3 Strand Braided Ring

thingiverse

So about a week ago, I had a brilliant idea - why not make a 3D printable thing that looks like it was braided together? Well, now I know why no one else has really done it: it requires an excessive amount of trial and error, and math. I'm excited to see how I can port this into OpenSCAD. So yeah, about a week later, and a lot of time I should have spent studying or doing homework, I finally got this to where I am happy with it. The STL files are for a size 7 ring, and the Inventor IPT files include all the necessary information for how it works. I'll explain how I designed this later. Hope you like it! How I Designed This Final Steps: Make a 3D line that follows the equation below. Draw an ellipse on a plane perpendicular to that line. Sweep the ellipse along this line. Create a circular pattern of two more of them within 40 degrees. That's it. Logic Behind the Formula: Just deciding on the type So I guess I probably posted my rough drafts of how I decided to braid stuff. It was a lot of trial and error, but in a nutshell, it was just a triangle that flipped 180 each 'step' of circles rotating clockwise which circle they went through. So my six planes ended up looking like this: ▶ ▶ ▶ ▶. I needed six, since the period of rotation was top middle, bottom, bottom, middle, top. (see, with three strands, they need to wait two periods before they cross back through the middle.) I decided circles were too wide and not tall enough, so I quickly scratched that and went with ellipses. I know that trig functions oscillate, which is useful for 'bouncing' values back and forth. I needed to bounce height and distance from center, so that's how I decided on using a cylindrical function. So the equation that does it all: Logic Behind the Formula: Where the Values Came From r(t) = ringRadi + ellipseWidth + ellipseWidth(sin(periods * 2 * t)) θ(t) = t z(t) = ellipseHeight * fudgeFactor * cos(periods / 2 * t)^2 Domain: 0 to 360 So that's what those values mean. The half and double are just because of how trig works. See, you want z(t) aka height to oscillate six whole periods. Or at least that's what I wanted when I made this one. So, to keep the min height equal to zero and also fudge the local maxima to have a lesser slope, I chose to square a cos function with half the desired period. Since the number of periods it would then double. Using ellipseWidth for the xy plane makes sense, since that's where you tell the thickness of the ring. Using ellipseHeight for the z makes sense because well, that's the height and it needs to adjust accordingly.