Ex 07 | Machine Development

Analog Drawing Machine // Harmonograph

Up to date //   10/18

Initial Concept and Sketches

We set out to design a parametrically expandable two pendulum harmonograph; much like the one you see on your right. We designed a masonite base which sits at the corner of any table, and snaps together to create a drawing platform and to house all of the joints. In this harmonograph, two single axis pendulum come together to produce a 2 dimensional pendulum movement, giving more control to each of the vectors individually. We used basswood dowels for the arm assembly, where each joint is 3d printed. This allows you to scale, swap components, and experiment with different combinations without reproducing large parts. 1986_dennisburkholder_pendulum_design_machine_patent_us4703562-1


Parts Development


Masonite Stage that hold both arms and the drawing surface.

Lasercut with pressfit slot and joints.


//Mid Section

Houses a single ball bearing (8x22x7mm) – Available from Amazon here!

The dowel slots through, and an adjustable screw notches into the top to fix rotation and level.



Initially we intended to use a fluid weight at the bottom of each pendulum. We thought the movement of the fluid within this canister would create noise in the drawn artifacts. The piston controls the movement of the water by limiting the volume that it can occupy. More on the successes and failures of this concept below.


//Top Section

This joint translates the movement of the pendulum arm to the drawing apparatus with minimum friction/resistance.


//Drawing Arm Joint

This is the second unit for the joint between the drawing arm and the pendulum arm, and interfaces with the above item (Top Section). It houses a rivet that sits in the bowl of the Top Section.



Download all of these files from Dropbox.


Initial Assembly p1040067
We used a clipboard as a drawing surface, as it allowed us to quickly swap paper. p1040068
The joint where the two arms come together and meet the pen is the simplest. Just binding them together with a few rubber bands works like a charm! p1040083
The rivets we used were quite long, causing the arms to wobble side to side as they tried to balance. We recommend cutting the rivet stems down to about 3/4″. p1040071
Here you can see the Mid Section, connected to the stage with a dowel, the Top Section, and the Arm End. p1040088



//Index 0 Drawings//


Double Pendulum

//Concept and Modelling

We wanted to create more noise within the system, so we introduced a second join in the middle of the pendulum arm. This joint is free to move in a single axis, and acts another pendulum within each axis.

We split each arm and inserted this joint. It uses the same ball bearings as listed above. harmonograph_v02-v21_01


Double configuration. p1040099





//Index 1 Drawings//


Linear/Radial Movement

//Concept and Modeling

We wanted to see how we can manipulate the drawn artifacts by restricting each pendulum to a singular motion. One pendulum creates strictly linear motion and second creates strictly rotary motion. The degree of distortion correlates to the distance of the drawing from the rotary center point. Pictured on the right is an insert that accepts another ball bearing and supports the circular drawing bed with a dowel.



You can see how the pendulum on the left is connected to the drawing bed, and the pendulum on the right is restricted to linear movement by a rail on the far end of the arm.




//Index 2 Drawings//



Spinning Bed

//Bed Assembly

We placed a small DC motor beneath the bed to give us a constant rotation and went back to the original arm and pendulum assembly.

DC motor info:

Electricity Input 12V ; Spin speed 9 RPM



//Flexure Arm

Later in this drawing set, we decided to change the drawing arms to something that would act a bit more erratically and respond to obstacles on the spinning bed.

Using piano wire, we created to bends which let us pin into the top of the pendulum arm, and hold the pen somewhat perpendicular to the drawing surface. A small hole in the top end of each dowel accepts the piano wire.


//Pen Assembly

Electrical tape keeps the piano wire from sliding up and down the pen. Moving these arms closer to the pen point minimizes wobble.



We used a variety of obstacles that we adhered to the spinning bed.

We tried:

  1. Circular obstacles with centers that align with the bed center
  2. Linear obstacles which start at the center and continue to the drawing edge
  3. Linear Obstacles which cross the whole bed at its center
  4. Point obstacles
  5. Elastic Linear Obstacles (two rivets, bridged by a rubber band)





//Index 3 Drawings//

//Index 4 Drawings//

Spinning Bed / Variable Speed 

//DC Motor Control

We purchased a DC Motor control so we can begin to vary the speed of the rotating bed. You can get one from Amazon here!



Wiring this controller is insanely simple. It lets us work with 1 – 12 RPM.


//DC Motor Housing

We revisited the spinning bed apparatus, now that the motor is driving it instead of the pendulum. The bed now sits on a thrust bearing (30x47x11), instead of resting on the drive shaft. There is both a top and bottom of this housing, so that we can switch the top to work for new functions (see paper feeder below).



You can see how the thrust bearing sits in the top of the housing. We had to extend the drive shaft, and convert it from a rod to a hexagonal insert.


//Bed Assembly

The bed now notches into both the drive shaft and the thrust bearing. Note that the bed doesn’t actually rest on the shaft, but rather is flush and notched onto the bearing.





//Index 5 Drawings//



Linear Paper Feed 

//Fusion Modelling

We wanted to re-purpase the DC motor to move/feed the paper linearly over the course of the drawing.

The motor is attached directly to a 1/4″ aluminum rod using a 3d printed collar. Electrical tape acts as paper rollers to grip and feed the paper through as the rod rotates.

We designed a new top half of the motor housing that would attach onto a drawing bed bracket. This part accepts a plastic bushing to minimize friction in the rods rotation, and can slide up and down the bracket to adjust paper pressure. The bracket mounts onto 3/4″ MDF.

A similar bracket mounts to the other side to keep the roller straight.



The harmonograph draws between the two rods. The rod on the left feeds the paper through at various speeds.



Here you can see the DC motor assembly on the left, with the same bottom half of the housing as the spinning bed example, but with a new top half and collar. On the right is the other bracket; which we improvised an easy paper release with rubber bands. Pulling it up releases the paper.

p1040106 p1040108


 //Index 6 Drawings//



 //Index 7 Drawings//