The first photo is the grinder spindle where the grinding rock normally fits. The adaptor slips over the nut (where the rock would fit) and setscrews lock it to the spindle.
Just in case you wanted to buy rather than make....
http://www.travers.com/product.asp?r=b&n=UserSearch=item_id+'53-111-956'
Gene
I made this adaptor for my surface grinder spindle. I have two collets 1/8" and 1/4" to use carbide burs, small dremel cutoff wheels ect... Works pretty good. Collets are from old die grinders.