# Formula for converting linear to rotational motion

I am trying to design something that rotates 90 degrees based on a small (10mm or so) linear motion, using this basic setup as an example.

There are a lot of questions about how long the arms need to be, how far they need to anchor from the point of rotation, etc. that i need to know. I am assuming there is some formula that governs the relationship that someone can point me to? your given mechanism can be shown by figure above. the driving element is link DF, which moves linearly.

first of all calculate theta by, where x is distance travelled by DF.

Now position of C can be given by, (origin at A) Now you have 2 equations, both have common origin at A. notice that both are equation of circle, one at origin with radius of AB, other at point C with radius BC.

solve the second equation for y in terms of x, then substitute it in equation 1.

you will arrive at quadratic equation where you can easily solve for x.

also you know x = r cos alpha (alpha is the angle you want to be 90)

using the above information you can find your required term

There is a mechanism called: SLIDER CRANK MECHANISM

One can copy one of these mechanism for just converting linear to rotational motion. In most of the cases, this will do the trick.

But for general, if you want to design a mechanism that will do your desired motion, get ready to do some work!

First, here some links you will probably need for getting the dimensions for your particular shape:

Then you must start your motion (PVA) analysis, you can use some schema like that: I don't think you will need it, if you only want to perform your motion. But if you want to have an analysis over your mechanism (for every position of crank), you can start with inspecting these slides.

Here it comes, there are some example of mine because the process is much or less same.

## Four Bar Mechanism for Straight Line

This is the desired shape: These are the calculations for PVA analysis:  and some more of course...

After all, to sum up:

1. Finding the dimensions of linkes for the desired shape
2. Writing and solving Vector Loop
3. PVA Analysis
4. Test final mechanism in MATLAB or Solidworks.

Here is MATLAB generated mechanism: (Also here @youtube with Solidworks) Hope this helps, I wanted to help as much as I can because I've been experienced your suffer and it will be good to be informed when you are at the start.