Thought this requires a more detailed explanation.
The generic or the original intent of differential gear system is about transmitting the force/torque from one motor (or input) to 2 or multiple outputs. The most common example will be cars - 1 engine, 2 wheels.
Differential gear | Types, Uses & Benefits | Britannica
And here’s a wiki link that shows some other variations (and limitations) of differential gear system.
Differential (mechanical device) - Wikipedia
And if you look at the official differential gear system by VEX, it sticks to the original intent of 1 input to 2 outputs - Gears - VEX Robotics (look under Advanced Gear Kit).
I guess this should address your question on examples of differential gear system that has 1 input.
As usual (and rightly so), VRC teams adapted this idea of differential gear system to their needs and figure out some other variations as well.
But in the earlier years, the main focus was about shifting gear ratio (without using pneumatics transmission, and hence the development of planetary gear system), rather than having 1 input to 2 outputs (of different gear ratio).
This is one example of the work done by some of the old old timers on planetary gear - Planetary Gearset - VEX V5 General Discussion / General Forum - VEX Forum
Because it is such an old post, you might need to scroll down to post #9 to see the pics.
Here’s another interesting variation on planetary/differential gear system - VEX Planetary Guide - VEX V5 General Discussion - VEX Forum
This is a good example of how things have evolved and adapted to VRC context.
I do like this post - because it has good discussion on the pros and cons of such system (which interestingly, some of the limitations are also mentioned in the wiki page), especially those points that were mentioned by @technik3k
And do read his last post in that thread as well - it gives a good summary on when it makes sense to use differential and when it doesn’t.
Back to this thread, my points are:
- there is really no need for differential for this game
- if there is a need to use 2 motors (or inputs) for 2 outputs, then it might make a lot more sense to just dedicate 1 input to each separate output instead.