply
- Some wire to attach the DMX LED Decoder to the power supply
- Addressable LED light strip such as this one
- 4 wire LED cable
- Ballpoint pen tip (helpful for making the pinhole at end of the LED)
- Electric Tape
- Felt slides for chair feet
Step 2: The Table
Start by building the table.
The table top is made from a 3/4" thick 33"x33" piece of MDF
Then drill 3 holes in the table one hole for each pendulum. Drill these 1" in from their adjacent side and equidistant between neighboring sides of the table. We drilled a small hole and then opened it up to 3" using a jigsaw. We traced the hole diameter using the top of a Pringles can ;)
Each leg of the table is made from 2x 3/4" thick pieces of MDF cut to 4" x 33-1/2". These are butted with one edge over lapping the other and then drilled into the joined edge. The legs are attached using L-brackets to the underside of the table.
Step 3: The Pendulums
For the pen/LED Pendulums:
Cut 2x 3/4" thick dowels to 45" long
For the camera plate pendulum
Cut 1x 3/4" thick dowel to 34" long
For the drawing plate pendulum
Cut 1x 3/4" thick dowel to 42-1/2" long
Then drill some holes in the dowels using a 1/8" drill bit. These holes allow the pendulums to be adjusted up and down if necessary; they raise and lower either the pen/LED height or the drawing plate/camera height. We drilled 6 holes in 1" increments starting at 33" from the bottom of the dowel down to 27". In all of our tests thus far we have used the dowels supporting them at the 33" hole.
Step 4: The Arm
To make the arms start with 2x 1"x1"x24" balsa wood pieces.
Its important to make these out of a light material like balsa wood as the lighter they are allows for less friction between the drawing pen/LED and the drawing surface. Less friction means a longer more detailed drawing.
The two arms are different in our design. One holds the pen and the other supports the pen arm.
The Pen Arm:
The Pen Arm's main length is 17-1/4" long. Attached to the pendulum side is a 5/8" extension. This extension has a 1" finishing nail nailed into its center. The side without the nail point was then wood glued to the main arm. At the pen side of the arm we've glued the middle of a 2" long balsa piece with a 3/8" x 3/8" notch cut out of one corner for the pen to sit in. In the side of the pen attachment facing the support arm we placed two high-pull magnets. Holes for these were drilled to the depth of our magnets and the magnets were hammered in with a hard wood block. There need to be two magnets aligned so that the arms are supported by each and don't fall over vertically from the weight of the pen. About an 1" in from the pen attachment we place two finishing nails with about 1/4" sticking out to allow for a rubber band to be supported and wrap around the pen.
The Support Arm:
The main length for this arm measures 17". Again we've attached a 5/8" piece at the pendulum side with a finishing nail sticking out and then glued the flat side to the main length. At the support end we've glued a 2" long balsa piece at its middle vertically. This piece has two finishing nails that line up with the center of the magnets on the pen arm.
The Pendulum Arm Attachments:
The attachments that sit at the top of the pendulum are made from balsa wood also. Each attachment is 1-1/2" long. At one end a whole for a magnet has been drilled, then a magnet has been pounded into this hole with hard wood. The attachment is drilled into the top of the pen pendulums using a dry wall screw. We chose to hand screw these in so as to be gentle on the balsa wood and not split the dowels.
Step 5: The Gimbals and Pivots
The dowels are attached to the table using a gimbal support.
First create the 3 dowel supports. These are made from 1/4" thick 2" x 2" pieces of MDF with a 3/4" hole drilled from the middle of them.
Screw 2x 6-32 screws into the supports at about 1-1/2" apart from each other. We filed the ends of these screws to a sharp point so to reduce friction between the screw and the mending plate or washer they sit on.
On the top side of the washer drill two dimples 1-1/2" apart from each other. This is where the support screws will rest.
On the bottom side of the washer drill two more dimples at 90 degrees to the top dimples. This time drill them as close to the edge of the washer as possible. This extended distance allows the support provided by the mending plate to stay out of the way from the swinging dowel.
Next attach the mending plates to the table top. The mending plates will extend over the holes in the table. The mending plates for the drawing/camera pendulum should be parallel to that edge of the table. The mending plates for the pen/LED pendulums should be at 45 degrees to their neighboring table edges, so that the pendulums swing in an axis pointing towards the drawing/camera pendulum. Screw a 6-32 screw into one end of each of the mending plates. Using two nuts as spacers between the head of the screw and the mending plate, and one nut on the opposite side to keep the screw in place. Use the bottom side of the washer to align the mending plate screws far enough apart so that they sit in the dimples of the washer. Depending on the kind of mending plates you are using they may need to be offset from one another if the holes in the plates are offset like ours are.
Slip the dowel support onto the dowel and secure in place using finishing nail or hard wire pin. Next slip the washer onto the dowel making sure the top side is facing up. Rest the dowel support screws into the dimples on the top side of the washer. Lower the dowel until the bottom dimples of the washer rest on the points of the mending plate screws.
There are two variations for the dowel pivots. A 1 dimensional pivot which only uses the dowel support and the mending plates, and a 2 dimensional pivot which pinches a washer between the mending plate screws and the dowel support screws, where the mending plates and the dowel support screws are at 90 degrees to each other.
To allow for 1 dimensional pivot we simply retract the dowel support screws so that the points do not extend underneath, and rest the dowel support on on top of the washer.
Step 6: The Weights
At the bottom of each pendulum attach the weights using a clamp at the bottom to keep them from slipping off.
We've used 4x 1-1/4lb weights. You may use any other kind of weights, just make sure they are fixed on tightly to the dowel. We've found that around 5lbs total is best.
The weights can be raised or lowered to change the ratio of swing between the pendulums thus creating different patterns in the drawings or photographs.
Step 7: The Drawing Plate and the Camera Plate
The Drawing plate is made from a 1/4" thick by 9" x 13" piece of MDF. On the bottom side we've glued a 3/4" thick 2" x 2" block with a 3/4" hole cut half way into it. This hole sits on top of the drawing pendulum. You may find you want a larger or smaller drawing plate depending on how far your drawing pendulums are swinging.
The Camera Plate is made from a 1/2" thick by 4" x 7" piece of plywood. On the bottom side we've drilled a 3/4" hole. This hole sits on top of the camera pendulum. Depending on the camera you choose to use, you may find you need a smaller or larger plate, perhaps even with the ability to attach the camera to to keep it from falling off or moving during the exposure.
Step 8: Making a Harmonogram
Once you've attached all your parts its time to make a harmonogram!
When we first started we found it best to simplify all the pendulums to 1 dimensional pivots.
Start by placing some paper on your drawing plate. Tape it down so it doesn't move while the drawing takes place. Then take a scrap piece of paper and lay it on top of your nice paper.
Make sure your pen is attached with the rubber band holding the pen closer to the bottom. This will support the pen while the drawing takes place. If the pen is extended too far it has a tendency to create enough drag and leverage to break the magnetic connections of the arms.
Lift the pen up by the drawing arms or by holding the back of the pen so it's off the paper.
By holding the drawing pendulum below or above the table, start moving it backwards and forwards until you've achieved a swing with enough amplitude. Be careful to not over swing the pendulum. Too much and the pen may move off the pendulum and interrupt the drawing.
Now by holding the end of the pen arm, gently begin to move the pen in circles. Start this motion slowly so as not to break the magnetic connection of the arms. Once you've achieved a wide enough circle lower the pen onto the drawing plate.
After a couple of cycles remove the scrap paper and your drawing will begin.
Once the motion slows down, or you feel satisfied with your drawing, simply lift the pen off the paper. You can layer drawings and change the color of the pens to create more complex variations to the drawings.
Step 9: The Acrylic Plate
Adding the clear acrylic plate is the first step in transforming the traditional harmonograph into a light harmonograph.
The acrylic plate is 1/4" thick by 14" x 24"
It sits above the table on two rectangular frame pieces.
These frame pieces are each built from 2x 3/4" thick by 14"x2" pieces of ply wood and 2x 3/4" 9" x 2" pieces of ply wood.
The frames are then clamped to the table so they do not move during the drawing.
Step 10: The LED Pen
*The LED Pen that we used was designed using a technique we use often to create LED lighting installations. There are more simplified ways to get a single RGB LED to change color that do not require the software and hardware that we use in this example. If you are interested in LED installation art then this might be a good way to begin understanding the basics.
To make the LED Pen we first cut off a section of 3 LEDs from a LED light strip. Make sure to cut along the cut point on the strip otherwise you will damage the LEDs.
Our LED strip has a waterproof coating on it. If yours does as well strip back this coating using a razor being careful to not cut through the PCB of the strip. This will reveal the solder points on the strip.
We're using LED strip connectors to quickly connect the strip to wires. Push the solder points under the feet of the connectors and close the cover making sure it clips.
Next solder on an extension to the section of LEDs using heat shrink to cover the solder points.
The section of LEDs is wrapped around the eraser end of a pencil and zip tied in place. The middle LED is the one facing outward and will emit the light we need to make a drawing.
Find a ball point pen or a mechanical pencil with a tip that can be detached. Use the tip to cover the LED and then tape down using electrical tape. Continue to wrap the LED bundle with electrical tape so no light other than what shines out the tip of the pen cap can be seen.
Wrap some tape at the end of the pencil to connect the wire lead. This will keep the wires out of the way of the drawing.
Step 11: Connecting the LED
A more in depth description on how to connect and control LED lights using the method in this instructable can be found here. (Thanks to the people at Madmapper and Garage Cube!)
The 4 wire cable connected to the LED is connected to the 1st channel on the DMX LED decoder.
Black wire (communication) -> Communication port
Blue Wire -> Blue Port
Red Wire -> Red Port
Green Wire -> Green Port
The DMX LED Decoder should then be wired to the power supply.
Also on the DMX LED Decoder, make sure the dip switches are all switched off. Alternatively if you would like to see if the LED is working you may turn dip switch 10 on to enable a test mode (*this may be specific to the decoder we have, the test mode may differ between models).
You may need to make a quick power cable to connect your power supply to a wall outlet. This can be done with any grounded AC wall outlet cable you may have around. We used one that was made to power a projector. Simply cut off the end that doesn't go into the wall, strip back the wires and connect it to the power supply terminals.
Connect the Enttec DMX USB Pro to the Decoder using a 5 pin DMX to 3 pin DMX cable. Then connect the Ennttec box to your computer using a USB cable.
Step 12: Controlling the LED
Resolume is a vj program that has the ability to generate content in real time like a changing color.
To understand more about generating content in Resolume check out this tutorial.
Resolume then send the video content to Madmapper via Syphon.
Madmapper then samples this video and sends the color data via DMX to the LED
Again a thorough tutorial on how to video map LEDs can be found here.
Please feel free to message us if you have any questions about this process :)
Step 13: Making a Light Harmonogram
Before we mount our pen first attach a piece of felt to the head of a dry wall screw. Then screw this into the bottom of the pen mount on the pen arm. The felt will allow the arms to be supported on the acrylic plate while the LED pen hovers above the plate.
Mount your LED pen to the pen arm using the rubber band to fix it in place. Make sure the LED pen does not touch the surface of the acrylic.
Change out the drawing pendulum for the camera pendulum, and attach the camera plate to the camera pendulum.
Set the camera to the appropriate settings for a long exposure. For our camera we used and F-stop of 8 (the smallest aperture our camera would allow) a shutter speed of 60 seconds, and an ISO of 100. Feel free to experiment with your camera setting to get different results. Place the camera on the camera plate. Make sure the camera is focused to the point of the LED pen.
Begin the motion by first moving the camera pendulum. Once you've achieved a swing or rotation appropriate then move to the pen arm. While holding the 4 wire LED cable high and out of the way with enough slack to allow the LED pen to move, grab the pen arm and move gently to achieve a circular motion. Once this motion feels good lower the arms till the felt touches and slides along the surface of the acrylic.
Then carefully press the shutter button of your camera to begin the exposure.
The exposure may be stopped by covering the LED or covering the lens of the camera.
If the arms have stopped moving due to friction, don't worry if you'r camera's still exposing, as long as the camera plate is still in motion, the drawing will keep recording the LED as if it were in motion due to the relative motion of the camera. This can create some great effects.
This is how to create a Light Harmonogram. We hope you enjoy this method. Please share with us other versions you create and your long exposure results. Feel free to reach out and ask questions, we're happy to help!
Chris & Kat