The Idea Dump

That one in particular was a gigantic, disengageable worm gear with a ridiculously large pitch. I haven't touched the CAD files in a loooooooooong time though. Personally, I have an immense distrust of using chain for any kind of power transmission where you're going to have a huge impulse (big force applied over a tiny space of time); most chains couldn't handle the forces and would just shear apart at the pins.

On the topic of drive systems, there are a few different options. Of course you mentioned the two most common drive configurations (both are tank-drive layouts, so named because of how their steering works), which are popular because of their durability and low cost. Other drive systems used in battlebots are Omnidirectional drives (which allow for front/back & left/right movement without turning), shufflers (halfway between a walking robot and a wheeled robot) and tank treads (which are much less frequently seen and used because they're easier to hit, are usually much heavier than wheels, and are way more complex).

shufflers (halfway between a walking robot and a wheeled robot)

what would that look like? the only thing I can think of would look like a spider with wheels on the end, and are there any other "heavyer duty" chains out there? they are a great way to exchange kinetic energy in a very flexible way, but i guess you could do the same with many interlocking gears, but that is more weight AND more expensive.

shuffle bots