This is a good example of what the generation looks like: as the circle rolls tangentially along the path, it oscillates based on the adjustable tracing radius. This creates an arc in such a way that, when the cycloid is generated tangentially around a circle, there is a particular relationship that allows all the pins of the stator to contact the cycloidal gear in a consistent radial pattern.
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At the start of 2022, I was inspired by many hours of YouTube videos about gear reducers and actuators—specifically, actuators that can use a motor’s torque as suspension. As some may know, this is what many robust robots use. For example, Spot the dog from Boston Dynamics uses powerful planetary reducers, while MIT’s robot dogs use a pancake-style planetary reducer.
With even deeper research, I discovered the world of cycloidal drives and harmonic motion—mechanisms that allow a rigid object to “weave” between cogs and pins using its unique shape to smoothly transfer energy with effectively zero backlash. All this information excited me, and I decided to take charge and attempt to design one myself.
Getting Started: The Cycloidal Challenge
As with any complex project, the first challenge was clear: How was I supposed to generate a cycloid accurately? I began by learning what actually comprises a cycloidal disk. In simple terms, it's the path traced by a point on the radius of a circle as that circle rolls around another fixed circle. By maintaining a common ratio between the circles, a continuous spline can be achieved.
To generate this spline—especially since I didn’t yet fully understand the underlying math—I opted to use a parametric spline generator add-on in Fusion 360. Using Omar Younis’s paper (linked here), I defined a few key parameters and relationships, such as eccentricity, number of teeth, and roller size.
V1: From Concept to Print
Because I was so excited about the topic, I jumped into designing right away. My main goal for Version 1 was to understand how I could apply the parametric equations from Omar’s paper to successfully generate different contracted cycloids.
After some experimentation in Fusion 360, I settled on a larger disk for simplicity. I believe the gear reduction was 14:1, with an eccentricity of 2 mm and a disk diameter of about 50 mm. I 3D printed the design to test whether the disk would fit and rotate correctly within the stator housing I had also modeled.
Luckily, it worked on the first try! However, I did run into some issues—mainly with tolerances. The fit was too loose, which introduced too much backlash, defeating the purpose of the design.