Torus Drawing Machine




Introduction: Torus Drawing Machine

About: My name is Randy and I am a Community Manager in these here parts. In a previous life I had founded and run the Instructables Design Studio (RIP) @ Autodesk's Pier 9 Technology Center. I'm also the author ...

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

(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.

(Note that some of the links on this page are affiliate links. This does not change the cost of the item for you. I reinvest whatever proceeds I receive into making new projects. If you would like any suggestions for alternative suppliers, please let me know.)

Step 2:

For this project you will need to 3D print one marker bracket, one offset wheel, and a set of parts to create one wheel hub. You can download the files from the Tinkercad website by clicking through on the parts shown above.

Step 3: Modify the Continuous Servo Motors

You will need to modify one continuous rotation servo for direct drive. The full instructions for modifying the continuous rotation servo motor for direct drive can be found in the Instructable for Removing a Servo Controller.

Step 4: Create the Center Pivot

The center pivot consists of a bolt with a stack of fender washers and rubber feet for support. The weight from the pivot keeps the machine in place and prevents it from drifting.

To build the center pivot, slide 25 two inch fender washers onto a 3/8-16 x 3" bolt. Lock the washers in place with a 3/8-16 nut.

Finally, place adhesive rubber feet on the bottom of the stack of washers to help keep the whole thing upright.

Step 5: Drill the Ruler

Use a metal punch to make an indent on the ruler on center at approximately 4-3/4" from the end without the mounting hole (my mark was intentionally a little shy). If you don't have a punch, you can just mark it with a pencil or marker.

Clamp the ruler in a table vise, or alternately, to the end of your workbench with a C-clamp and backing board.

Drill the marking with an 1/8" drill bit, and then proceed to increase the drill bit sizes until you reach 3/8".

Optionally, widen the ruler's mounting ring with a 1/2" drill bit. This is not entirely necessary, but will help greaty in removing friction from the 3D printed offset wheel.

Step 6: Attach the First Motor

Place two self-adhesive zip tie mounts on the front-facing edge of the ruler without the pre-drilled hole.

Using two zip ties (one for each mount), attach the motor the end of the ruler with the shaft pointing outwards.

Step 7: Attach the Batteries

Put the batteries in the battery holder.

Attach the batteries to the ruler using the adhesive zip tie mounts. Slide a zip tie through both mounts and fasten the battery holder in place on top of them.

Step 8: Insert the Wheel Hub

Insert the part of the hub with the stem through the skate wheel. Slide the ring onto the stem from the other side to complete the hub.

Step 9: Attach the Wheel

Remove the servo horn (the plastic bracket) from the servo shaft and using the horn's mounting screw, attach the skate wheel instead.

Step 10: Slide on the Marker Bracket

Slide the marker bracket onto the ruler such that the end with bolt mounting hole is closest to the edge of the ruler.

Step 11: Attach the Second Motor

Insert the shaft of the second servo through the ruler's mounting hole.

Zip the motor to the ruler by wrapping the zip ties around both of the servo's mounting holes. Trim away the excess zip tie tails.

Step 12: Attach the Offset Wheel

Attach the 3D printed offset wheel to the servo by pressing it on and using the servo horn's mounting hardware to fasten it.

Step 13: Assemble the Linkage

Assemble the linkage by removing the set screws from the shaft collar. Next, thread the shaft collars onto the ends of a 3" thread rod in such a way that you can still pass the thumbscrew through the shaft collar.

Step 14: Wire the Circuit

Strip 1/2" of insulation off the end of both the battery holder and motor wires.

Insert the red battery wire into the terminal labeled with a + sign on the male plug and tighten the set screw to hold it in place. Insert the black battery wire into the male plug terminal labeled with a - sign and fasten that in place as well.

Next, the motor wires need to be attached to the female plug. Once again the red wires from both motors should go to the terminal labeled with a + sign and the black wire from both motors should go to the terminal labeled with a - sign.

Optionally, clean up the wiring with zip ties once completed.

Step 15: Attach the Linkage

Insert the thumbscrews through the linkage openings.

Twist the thumbscrew into the bolt mounting hole of the marker bracket.

Twist the other thumbscrew into any of the bolt mounting holes in the offset wheel. Keep in mind the different holes will produce a different sized torus.

Step 16: Insert the Marker

Insert the marker into the marker bracket.

Step 17: Draw a Torus

Place the weighted pivot in the center of a large sheet of paper (at least 12" square)

Remove the marker cap, and then attach the plugs together to power it on. Once you do this, both motors should start turning, and the marker should slide back and forth. If it does not, disconnect the power and troubleshoot by checking your wiring and construction.

Finally, using the hole drilled in the center of the ruler, slide the machine down upon the weighted pivot and let the machine go free. The machine should now begin to draw a torus around the pivot point.

Change the position of the thumbscrew attached to the offset wheel to create designs of different size.

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18 Discussions


7 months ago

Awesome!! Hoping to get one as a gift one day! :-)


Reply 3 months ago

Still hoping to get one as a gift one day! :-)


Question 11 months ago on Step 17

My ruler rides up the bolt and lifts the pen off the paper? Any ideas on what's wrong with my set-up?


Answer 11 months 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)


Reply 11 months ago

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.


Question 1 year 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?


Answer 1 year 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?


Reply 1 year 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 ;-)


1 year ago

Very cool....nice job!


Reply 1 year 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


1 year ago

Any chance of adding a video of it performing?

M.C. Langer
M.C. Langer

1 year ago

Amazing project Randy! This goes to my personal list of projects to build one day!


1 year ago

Hi Randy,
Got a video? Would love to see it in action.
Cool project


Reply 1 year ago

That's so cool..nothing wrong with that display.