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.
This problem has 5 variables:
- – Length of the linkage when fully extended
- – Length of the linkage when fully retracted
- – Length of the linkage attached to the rotary actuator
- – Length of the linkage attached to the bolt
- – The number of degrees of rotation required to fully retract the bolt
To the Mathing!
I am going to start by assuming that and are the two unknowns as it simplifies the process dramatically. This is followed by a fairly straight forward application of the Law of Cosines which solves the problem nicely with a bit of manipulation:
Solving for two variables is hard so since we can substitute in so we only have to solve one variable:
Expand the polynomial:
Cancel out the on both sides:
Move the constants to the left and all of the terms to the right:
Dive through by so we are left with :
Tidying it up and bringing all of the variables over to the left hand side we are left with:
I am hoping to have the full build for the box done by September and will be posting full build details and schematics.