I think that the simulation is a blend of physics and paths.
For example the part that is moved 'horizontally' is moved by physics but it has a constraint put on it so that it can only move in a straight line.
The constraint is necessary because I haven't included the base as an active part of the simulation.
The part that is moved vertically and one can see wobbling is physics only. It is restrained by interaction with the part within which it slides. And I have to give quite a bit of clearance at the design stage to cope with the inaccuracies of the 3D printing process that I'm using.
The gears and other rotating parts are constrained to rotate around a fixed axis.

As for the pdf.
I'm using Windows 10 64 bit.
The pdf does do something odd with the colours so that they are sometime quite different from the videos but for me they are always coloured and do not need to clicked on.

I planned to attach a pdf of the final design to see if that worked better for you but it's 24Mb so I've attached a pdf of an earlier project which is rendered in wood!