Taran,
The fact that you CADded, built, and spent time filming and explaining various types of differentials - very nice!
The fact that you didn’t link to any of the previously posted tutorials, videos, or robot reveals - boo!
393 gears are the most important part of this design that prevents additional friction losses and makes it feasible. Without them friction losses are going to be large and you will be better off not doing differential at all. But when cores and motor outputs are mechanically isolated with 393s - you get almost no additional friction over a regular drivetrain. Also, using chain to close the differential loop makes it tricky to tune - in this case all gears design is much more smooth and robust.
I’ve seen a good number of teams at ITZ Worlds that used less gears and were very successful with 4-bar differential design.
I believe, this half-differential idea had originated in Utah - many 2131 teams used this type of differential for their MoGo lifts. By the way they did very well in rankings and their club won Excellence at 2018 VEX Worlds.
The advantage of such design is that only half the motors motors (2 out of 4) have to ride on the 4-bar thus reducing friction losses. The flip side is that those two motors will only contribute power in one direction, depending on which end of the range they are parked. They cannot contribute any power while not at the end of the range.
Therefore this is not a viable design for the variable position hood.
This is very unfortunate - would have been epic if someone actually built it. Friction losses would be humongous because of the limitations of available vex parts though.
However, @Kyle1’s innovative way to build differential core without bevel gears offers some very interesting design opportunities, if friction losses could be reduced and input torques are properly balanced.
Taran, you could improve your topic by a lot, if you offer readers who are interested to further study this subject, some easy to follow links to: vexforum, chiefdelphi, or external resources like this one:
Conclusion
Please, try to avoid making general conclusions based on the limited amount of testing of unoptimized prototypes.
There is a number of teams who have qualified to Worlds with their optimized version of differentials and shared in-depth analysis and lessons learned about performance of different designs:
Plus many more that were shared on VTOW but didn’t make it to vexforum.
Based on those reports, I could say that when built well with understanding of underlying physics and paying attentions to details, 4-bar differential could be very efficient and rotating core design using 393 gears could have almost no additional friction losses over the regular drivetrains.
Half-differentials could have niche applications like with 2131 MoGo lift, but are not suitable for general application like variable position hood.
@Kyle1’s design for continuous dual motor differential transmission has some intriguing potential but is, probably, too complicated to be done with vex parts, unless somebody comes up with a clever way to minimize friction.