This is part of a project I have been playing with on and off for the last 9 months. It is similar in concept to a reverse geocaching box but with cooler locking mechanism. I have always appreciated the giant vault door bolt mechanisms and figured designing a laser cut version controlled by a servo would be an interesting learning exercise.
To accomplish the desired effect I had to solve a fairly simple geometry problem for the linkage mechanism. I figured this might be of use to someone else or my future self so I will walk through the derivation of the basic equations for finding functional linkage lengths.