Another Drawing Machine?
This is my fourth and final drawing machine. My Cycloid Drawing Machine was the best drawing machine that I'm capable of making. I thought it would be the last drawing machine I would ever make, but some people asked about getting one of my very first drawing machines. I called it the PrimoGraf, not because it was my first but rather because it drew Lissajous curves based on the relationship of prime numbers. (Lissajous curves are usually produced on harmonographs.) It was a beautiful little toy that came in a wooden box and had only 7 gears. It was limited but fun. The PrimoGraf was a nice project and many people enjoyed playing with the machine.
I wanted to produce a new batch of them but modify some things I learned from the Cycloid like a revised penholder and different gear supports. Then I wondered about adding a turntable so it could be either a linkage lateral harmonograph or an epicycloid toy. I still wanted it to be small and portable. The Cycloid is a wonderful machine but it is a monster. Usually it takes me a day to clear off enough of my desk to use it. The Cycloid is big and capable of infinite setups but it is really complicated. Teachers have been daunted about using it in classrooms. I wanted the new toy, the DuoGraph, to maintain the charm of the little PrimoGraf. Dimensions of the DuoGraph are 14-1/2 inches x 6-3/4 inches. Small enough to fit on any desk.
The new DuoGraph meets my dream of a small sophisticated epicycloid machine that won't be too large. It offers the opportunity of making Lissajous curves as well. The DuoGraph continues the moving fulcrum capability of the Cycloid. The only Cycloid features it doesn't have are the planetary gear setups. There just isn't room for them on the smaller sized gears.
The drawing size for the epicycloid patterns on the DuoGraph is 5-3/4 inches in diameter versus the Cycloid's 9-inch diameter patterns. One beta user called it 'cute'.
It is cute. And less forbidding than the Cycloid. It's there to have fun and not take itself too seriously!
A full complicated pattern shown from start to finish.
These are just a few patterns that I've liked. I'm sure you'll discover many more.
The Math behind the Curtain
The turntable has 60 teeth. When combined with a drive gear that has 30 teeth you'll get a pattern that has 2 nodes.
This table shows the number of nodes (loops) that each gear creates.
Adding a prime number gear for the fulcrum makes the drawing into a non-repeating line. Using a stationary fulcrum the line will draw back onto itself after a number of turns.
Changing the penholder positions adds even more complexity to the drawings. Here's a chart for the pattern that is shown in the opening video. All of these drawings used the same setup: a 30 tooth gear as a moving fulcrum and a 41 tooth gear as the drive. The only difference is the position of the penholder. Infinite variations are possible. Imagine how many possibilities there are using the 16 gears in various combinations.
What's in the Box?
The DuoGraph Drawing Machine consists of:
- the base geared turntable with 60 teeth
- prime set of wooden gears consisting of 19, 23, 29, 31, 37, 41, and 47 teeth
- divisible set of wooden gears with 20, 25, 30, 35, 36, 39, 40, 42, and 45 teeth
- 3 connecting rods
- maple penholder for epicycloid setup
- maple penholder for the Lissajous setup
- maple linkage rods for Lissajous setup
- 100 sheets of round 5-3/4 inch diameter heavy paper
- colored pens (black Pilot G-2 gel pen and a 4-color fine tip ballpoint))
- roll of 3M Magic tape
- Lots and lots of brass screws, knurled nuts, brass washers, and small wooden bearings
- a comprehensive manual
Setup is very easy but please be aware that there are many small parts--we provide extra screws and knurled nuts--so this toy is not appropriate for children to play with on their own. It is best to work together and see what they'll come up with. After you are done playing, the DuoGraph Drawing Machine can be disassembled in minutes and put back into the box for storage. It all lives in a 16-1/2 x 11-1/2 x 2 inch box. Finally a drawing machine that can fit on a shelf!
Design and Materials
The design is complete and has been sent to three beta users. The DuoGraph Drawing Machine is carefully crafted using laser cutters. All the production of the drawing machines will be done in-house. I will be doing all the cutting, gluing and assembly myself.
The base and turntable use Roseburg FSC plywood made here in Oregon. The rods and the penholder will be made from maple hardwood harvested and milled in Michigan. The gears will be made of basswood also from Michigan. The washers and bearings are walnut. All the hardware will be brass. Our goal is to build a toy that will provide tons of fun and last for years.
Production is limited to 100 units this year. Shipping will be done on a rolling basis as the units are completed. The first batch of DuoGraphs will leave in early June. The final orders may not ship until late September.
Risks and challenges
I have finished 5 successful Kickstarter projects. My last project, the Lo-Fi Smarthphone Camera Box, had all the rewards shipped in the first week! The DuoGraph is a complicated project containing many parts. I will be producing all of the parts myself on our in-house laser cutters. This negates the delays that can be caused by outside vendors. The biggest time requirement is gluing all the gears and little bearings. I will produce the manual and have the sheets diecut while the project is still underway. Shipping will be on a biweekly basis with the first batch starting three weeks after the project closes. Delivery of the final machines may be as late as September 30, 2016.Learn about accountability on Kickstarter
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