I am struggling to understand the concept of Uvdin Dechol, where it originates from and how far it extends to.

We famously dont ride bikes / electric trams on Shabbos partly due to Uvdin Dechol, but many Poskim allow Shabbos lifts, which would seem should also be categorised as Uvdin Dechol.

Even stranger was when I just saw the Magen Avrohom when discussing playing chess on Shabbos, that they used to play with silver pieces so as not to appear like Uvdin Dechol.

I am ideally looking for a thesis that someone has published with guidelines, sources etc clearly defining what it or isn't Uvdin Dechol.

If no such publication is out there, and you have knowledge to share on this, please share all sourceable information that you have.