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Picture of Torus Drawing Machine

This is a machine which draws a torus. It is based on a ruler, two modified servo motors and some 3D printed parts. One of the motors has a 3D printed wheel attached with offset mounting holes. The marker slider is attached to this wheel with a metal linkage. As the 3D printed wheel turns, the marker slider moves back and forth linearly across the ruler. At the same time the other servo drives the entire machine in circles around a center pivot using a skate wheel. These two simultaneous movements ultimately move the marker and draw the torus design.

This was created to help support a 7th grade curriculum, but surely can be used at other grade levels. See the attached lesson plan for how you might use it in the classroom to explore area and circumference.

If you are looking for a machine for younger students that demonstrates simpler mathematical and engineering principles, check out the Circle Drawing Machine.

Step 1: Materials

Picture of Materials

(x2) Continuous rotation servos (modified for direct drive)***
(x1) 12" Ruler
(x1) 3D Printed sliding marker bracket
(x1) 3D Printed servo skate wheel hub
(x1) 3D Printed offset wheel
(x1) 3XAA Battery Holder
(x3) AA Batteries (not pictured)
(x1) Sharpie marker (not pictured)
(x1) 76mm Skate wheel
(x1) 3/8-16 x 3" Bolt
(x1) 3/8-16 Nut
(x20) 3/8" x 2" Fender Washer
(x2) 1/4-20 x 3/4" Thumbscrews
(x1) 1/4-20 Nut
(x2) 1/4" Shaft collars
(x1) 10-32 x 3" Threaded rod
(x1) 5.5mm male screw terminal power plug
(x1) 5.5mm female screw terminal power socket
(x4) Rubber adhesive feet
(x2) Self-adhesive zip tie mounts
(x3) 8" Zip ties
(x4) 4" Zip ties
(x1) Large sheet of paper (at least 12" square)

*** See Step 3 for more details about modifying a servo.

Terry2713 made it!23 days ago
After many trial/errors this is what I eneded up with. I used lock nuts to secure the ruler to the base to eliminate the rise of the nuts and the ruler. The pen is almost level. I will have to reprint the black disk since it's not level and this causes my yellow pen holder part to stick around the 5 inch mark on the ruler.
Drawings.JPGBlack disk.JPG
randofo (author)  Terry271323 days ago
Cool! Glad to see this in action. :)

Are you using this in a classroom?
Not yet but plan on it. I have the parts to build 10 more. I'm printing a new black disk right now. Trying to make sure it's correct and doesn't cause a skip on the ruler.
Terry271329 days ago
My ruler rides up the bolt and lifts the pen off the paper? Any ideas on what's wrong with my set-up?
randofo (author)  Terry271328 days ago
My best guess is the following:
- Whatever you are using to draw has too much friction on the drawing surface.
- The hole you drilled is slightly too small or irregular and this is creating friction which sends it up the bolt.

Some ways you may be able to fix this include:
- Widening the hole slightly, and making sure the hole is nice and smooth all the way around.
- You can also try changing your marker or paper.
- You can also add another nut on top of the ruler. If this nut ends up getting unwound by the ruler and not helping much, use a lock not (it's a nut with nylon inside to hold it in place)
Thanks for the ideas to trouble shoot. I did look closer and my hole is not perfect since used a drill bit to widen the hole slightly. I will get a 5/8 bit and try to get the hole perfect. I did try the nut and it did run up the bolt If the new hole doesn't do the trick, I'll get the lock nut next.
jack tech1 month ago
stoppi713 months ago
Hi! I don't really see the sense in making this project with my class? What do they learn from this except drawing a torus?
randofo (author)  stoppi713 months ago
By changing the position of the bolt attached to the wheel you can draw tori of different sizes. This changes the ID and OD, and thus the surface area it takes up on the paper. Students can calculate the difference in surface area. It also demonstrates translation of motion from rotary to reciprocating. You can also calculate the width of the torus based on the rotational diameter of the bolt attached to the wheel.

What subject and grade do you teach?
stoppi71 randofo3 months ago
Hi randofo!
Thank's for the response. I teach mathematics, physics and practical physics at a high school (from 11 to 18 years) in austria ;-)
mtairymd3 months ago
Very cool....nice job!
randofo (author)  mtairymd3 months ago
As already commented by Naevus Spirograph produces similar curves (hypotrochoids?) and with gearing it closes the curve, achieving a precise pattern, whereas your machine would - I suspect - eventually fill in a solid black ring, if left to run
Wynfordeagle3 months ago
Any chance of adding a video of it performing?
Naevus3 months ago
When I was a kid, I had this:
M.C. Langer3 months ago
Amazing project Randy! This goes to my personal list of projects to build one day!
AussieAlf3 months ago
Hi Randy,
Got a video? Would love to see it in action.
Cool project
randofo (author)  AussieAlf3 months ago
Here is one I made while testing:

Perhaps I will make a better one eventually and put it in the Instructable.
AussieAlf randofo3 months ago
That's so cool..nothing wrong with that display.