Here's version II. It works much better.
|The cup easily holds the full capacity of the grinder.|
As you can see, after investigation I found that the mill section could be of a smaller diameter. Thus it's even easier to hold. By making the "cup" for the grounds in a direct line and the same diameter as the mill exit the solution is far superior to the "square drawer" of conventional grinder designs. They tend to leave coffee grounds on the drawer edge and the round shape makes it easier to pour into the usually round coffee maker.
This unit is made of 4 cedar parts. All made with hole saws, but it could easily be turned from a single block on lathe.