I'm usually a fan of just one transmission ratio.... Of course, it depends on the game. Games such as 1999 and 2002 have clear advantages to having a transmission, where speed is important to get around the field quickly, AND power is important for moving the mobile goals. In general, if designed correctly a simple one-speed transmission can do just fine. Of course, a two speed transmission, if designed correctly, can do better... but unless you have the time to design these transmissions before the season starts, it's not worth your time during the build season.
So, I vote... one... but sometimes two
Three I don't see the need for, since a middle speed is rarely an advantage.
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Systems Engineer - Kiva Systems, Woburn MA
Alumni, Former Mechanical Team Leader - Cornell University Robocup - 1999, 2000, 2002, 2003 World Champions
Founder - Team 639 - Ithaca High School / Cornell University
Alumni - Team 190 - Mass Academy / WPI