The principle and mathematics behind Klein's construction?

[Sanchayan Ghosh]

Hello,
I tried looking this up a lot and just could not find it. For four bar linkage, Klein's construction is used to find velocity and acceleration of piston and connecting rod. Here is a link for the procedure of the same

http://www.mechdiploma.com/content/q1explain-kleins-construction-method-finding-velocity-and-acceleration-various-linkspoints

I, unfortunately do not understand the principle of this and looking for a derivation yields no result. I need the mathematics behind it as I keep forgetting the procedure as it seems so arbitrary and confusing without any derivation for the same.

Please do explain me the mathematics behind how Klein's construction was theorized.
Thank You

 

[Dr.D]

As an aside, let me ask why you want to study this obscure topic? I have done serous work in kinematics for years and analyzed hundreds of slider-crank assemblies, but I never heard of Klein's construction until now. There are much simpler ways to get the results, and they don't rely on graphical constructions. Why not use an analytical approach?