I decided that I wanted to build my girlfriend a new sewing box for her birthday, and instantly knew that I wanted to make one that cantilevered, just like tackle boxes and traditional sewing boxes. Searching the internet for mathematical help, I discovered that none exists. As a result, I have decided to just figure it out the hard way and share my results.
Step 1: How my box works
My box will be 300mm long by 200mm deep, and have 2 tiers, plus a lid. I want there to be approximately 30mm of overhang between the top and bottom tiers when the box is open. The lid will be opened with the same movement as the rest of the box. The top tier will be about 60mm deep inside, which is the approximate length of a spool of thread, and will be divided into compartments. The bottom will be about 100mm deep, and will be a spot to keep larger things. If you want the same dimensions, carry on with the instructable. If not, now is the time to sit down and think about what you want. If your dimensions differ from mine, you'll have to alter the instructions to suit, obviously.