Ok my genius friends, here is a puzzle for you. Imagine you have a conical gear, such as a miter gear. its teeth mesh with radial teeth on a flat disk. (I know this disk cant actually be flat, but just for the example…) If you want to rotate this cone, it moves around the platter in a circle. Basic physics here, nothing special. Now, let’s say you want to add elements to this cone that sync to related elements on the platter it meshes with. We now have a situation where rotation around the center pivot of the platter must be synchronized with rotation around the pole of the cone in order to maintain synchronous mesh of the teeth and design elements between the objects. Now, I know this can be scripted, and I’m certain it can be done with grasshopper, but I suddenly found myself intrigued by the fact that in 15 years of using rhino, the need for a multi-axis sychronized rotation has not come up in my practice. When I think about it, it seems ridiculous. This is such a basic physical movement, when I started looking for ways to do it, I was quite surprised to find I didn’t know how. I’m a smart guy, I can figure it out, but I can’t be the first person to look into this. I can look up or work out an equation to tell me the rotational ratio based on cone angle, but I’m wondering if I’m missing something simple by overcomplicating my thoughts?

Can’t wait to see what the community knows.

Bongo ?

Yep, I use bongo and that will be my go-to on this one, but im currious to know if there is a method native to rhino without 3rd party plugs.

The ratio of the shaft speeds is the inverse of the ratio of the number of teeth. For example gear A has 11 teeth and gear B has 44 teeth so the gear ratio is 1:4. Shaft speed of gear A will be 4 times the shaft speed of gear B.

For cone angle: Extend the axes of ratio of the gears until they intersect. The line of contact between the two cones will extend through the intersection of the axes of rotation.