Originally Posted by Jon Stratis
Well, that's a pretty wide open question.
Lets start with mecanum wheels. You need 4, one in each corner of a "normal" rectangular robot. Power each one separately (4 motors, 4 gearboxes), and set them up so the rollers form an "X" when looking from the top of the robot. With this setup, you can drive and turn like you do with a "normal" tank drive, but you can also strafe - move sideways or at an angle without rotating the robot.
With omni wheels, there are a number ways to set them up. Assuming you can keep them all level, you can set them up to get similar control as mecanum drive, by having a pair parallel to each other, and another pair perpendicular to the first (either one in each corner, turned 45 degrees, or one on each side: left, right, front, and back). You can also use them to make turning easier. For example, if you find it difficult to turn, or see that your robot bounces around when turning, having a "normal" traction wheel in the middle and an omni in each corner on each side will make the robot turn a lot smoother. Or if you have 4-wheel drive, having one pair of omni's and one pair of traction (omni's probably in the front) makes turning easy, but it puts your center of rotation towards the traction wheels.
There are other drive train configurations available, like swerve, octocanum, and apparently something my students were talking about today called "butterfly"... I'm still not entirely clear on how that one works, but apparently they got it from another team at the regional. However, those are drastically more complex and difficult to do right.
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