This entry is part 2 of 5 in the series Ball joint

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In this previous post I modelled the cross spherical gear part of a cool joint I found online – you can see a video of it here, and a paper describing it here. I actually tried to model the MP-gear part too, in Fusion 360 but got it totally wrong and so removed that part of the post.

How to model the damned thing has really bugged me since. I don’t know if there is a ‘closed solution’ to creating the MP-gear. The authors of the paper do not divoluge, but they do hint at how the MP-gear is formed.

*K. Abe, K. Tadakuma and R. Tadakuma, “ABENICS: Active Ball Joint Mechanism With Three-DoF Based on Spherical Gear Meshings,” in IEEE Transactions on Robotics, doi: 10.1109/TRO.2021.3070124.*

I ended up giving up on Fusion 360 (for this step) and using Rhino3D and a Grasshopper script to essentially virtually machine the gear from a 25mm long bit of virtual solid round bar made of blue stuff 😜. I imported the 2D gears from the original Fusion 360 model – I used a script in Fusion to create them.

The animation below shows what the GH script does, rotating a virtual cutting tool (red) around our workpiece (blue) as per the diagram above. The cuts, of course, accumulate on the blue piece, as they would on a physical process, but I wrote a bit of custom code in a Python component to do this iteration so cannot so easily animate that.

You get the idea.

The finished workpiece (I feel like I machined it….badly) is rather dependent on how many steps you take in the revolution and the size of each step. 30 steps (for 1 revolution, 12° per step) took 8 minutes to solve. Beyond this, it rapidly becomes unmanageable since the irregular form of the cut piece becomes more and more complex (& so the intersection operation takes longer).

Finishing the gear

1. Rhino to Fusion 350

Baking the workpiece in Grasshopper (it’s a closed BRep) and saving it as a Rhino 7 file, Fusion 360 imported the Rhino file straight off the bat, no issues. A first! You can see its a little rough and ready. That’s okay though for now – I am dreaming if I think that is going to make a difference with my crappy 3D printer! This first (well…second!) go is likely wrong anyway and will need some adjustment.

MP-gear imported in Fusion, as ‘machined’ in Grasshopper

2. Bevel

The MP-gear in the original vid and research has an edge bevel. Maybe it helps the gears to mesh together? Maybe just look better? Either way, you can recreate in Fusion 360:

Sketch sketch on global XZ plane (I have my origin at gear centre) and use intersect tool to create section lines.
draw s shape to create a bevel. The shaded bit shows the nick that will be taken out on this section. The dimensions are somewhat arbitrary – easy to go back and change done.
Cute bevel using solid revolution tool in cut mode. Then mirror this feature on the centre plane