Sahil,
I'd like to see you submit these PRs to SymPy ASAP. Maybe it would be a good idea to submit them in order so that we can be sure to merge fully functional classes at each step. I think that would look something like: Body, then the XJoint classes, and finally JointMethod. Each class can be a PR and should include the class, unit tests with full coverage, and numpy style docstrings for all public methods/attributes/classes.
Additionally, prose documentation for the Sphinx docs will be needed in a separate PR that explains how to use the new classes. This should include the examples you've been working on. I would really like to see the example I created, that includes all of the joints, implemented with the JointMethod.
If all of this is done, you should have a fully functional new module that can be included in the next SymPy release.