Here is an offering showing how bevel gears work. They change the rotating shaft angle by 90 degrees. 

This finger fidget allows one input (your thimb) to drive the three other bevel gears.

The gears were easily downloaded to Fusion 360 from McMaster-Carr.

The four gears need to be put into the frame all at one time.

It’s not possible to put three of the gears into the frame and then add the fourth one because the adjacent teeth need to turn in the same direction to allow the insertion, but they always turn in opposite directions.

So - line up all four gears outside of the frame by placing them in the thin wall box.   Turn the thin wall box upside down over the frame, and the gears will fall into the frame.  Then put one or two axles into the assembly. 

The slip fit between the axles, and the frame is quite smooth with very little clearance (tolerance).  I used a clearance of 0.305 mm between the ID and OD.