Thank you everyone for you recommendations. Can someone check my understanding of how gearing, shifting and game play work?
First, from game play, there are two main criteria that define a drive train's performance, outside of reliability, maintenance and so forth; Namely they are: speed(linear speed) and pushing power(acceleration).
The best way to address both these criteria is through gearing and shifting.
With no opposition, we want to go fast. Aiming for around 15ft-18ft/s. At this speed it would be easy to get pushed. Although we would be agile.
For the above situation, you want to gear it such that you have the highest speed possible, enough torque to overcome dynamic friction and accelerate (dependent on mass of robot) fairly fast.
Amperage draw for each motor would like to be under 40 for the sake of motor "health." In the powerpoint,
http://www.chiefdelphi.com/media/papers/2429 it says to design max power for 40 amps. How would you go about doing this in choosing the gearing? To do this, I would pick the point at which I get max power out of the motor at 40 amps(data), determine what torque I need for the situation above(experimenting/estimation), adjust the speed accordingly to get the same power output as the motor(calculation), and then after that choose the appropriate gearing(calculation).
For opposition and turning, namely times when the robot is at a low speed, the robot will be in low gear. The gear needs to be low enough such that it can generate enough force to push other robots. Low enough to turn against whatever friction the design requires. High enough to turn quickly.
Again would I use the same process of calculation as above. Matching my max power for max power needed when pushing a robot. Determine torque needed. Determine speed and gear, "design" accordingly.
Following the advice above, I think the best drive train setup for us would be a KITBOT on Steroids with custom gears to fit our need for the game.
Does anyone have a recommendation to what type of transmission mechanism to use: super shifter, or vex pro shifters.
Thank you for your help everyone. All the best.