Since this video was limited to 2 minutes, I didn't have a chance to mention that the prototype I show here in the video isn't fully functional. Even though all the dimensions in this prototype are correct, there is not enough grip between the brass sphere and the 3D printed parts. This means that the integrator portion isn't functional, and that the correct area isn't outputted.
If I were to make a second prototype, I would look into improving grip by trialing with rubber spheres or a rubber padding on the 3D printed parts.
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