Joe Freedman's Amazing Cycloid Drawing Machine


Joe Freedman's Amazing Cycloid Drawing Machine:

I'm going to be saying a lot of good things about Mr. Freedman's drawing machine, so I need to clarify at the start that I have not invested in his enterprise, I do not receive a commission on any sales, he is not paying me to post this review and has not asked me to do so. Mr. Freedman is not a friend. In fact I have never met the gentleman. I'm doing this because as an engineer, I appreciate and value outstanding design and superior manufacturing. This drawing machine has both of these attributes in abundance and as such deserves to be acknowledged.


You may not be able to judge a book by its cover, but in my experience you usually can guess the quality of a product by how carefully it was packed for shipment. In the case of this drawing machine, I discovered that it had been packaged for shipment more carefully than anything else I have ever received through the mail. It was double boxed in top quality, heavy duty boxes. The inner box wasn't merely dropped in the outer box then the voids filled with packing popcorn. Instead, a dense layer of popcorn was laid down first, the inner box centered on top of it, then more popcorn was carefully packed in around the sides and top. The density of the packing was such that after several days in shipment, when I opened the outer box the inner box was still perfectly centered in the popcorn and fully cushioned on all six sides. This level of packing hinted that something of extreme quality was inside... and it was.

The inner box was sized perfectly to hold the drawing machine so that it couldn't shift around and be damaged.

An additional benefit is that the inner box turned out to be perfect for long term storage.

When the inner box was opened, here's what I saw:

To an engineer with an orderly frame of mind, this was nothing short of beautiful. Mr. Freedman's cycloid drawing machine comes with a specially designed organizer that holds all the gears and small parts in a safe and orderly manner. As I inspected it, I discovered that every single gear and part was absolutely perfect. There wasn't a single missing, scratched, dented or broken piece. This demonstrates the very highest standard for pride of construction.


Lifting out the organizer discloses the actual cycloid drawing machine. It was already assembled in the first drawing configuration suggested in the manual. All that was needed was to add two bolts and the machine was operational in less than one minute.

Underneath the drawing machine were two more main gears. The one on the machine was a 150-tooth gear. The two under it were 120 and 144-tooth gears.


The manual that came with the drawing machine was nothing less that the very best, easiest to understand manual for any device I have ever had. Besides complete explanations of how to machine works and the usual parts lists and descriptions, it features detailed suggestions for five different configurations, each of which is explained three different ways: with text, through a menu format, and with sharp, full color pictures. The configurations are ordered in increasing complexity so that working through them is like working through a carefully thought-out tutorial that's both informative and fun.


As I began creating my first drawing, I got another pleasant surprise. Although the cycloid drawing machine is constructed of the finest materials, it is still a wooden machine. I expected there to be a breaking-in period to give any rough edges a chance to wear off. There wasn't. My machine ran perfectly from the very first turn. It ran as smoothly then as it did after many hours of use.

With 21 gears, half a dozen pen holder arms and an extremely adaptable base, this drawing machine can be configured in an enormous rates of setups: everything from the very simplest above, which produces spirograph-like drawings such as these: very complicated systems like the following:


Once you've used Mr. Freedman's cycloid drawing machine for a while, you'll develop an almost overwhelming sense of appreciation for the incredible range of drawings it can create. For example, consider the following configuration, which is the second simplest setup suggested in the manual:

By merely adding two gears, the image has changed from a simple spirograph-like pattern, to a beautifully complex design that, to me, looks like wrapping ribbon entwined in a mobius strip. Now consider: the design can be altered by repositioning the pen back and forth along the length of the long pen holder arm. It can also be altered by changing the length of the shorter pen arm. The radius of the drive bolt on the right hand drive gear can be changed. The radius of the fulcrum pivot on the left gear can be changed. finally, the gears themselves can be changed. Each of these will have a profound affect on the resulting drawing. And just when you think you've completely mastered this simple configuration...


... you can reverse the pen arm so the pivoting fulcrum is now on the right and the drive bolt is on the left (I haven't repositioned the pen yet to place it on the paper.) and you'll get an entirely different set of drawings. In effect this one step turns all the previous drawings inside out. So now you get to go through all the changes again and discover an whole new set of patterns. And this is one of the simplest setups.

Considering the wide range of possible configurations possible for this drawing machine, anyone who is fortunate enough to acquire one of these drawing machines will never run out of new patterns to discover.

While this flexibility is one of the great virtues of this drawing machine, it also represents one of its greatest challenges. It's tempting to start throwing gears on it to see what they do. The problem is that doing so is like parachuting into the middle of an Amazonian jungle. You may find beautiful things, but because you don't know where you are you can't have the same appreciation as you would by blazing your own trail to that spot. For this reason I recommend a more structured approach to working with this machine.

Start by selecting a setup. Adjust the pen so that it is as close to the pen holder arm and as far to the right as possible. Make a drawing and move the pen halfway to the left of the maximum range of positions that keep the pen on the paper. Make a second trace then repeat with the pen moved as far to the left as possible. That's what I did to create the top three images from right to left in the image below.

The drawing machine was setup the same as in the previous image with the exception that the gears were changed to create three-lobed patterns.

The pen was moved back to the right, lowered half of its vertical range down and the right-to-left sequence repeated to create the middle row. The bottom row is the same, with the short pen arm now extended downward to its maximum extent.

What this creates is a matrix of patterns that shows how the image evolves as the pen position is changed.

Don't expect the changes to follow a simple, predictable pattern. Every once in a while you'll hit a point where a unique combination of gear ratios and pen position to create a sudden, unexpected pattern. This is one of the joys of this drawing machine: order with the occasional surprise.

A test matrix like this can also be used to fine tune a design. For example: the middle and bottom patterns on the far right were the most interesting to me, but I thought they'd be more attractive if the size of the lobes were the same. By positioning the pen one quarter of the way between the middle and bottom setup, I was able to obtain the following pattern with more equally sized lobes:


Here are a few more examples of how patterns can be manipulated by changing the setup:

Here again is the twisted-ribbon pattern.

By reducing the radius of the drive bolt the width of the ribbon is reduced.

Note that it has the same number lines, they're just compressed.

The following three images show what can happen as the position of the pen is moved so that it oscillates more closely around the center of the paper:




Here's another example of the same idea:



The number of lobes a drawing has is determined by the number of teeth in the main gear and the pen driving gear. In the following example the main gear has 150 teeth and the pen driving gear 100 teeth:

To calculate how many lobes to expect, start by factoring the number of teeth in each gear down to their smallest whole factors. For example: 150 = 2 x 3 x 5 x 5 and 100 = 2 x 2 x 5 x 5. The largest common factor for both gears is 2 x 5 x 5 = 50. Divide this into the main gear and you get 150/50 = 3, which tells that this configuration will produce patterns with three lobes.


Switching to 144 and 108-toothed gears gives: 144 = 2 x 2 x 2 x 2 x 3 x 3 and 108 = 2 x 2 x 3 x 3 x 3, which gives a largest common factor of 2 x 2 x 3 x 3 = 36. 144/36 = 4 so there will be four lobes in the pattern.



Using a 120-tooth main gear (120 = 2 x 2 x 2 x 3 x 5) and a 100-tooth pen drive gear (100 = 2 x 2 x 5 x 5) yields a largest common factor of 2 x 2 x 5 = 20. Divide 120 by 20 and you get 6, which means the image should have six lobes.

Note that by keeping the pen positions the same, while the number of lobes increases the basic shape of the lobes doesn't.

While many of the complex patterns this drawing machine can make are interesting, please don't ignore the simpler spirograph-type patterns it can also create.


They exhibit such extreme symmetry that they possess a beauty all their own.

Changing the color of the pen can create rainbow-like patterns.

As pretty as these can be, I have to confess that it's hard not to be seduced by the more abstract images this machine can create.


Here is my final review: I have made and purchased several drawing machines and have studied many more. In my informed opinion and for the following reasons, Mr. Joe Freedman's cycloid drawing machine is the finest drawing machine in the world.

1. Adaptability: The images on this page barely hint at the full range of patterns types this drawing machine can produce. I have never had nor seen anything that comes close to it. I've put in well over 20 hours working with it and haven't come close to covering even its basic capabilities. Anyone fortunate enough to obtain one can look forward to years of satisfying entertainment with it.

2. Storability: This isn't as minor a point as might be imagined. Most drawing machines are large, fragile and take up a lot of storage room. Joe Freedman's drawing machine fits in a small box that will fit on any shelf.

3. Convenience of use: Drawing machines are notorious for taking a long time to set up and requiring large areas for use. This machine even in it's most complex configuration is a compact table-top size that will fit anywhere. It's light weight and can be easily moved "without disturbing its setup." This last is unique in the world of drawing machines. Try moving a harmonograph or a heavy motor-driven drawing machine and you'll understand what I'm talking about. They have to be torn almost completely apart to do so safely. Even the simplest plastic spirograph can't be moved without throwing it out of alignment. With the cycloid drawing machine, it's possible to draw half a figure, stop, move the machine to a new location and start drawing again with little more impact on the design than a slight smudge where a little extra ink leaked out of the pen. Retract the pen before moving it and you won't even have that.

4. Reliability: Most drawing machines are finicky. Sometimes they work, sometimes they don't. I've set up Mr. Freedman's drawing machine and ground out images for hours without a single jam or hitch of any kind.

5. Quality of manufacture: I've already commented on the high quality and attention to detail that went into the design and construction of this drawing machine. All pieces are precisely cut using a computer control laser cutter. After that, those requiring assembly are skillfully glued together. I have not had a single gear that failed to mesh or part that refused to fit where it was supposed to.

6. Uniqueness: These drawing machines are hand made, one at a time. They are not mass produced. If you're fortunate enough to get one you can take pride in knowing that you are one of a lucky handful of people in the entire world who do.

7. Fun factor: Now we get down to the real reason to purchase on of these drawing machines: is it fun, interesting and entertaining? Absolutely on all levels. First, the quality of construction and the beauty of the design makes it a delight simply handling it. My father once mentioned that there is a joy in owning something that is the best. It doesn't matter what it is or even if anyone knows you have it. It's not about ego or showing off. It's hard to put into worlds, but when I work with this machine I feel it in abundance. Putting that aside, even if you never draw a single picture with it the machine is fun to put together. It's like an erector set or legos for grown ups. It's great just to sit down and tinker a gear train together whether you draw with it or not. But if you do click the pen on and start cranking away, the enjoyment is doubled. There's something hypnotic about watching it work. And I'm not talking about the effect of watching a spinning spiral. You start turning the crank and at first all you see is a confusing of randomly wandering lines. It doesn't seem possible that anything could possibly come out of it. You crank away hoping for the best and just when it seems like things couldn't get worse... they get worse. But then, strangely, impossibly, a hint of order begins to emerge out of the chaos. You lean closer, turning the crank slower, pulled in by what's forming in front of your eyes. The image expands, seeming to grow magically on its own and all of a sudden there it is: something completely unexpected. You blink, wondering how it happened, then unconsciously reach for another piece of paper trying to imagine what the next pattern will look like.

If my prose strikes you as being overly flowery, please believe me that none of it is exaggeration. This is a great machine. Without a doubt, it's one of the best investments I have ever made.

Speaking of investment, because I have no financial connection to Mr. Freedman or his company, it would be inappropriate for me to comment on how much one of his cycloid drawing machines cost. For that I invite anyone interested to visit his website at for pricing and availability.

Thank you for visiting this page. If you'd like to view Mr. Freedman's drawing machine in operation, he has many videos of it posted on his webpage as well as a very interesting video of his laser cutter in operation. His videos are also available on YouTube. To find them, use the keyword search string, "cycloid drawing machine." I've made a video version of this page, which you can watch by clicking on the following:




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