## Linear Motion from a Rotary Actuator

By Kevin Loney on June 10, 2013 in Mathematics, ProjectsThis 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.

## The Setup

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:

Factor:

Dive through by so we are left with :

## End Result

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.

[...] [Kevin] is trying to build a better reverse geocache box. It’s not the GPS that he’s improving, it’s the latching mechanism. He’s got four linear latches actuated by a single servo. [...]

[...] [Kevin] is trying to build a better reverse geocache box. It’s not the GPS that he’s improving, it’s the latching mechanism. He’s got four linear latches actuated by a single servo. [...]

[...] [Kevin] is trying to build a better reverse geocache box. It’s not the GPS that he’s improving, it’s the latching mechanism. He’s got four linear latches actuated by a single servo. [...]

Hi, this is Albert from Saskatoon Techworks. We met at Calgary Maker Faire 2013. I was wondering if you could send me the cut files for the lockbox mechanism and the coin sorter thing I saw at the space. Thanks