Second order roulette drawing machine
Print Profile(5)
Bill of Materials
- Ballpoint pen refill x 1: Recommended refill is a ZEBRA SARASA. I use RNJK5-BKRBLG-8AZ.
Description
Updated April 16, 2025
Added a feature to preview curve shapes.
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This is a machine for drawing a second-order roulette. The following video demonstrates the patterns it can create.
Note: This "roulette" is a mathematical term representing a specific curve, not a gambling device.
https://en.wikipedia.org/wiki/Roulette_(curve)
Referenced Information
The following blog served as a reference for creating this model.
https://glagolj.github.io/gg-blog/
The process of drawing using Wild Gears can be viewed on the following website.
https://spirographicart.com/2021/03/02/wheel-within-a-wheel-exploration-with-wild-gears/
Assembly Guide
A video outlining the assembly process is provided.
Modifying the Shapes
As shown in the introductory video, altering the four gears modifies the resulting shapes. Additional methods include:
- Adjusting the pen position
- Altering the planetary gear phase
- Altering the side gear phase
- Modifying the planetary gear bar's fixed position
Adjusting the Pen Position
Altering the Planetary Gear Phase
Altering the Side Gear Phase
Modifying the Planetary Gear Bar's Fixed Position
Regarding Pens
Pilot Acro Ink, Pentel EnerGel, and Zebra Sarasa refills were tested as ballpoint pen options; only Sarasa functioned effectively.
All products performed adequately for handwriting; the issue pertains to their use within this model.
Pilot Acro Ink released excessive ink, accumulating at the drawing point and smudging the paper.
Pentel EnerGel exhibited insufficient ink, resulting in broken lines.
Sarasa's success might be attributed to its water-based ink.
2mm diameter mechanical pencil leads (HB and 2B) were also tested, but resulted in faint patterns, thus were deemed unsuitable.
Initially, the refill was secured using a screw mechanism, but precise height adjustment proved challenging. It was subsequently redesigned with a spring mechanism. Spring functionality has only been verified using PETG; other materials may not yield satisfactory results.
The refill is designed for a 3mm diameter and 98.2mm length.
Table Dimensions
Three table sizes are available: 180mm, 150mm, and 120mm in diameter.
180mm represents the maximum printable size for the A1 mini. The 150mm size allows two circles to be cut from an A4 sheet, while 120mm accommodates three.
An A1 mini printing profile was created, but since I do not own an A1 mini, printing verification is impossible and the profile cannot be released. Substituting the slide bars with "slide bar mini long.step" and "slide bar mini short.step" should suffice; users requiring A1 mini compatibility are encouraged to create their own profile.
A circle cutter is recommended for cutting paper circles. I utilize the Olfa Ratchet Compass Cutter.
https://www.olfa.co.jp/products/742.html
Information for Creating Gears with Unlisted Tooth Counts
Gears are created using the Autodesk Fusion Helical Gear+ add-in.
Gear thickness is 5mm, except for the center gear, which is 5.2mm.
A module of 1mm is consistently used, with a helix angle of 0 degrees to create spur gears. Backlash is set at 0.4mm.
Refer to the f3d file for post-add-in gear processing methods.
Simplification
Utilizing "no gear shaft" and "no gear shaft base" simplifies the assembly to a single gear set instead of two. Secure the connection with the supporter guide using an M3x12mm bolt.
Previewing Curve Shapes
The macOS application Grapher now accurately simulates the curves produced by the second-order roulette drawing machine. The file "144_140_63_36.zip" is attached for use, limited to cases where the side gear's initial phase is zero.
The curve shapes should be highly accurate.
Parameter Definitions
- Enter the number of teeth for gears n0-n3. n0 represents the center gear, n1 the side gear, n2 the sun gear, and n3 the planetary gear.
- Enter the initial phase of the planetary gear in radians for t3ini.
- p represents the position of the M3x12mm screw on the planetary gear. Enter the distance from the planetary gear's center to the screw, divided by the planetary gear's radius.
The maximum value of p for each planetary gear is listed in the table below; this represents the screw's outermost position. - Modifying the offset value is equivalent to changing the pen's position. Adjust within the limits of the table dimensions.
- T represents the number of rotations of the center gear. While a formula exists, it was not implemented due to Grapher's lack of a greatest common divisor function. A sufficiently large value has been used; increase if necessary.
| teeth | pmax | teeth | pmax | teeth | pmax |
| 22 | 0.54 | 30 | 0.66 | 42 | 0.72 |
| 24 | 0.58 | 32 | 0.63 | 45 | 0.74 |
| 25 | 0.60 | 35 | 0.66 | 48 | 0.75 |
| 26 | 0.61 | 36 | 0.67 | 56 | 0.79 |
| 28 | 0.64 | 40 | 0.70 | 63 | 0.81 |
June 6, 2025 Correction
The quantity of Maker's Supply components has been revised. Previously, the number of components to be used was specified; however, for items such as a 20-piece pack, one purchase suffices. The quantity has therefore been adjusted to 1. The required component quantities are:
- D6x3mm Round Magnet: 8
- M3x8 SHCS Machine Screw: 5
- M3x12 SHCS Machine Screw: 1
- M3 Carbon Steel Hex Nut: 7
- 6mm Stainless Steel Balls: 4
- R188 Open Hybrid Ceramic: 1
License
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