I'm working on modelling a feller buncher, its end effector consists of a saw to cut trees and claws to bundle them together. I'm looking for a free/open source software that can simulate dynamics of multiple constrained bodies, any recommendations?
If you are less comfortable with programming (as in you will still need to code, but this softwear at least has a GUI) you can use a robotics framework for simulation like Gazebo.
You could take a look at MBDyn which has a declarative way of defining a simulation. May be simpler then the ones above.
I doubt that any automotive simulation framework would allow you to implement the mechanical linkages of yout vehicle.
If you have some CAD tools available, most of them have add-onds for simulating multi-body systems, but most-of them are not free...
If you do not want to code, I do not know any free solutions. If this is a hobby project, you could try the Matlab Home edition (Mechatronics option) for under 300 USD, (if it is a commercial project the matlab licenses will cost well above 15k). Students also get free/cheap Matlab versions. Other then Matlab, you can try MapleSim or other commercial software.
I think FreeCAD already has some capabilities in this regard. Also, if you are a hobbyist or a startup below $100K/year income, you are eligible to have Autodesk Fusion 360 for a year for free. It is the little brother of the Autodesk Inventor with more limited capabilities and using cloud to compute and store your models. It has dynamic simulation and constraining features. Personally, I am using the latter, but only because I used to Autodesk products already. Had a look on FreeCad too, it looks really promising for me considering that it is completely free.
If you don't want to create your 3D model, then Matlab has various really nice toolboxes, oh right, that would not be free... Hope this helps a bit.