A Collaboration between Alicia Blakey and Vanessa Krause
Who the f**k is Fibonacci ?
Based on Alicia’s design (the nested planetary gears) we decided to collaborate to try and create a working system of gears that can be displayed in an upright position. Ideally, we want our audience to feel comfortable and compelled to interact with this design. By using a variety of methods outlined in this document, we will speak to the design process and how we struggled through mathematical issues, logic and material choices.
Enlisting our math inclined siblings to help: My brother Joey sent me a Binet’s Formula...with no explanation on how to use it. When I texted him and said “Hey Joey, could you explain it to me?” to which he responded: “Which part?”
Since I have absolutely no mathematical inclination, we asked Alicia’s brother Merrick to explain how the formula could be applied to make the nesting gears. He spent about ten minutes solving it, responded with “yea, it works” and then said “I gotto go” and left us with no answers and no translated formula.
We spent another 30 minutes searching for an answer to our query...
The Internet has Answers
To get beyond the Binet Barrier, we decided to scour the internet for answers and suggestions on solving our riddle. We found several sites that are able to create compatible gears.
Some of these sites are:
Once we had these gear generators to help with the mathematical aspects of this project, we moved into Adobe Illustrator to create lines versions of these gears. Alicia focused on rendering each gear to be compatible with the Laser Cutters at 100 McCaul RP center. We decided to use Baltic Birch ⅛” plywood for the initial cut, to ensure that the math aligned properly. Alicia made over 3 small maquettes of what these gears could potentially look like. With each iteration, there were issues with the laser cutter taking too little, or too much off of the small gear systems, so that they would no longer effectively interlock and turn (she used both acrylic and plywood (⅛”). This process was frustrating, but helped us to realize the limitations of laser cutting for this project.
Prof Knows Best
Alicia and I are both very stubborn and determined to solve the riddle of nested gears. I was willing to settle on planetary interlocking gears, however, Alicia needed answers! In a final attempt to find solace with mathematics, Alicia contacted a retired professor from Queen’s University. He explained that to easily measure the distances between each of the gears, she would have to divide and measure 37 segments. This would allow all the teeth to properly align. By spending the time on solving the riddle, there was still a small mathematical issue with alignment. We settled on Planetary gears, given our overall timecontsraint.
While Alicia was solving deep mathematical issues, I focused on printing 3D spaceships. This helped to solidify the overall theme, and also give the our piece a more welcoming interactive quality. By using Thingiverse, I was able to find a fun retro spaceship design (created by cerberus333). This design allowed me to modify the scale to be much smaller. By adding the spaceship, our audience will be able to hold onto it, as the gears spin together. This was a very simple solution to make the piece more welcoming to others. Based on the open-source nature of Thingiverse, anyone with a computer and access to a 3D printer can create this object for themselves. The print was also relatively fast (it took less than 2 hours to print 7 spaceships). We only ended up using 3 or the 7 printed copies.
Shoot for the moon…
Based on the initial design idea, Alicia and I wanted to create planetary gears with many embedded LED lights that would be activated by our magnets (attached to the back of each gear) so that the model could stand upright and light up each “star” system as it spins. Alicia went to Home Hardware and purchased Reed switch LED circuit and Magnetic sensors. I used a drill and hand-saw to make the correct opening for the LED and magnetic sensor to fit into the wooden plywood board. We realized later that the battery packs purchased from Home Hardware on College and Spadina were actually faulty and only lit up one LED light bulb as the magnet passed by.
More than just Vandalism
For this project, I also wanted to apply some more hands on creative techniques. Although the wood and acrylic gears were beautiful on their own, they lacked a common theme with the spaceships. I decided to use Molotow Acrylic Spray paint to create a galaxy motif for the gear systems. Although we were planning on spray painting the entire board, we were met with the small scale of the spray booth located in the Maker Lab at our Graduate facility. Based on this size limitation, we decided to just spray paint the gears in asymmetrical ways. This way, the spaceship could sit on one of the the plain or spray-painted gears to help the participant’s understanding of our overall theme.
Once all of the large scale gears were assembled, Alicia used the soldering tools to weld together the magnetic sensor and the LED. We decided on the placement of the 1 working LED and put it near the middle gear. When 3 strong magnets were placed underneath the spaceship, the desired result happened! We had light! However, having other magnets under the gears (to hold them up vertically) would have interfered with the magnet sensor. Therefore, we decided that the design needed to remain as a table-top version instead.
Dark Side of the Moon
The main challenges we faced in this collaborative iteration was the limitations of laser cutting and battery technology. The design file, 3D printing spaceships and manual assembly (using traditional tools such as drills, a hand-saw, glue and clamps was surprisingly easy). If someone where to re-create this piece, the main challenge would be for them to use mathematics to map out the most ideal design the laser can cut. We also struggled with the time limitation, and would ideally like to revisit this project in the near future to keep expanding on this concept.
Tools & Technology
To create this project faithfully, they would need to have basic knowledge of the design process, mathematics, how to use AI and set up correctly for a laser file to be cut. Next, they would need some basic understanding of electricity (LED, magnetic sensor and soldering). They will need access to a well ventilated area for spray-painting and custom designing these gears. A Taz Lulzbot 6 was used to print the spaceship, along with PLA Village Plastics filament (any colour will do, as you can also spray paint these). Finally, they will need basic knowledge of how to use a drill and hand-saw to cut the proper dimensions of holes for each LED and magnetic sensor (this needs to be measured carefully, as the sensor is not very strong and needs to be placed within a close distance to the magnet). Finally, if you want to faithfully recreate this project, you will need some assembly space too!
A Giant Leap for Humankind
We have reached MARS! Only joking! By using digital fabrications methods, we were able to create a mathematical gear system and make out of wood and acrylic (in the speed it takes to put on your astronaut helmet). This would not have been possible without the technology of Adobe Illustrator files combined with laser cutting. Lasers are extremely accurate and fast. Something which would have been impossible to achieve with traditional fabrication tools alone. Although traditional methods were not used in the main fabrication process, they became extremely important in the final assemblage and inclusion of technology.
Full STEAM Ahead
From an Educational standpoint, this planetary gear system incorporated all the foundations of learning by doing. Gamification plays a large role in the end-product to make it appealing for users. However, one of the main beneficiaries of this project is Education. This project can teach hands-on skills, beginning with mathematics, engineering, spatial reasoning and electronic cycles. It can give students a chance to see how math connects to the physical world, and how mechanical processes (such as laser cutting) depend on accurate calculations. Finally, students have a chance to apply creativity and visual arts to the process of adding paint, colour, collage to specify their design. It also allows them to create an interactive learning environment that supports STEAM in the classroom. STEAM is included in all the criteria of creating this project by effectively incorporating:
There has been a recent push in years to improve media literacy and development in students as young as Grade 1. As the Ontario Curriculum suggests, having cross-curricular opportunities for education is important in building students’ (K-12) love of learning. This project is a mindful approach to problem solving, collaboration, open source hands-on learning that is needed in many subjects across the Ontario Curriculum and beyond!
Finally, it is important to acknowledge that this design could be greatly improved on in the hands of other people. This means that although all the components are found here, there is still a lot of modification and remixing of this design that is possible. By working collaboratively, this design has unlimited potential. It is a great starter project for anyone interested in applying STEAM to their own learning practice. Because the design is based on mathematics, it can be changed, altered and remade in many different constellations. This project promotes the idea that there is no one-way of making.
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Step 1: Bin It!
Can you solve this puzzle?
Step 2: Generating the Gears
Utilizing the references section that can be found below we have provided you with tools to generate gears. There are 2 websites one that is exclusive to mathematical blueprints and the other site discusses the different materials and variances if you had to cut the gears yourself.
These are both important when planning and constructing your file for laser cut as they will both help you give consideration to the materials and understanding of how to work within the constructs of slight unforeseen variations.
Infamous for his shared knowledge Matthias is echoed in many gear projects because he provides streamlined information on how to hand cut your own gears. He also provides background information so you can start your project with a good foundation. This is essential in order to generate a system that works and problem solving skills to troubleshoot later. The below glossary provided is created and provided by: firstname.lastname@example.org
Step 3: Tooth Spacing
Number of millimeters from one tooth to the next, along the pitch diameter.
Gear 1 teeth: Number of teeth on gear to render for gear. Controls left gear when showing two gears. Enter negative value for ring gears.
Rack&Pinion: Change gear 1 to a linear gear (rack). You can also make the other gear a rack by entering "0" for the tooth count.
Measured cal distance (mm): After printing a test page, measure the distance between the lines marked "this should be 150 mm". If it's not 150 mm, enter the value in this field to compensate for printer scaling. The next printout should be the correct size.
Contact angle(deg): The pressure angle of the gears. For gears with smaller number of teeth, set this a bit larger, to get more sloped teeth that are less likely to jam.
Gear 2 teeth: Number of teeth for the gear on the right, if rendered. The checkbox controls whether one or two gears are rendered.
Two gears: When printing templates, it helps to have just one gear shown.
Spokes: Show the gear with spokes. Spokes are only shown for gears with 16 or more teeth.
Step 4: Mathematics
I found the below equation to help construct my gear arrangement and to determine that the gears will work and fit together.
Denote R, S, and P as the number of teeth on the gears.
The first constraint for a planetary gear to work out is that all teeth have the same pitch, or tooth spacing. This ensures that the teeth mesh. What I did was made 3 separate sides that had the same pitch but didn't match each other so that the gears always aligned but in a different pattern.
The second constraint is: R = 2 × P + S
That is to say, the number of teeth in the ring gear is equal to the number of teeth in the middle sun gear plus twice the number of teeth in the planet gears. An example of this would be 30 = 2 × 9 + 12. Or you can go to the gear generating website at https://geargenerator.com or https://demonstrations.wolfram.com/NoncircularPlanetaryDrive/#more
Step 5: SVG Files & Illustrator
If you are importing a file from gear generator and have not constructed in Illustrator you will have to follow the below instructions in working with SVG files in illustrator.
Illustrator provides a default set of SVG effects. You can use the effects with their default properties, edit the XML code to produce custom effects, or write new SVG effects.
To import an SVG file into Illustrator:
Choose Effect > SVG Filter > Import SVG Filter.
Select the SVG file you want to import effects from and click Open.
To manipulate SVG file in Illustrator: Select an object or group (or target a layer in the Layers panel).
Do one of the following: To apply an effect with its default settings, select the effect from the bottom section of the Effect > SVG Filters submenu.
To apply an effect with custom settings,
choose Effect > SVG Filters > Apply SVG Filter.
In the dialog box, select the effect, and click the Edit SVG Filter button fx.
Edit the default code and click OK.
To create and apply a new effect, choose Effect > SVG Filters > Apply SVG Filter.
In the dialog box, click the New SVG Filter button, enter the new code, and click OK.
When you apply an SVG filter effect, Illustrator displays a rasterized version of the effect on the artboard. You can control the resolution of this preview image by modifying the document’s rasterization resolution setting.
Step 6: Saving Your File
Export your file as .eps or .ai.
Go to settings and make sure you are working in RGB mode, NOT CMYK.
You can change this by going to:
Select File ->Document Colour Mode -> RGB
All cut lines need to be indicated using Red Blue and Green lines with a stroke weight of .01pt
The laser will interpret the colours as ordered cut lines working from the inside out.
Starting with Red (RGB: 255, 0, 0) followed by Blue (RGB 0,0,255), and finally Green (RGB 0,255,0).
All interior cuts should be cut first and therefore should be Red, with any further cuts being Blue, and the final exterior cuts being Green. Make sure all your gears fit together and there are no intersecting lines before setting up to print.
If your gears look like they are not formatted correctly then you can refer back to the gear generator page and reassess your calculations.
Save as .ai files and transfer into Bosslaser program.
This program also allows you to manipulate your file. You can use this program to send your file directly to the laser cutter.
Step 7: Thingiverse & 3D Printing
As mentioned in the main outline of this project, you can print your 3D spaceships anytime! Come up with your own design by using ThinkerCAD, OpenSCADFusion360, or Rhino, or go to Thingiverse and find a creative commons project to print! Maybe you can even modify some of the files to suit your unique design challenge!
These spaceships were printed on a Taz Lulzbot 6 with PLA Village Plastics at the highest speed (took less than 2 hours for 7 spaceships).
Step 8: Reed Switch LED Circuit
A reed switch is a electromagnetic switch that is switched on by a magnet being brought into its vicinity.
This circuit incorporates a reed switch, LED and 3 V power supply from 2 AA batteries.
This project forms the fundamentals of how reed switches operate.
From the schematic below you can discern where the LED and switch are placed.
The battery pack has 2 wires black and red. Black wire is ground and red wire is power.
The red wire is going to get soldered to either end of the reed switch.
The reed switch will get soldered to the long side + of the LED. LED - short side will get soldered to ground the black wire leading to the battery pack.
Step 9: Incorporating Circuit Into Board
It’s important that you measure the distance that the magnet needs to be in location to your switch. Without testing you could drill a hole that is to far from your magnet and then the switch will not work correctly. The strength of your magnet will mean there can be a wider or shorter gap between the Reed Switch and magnet. We measured this then drilled a hole for the LED and an opening for the switch in our birch board.
Step 10: Have Fun!
You've done a lot of hard work at this point. It's time to get creative!
Use acrylic (Molotow) spray paint to achieve a cosmos effect on the acrylic and wood alike. Use whichever colours suit your project. Be sure to wear a protective (ideally organic vapour half-face respirator, or mask), wear gloves to protect your hands and ALWAYS work in a well ventilated area (never inside!).
Let the gears dry for about 24hours before placing them on the board to avoid scratching the paint.
You can also spray paint your tiny spaceships!
Step 11: List of Materials & Other Resources
Here is a comprehensive list of materials and further useful references:
1 LED white
Illustrator CC app for creating vector files for laser cutting
Bosslaser program for setting up the file for the laser cutting machine.
Medium grade sandpaper.
1/8" Baltic Birch plywood 48 inches long x 27 inches high x 2
1/8" clear acrylic 48 inches long x 27 inches high x 1
Acrylic spray paint in various colours
Respirator with Organic Cartridge
Cordless drill (with various drill bits)
Instant Glue (for spaceships)
Taz Lulzbot 6
PLA Village Plastics Filament