Modeling of kinematic schemes?

Question

Physics

Maybe someone came across programming / analysis of kinematic schemes?
Here's something like this:

In some way, you need to describe the levers, their interconnections, movable and fixed joints - and then “click here” and watch how it moves.
Interested in general principles, descriptions of algorithms, possibly ready-made open source libraries.
Now I don't even know how to approach the problem. And, I suspect, digging on your own and hand-to-hand will be unimaginably long.

Answer 1

http://zarabotalo.com/

Answer 2

2009.it-edu.ru/docs/Sekziya_6/24_Gebel%27_Solonin_1253243889920373-1.doc

Answer 3

www.mathworks.com/products/simmechanics/

Answer 4

en.wikipedia.org/wiki/Tokamak_physics_engine

Answer 5

There is such a 2D modeling engine Phun
Example on YouTube