Table Harmonograph

The original harmonograph was created in 1844 by Professor Blackburn in attempt to understand spatial harmonies. The analog machine we sought to create was an interpretation of the original harmonograph that Professor Blackburn designed. The instructions for the machine are contained in the book provided in the link below or there is a shortened version on the “How-To” website. There are many ways to recreate this machine, but we chose to keep it as classic as possible because the scale allows more opportunity for modification and interruption to create more unpredictability within the machine.


While building there were a few issues that arose. The gimbals we chose to create were extremely in-expensive and basic. This created large difficulty to make them on center for the pendullums to operate, there were at-least a dozen failed attempts from which the wood cracked from frailty. In the future I would suggest to buy these gimbals or buy materiel that is actually “true” to size, not that home-depot garbage.

In addition, you need atleast five lb’s on each leg for them to operate satisfactory. These need to be able to spin freely, so make sure the hole are absolutely clear of any objections or protrusions. Make sure the washer’s are large enough or the dowel’s will also get in the way.

Basic Setup:

Three pendullum’s: two two-axis , one four-axis.

The two two-axis pendullum meet at a perpendicular point on top to join motion holding the preferred drawing tool.

The one four axis pendullum is connected to a flat square board where it is allowed to move freely on a gimbal making contact with the pen.


Weight Height

Adjust a pendulum’s weight height to change its swinging frequency. The frequency of a pendulum varies with the inverse of the square root of its length, so to swing twice as fast, the length between the fulcrum and its center-of-mass would need to be 1/4 of the original length (which may not be practical with this harmonograph). For a 3:2 or 4:3 frequency increase, the weights would be raised around 19″ or 15″ respectively, although you should probably do some timing tests to find and mark these heights experimentally.

Weight Amount

Add more weight to a pendulum to counteract friction and make the swinging last longer. I’ve found that 5 lb (2 x 2½) on the rotary pendulum, and 7½ lb (3 x 2½) on the other two works fairly well. Note that adding more weight does not generally change the frequency of the pendulum.

Phase and Amplitude

Each time you swing the pendulums to make a new drawing, the relative phases and amplitudes of each pendulum will vary. Try some where the rotary pendulum and the lateral pendulums are initially making circles in the same, or in opposite directions. Try some where the lateral pendulums are initially swinging in phase to make a diagonal line.

How-To Link: HereHarmono Graph Book Link: HereInformation:Lumber:1 3/4″ x 3’x3′ plywood for table top
4 1½” x 1½” x 40″ for legs (about 14′ total)
4 1½” x 8″ x 12″ for leg braces (about 4′ total)
4 3/4″ x 4′ dowels for pendulum and pen lifter
1 3/4″ x 1½” x 30″ oak to cut for pendulum supports, and other
1 11″ x 11″ x 1/8″ board for platform to hold paper

Hardware store:
3 3/4″ x 5″ long metal pipe nipples (plumbing section)
3 3/4″ to 1″ metal pipe bushings
3 1″ steel clamps
4 1¼” x 4″ metal plates (or 2 1¼” x 8″ plates cut in half)
1 large metal washer with 2½” outer diameter, 1″ inner diameter, for gimbal
1 screw-eye for pen lifter
various drill bits: 3″ circular, 3/4″, 1/8″, etc.
various #10 screws (1″, 1¼”, 1½”, 1¾”, 2″, 3″)
a few thin nails
tools: drill, saw, hammer, tape measure, file, sand paper, etc.

Sporting goods store:
2½ lb weights with 1″ hole, 8 to 12 of them

Art supplies store:
2 1/2″ x 1/4″ x 30″ balsa (and maybe a spare or two)
various pens such as: Silver Uni-Ball GEL Impact, Pigma Graphic 1 (1.0mm), and Sakura Identi Pen.
some string and rubber bands
paper, 8½” x 11″ (or 9″ x 12″) some black, some white

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Table Harmonograph 2.0

After reviewing the outcomes of the previous work, the harmonograph needed several additions to create a drawing that produces something with more clarity. The main issues were primarily reducing the load of the two axis pendulums so that their weight would allow it run smoothly without interference. This interference stopped the drawing to have range so that the production was primarily uncontrolled. To fix this issue we reworked the pin-connection and the makeup of the arms. In addition to fixing the two axis pendulum, we machined a new washer for the four axis pendulum and made height adjustments for it to run optimally. After these alterations within the four axis pendulum it still remained a means of abstracting the drawing and allowing noise to become an affect.


Two Axis Pendulum Alterations – Counter weights, pin connection

Pen Up – Pen Down

Smoother four axis pendulum

Basic Setup:

Two new arms, with new pin connections

Machined Gimbal

Heavy 5 lb weights, 15 lb on either leg.



Old arms that connected to the two two-axis pendulums. These are now replaced with new arms that have counterweights and different pin connections to allow a smoother flow of motion.


Tempered glass on top of the drawing bed to allow smoother drawings to be made with less friction.


Four additional connections to stop the drawing bed from warping motion as it spins.


Old pin connection used previous to the new arms.


New pin connection that balances the arms on a indented metal cylinder.


Top view of pin connection.


Bottom view of pin connection.


First test with counterweights as buckets.


The buckets caused additional problems as they swung, so we did a direct connection adding wood as counterweights.


Pen Up – Down Experiments


Affixing an arm to test the Pen-Up + Pen-Down. Below are results.


Affixing arm using string. This proved to be a better means for the application because it allowed less restriction on one axis.