I’ve been pondering a concept to 3D print which would use a combination of an internal spur gear (where a small normal involute spur gear interlocks with internalised teeth on a bigger spur-like involute gear) with a bevel gear, which switches angle of the shaft (by 90 degrees in the situations I’m thinking of). But I’m not sure if it is mathematically possible to get proper involute teeth to exist for this geometry. I’ve drawn up a diagram of the reference cones of such a gear system (see the attached picture), and I wonder if when real teeth are put on the cone surfaces they could ever run or would trying to combine bevel cones with an internal gar make the teeth jam? I have looked around online for the concept but seen nothing particularly about this combination of a bevel and internal gear, search terms for “internal bevel gear” bring up plenty about internal spur or external bevel gears, but nothing about combining the two.

I also wonder if anyone can suggest how I might calculate, if this design is possible, what the involute curve would be so I can model it by creating a equation surface/line in blender (methods fo any CAD software would translate across fine)? Would I start with the usual involute surve equation? I wondered whether any online calculators can generate an involute curve for this type of gear (I’ve found good ones which can for internal spur gears OR external bevels)? Or what sort of geometric procedure I might work through in CAD software to convert an internal gear profile or bevel gear profile to form an internal bevel?

Thanks