VEX Gearing

Hi guys! I just have a few questions about compound gearing: how do you calculate and build them and what are their benefits vs non compound gearing?

Thank you!!

this is an example of a compound gearing system (used last year)
http://puu.sh/hUEO8.png

the first stage connected to the motor is 12 teeth/36 teeth ( the small gear rotates 3 times for every 1 large gear rotation )

and the second stage is 12 teeth / 84 teeth ( the small gear rotates 7 times for every 1 large gear rotation )

this gives an equivalent of (12/36)*(12/84) = 1/21 = 21 rotations for every 1 output rotation

sometimes compound gearing is required for how much torque you need, ultra low ratios like 1/21 are impossible to get without it

you should check out http://curriculum.vexrobotics.com/curriculum/mechanical-power-transmission/gear-ratios