How big of a cut out can our robot have to pick up a ball?

That depends on the configuration of your frame, and where your ball pick up is located. You have to ensure that you first meet the Bumper Requirements, and can then determine how large of a gap you can have.

For example, if your ball pick up is located in a narrow 28 inch side, you would need 8 inches of bumpers from the two external vertices, which would require a minimum of 16 inches of bumpers on that side, leaving you with a 12 inch cut out. If you had a 38 inch side, you could have as much as a 22 inch cut out.

Do some thinking: Each corner needs 8" of bumper on each side. That bumper needs to be fully supported. Given that the maximum robot size is 28 inches x38 inches, and you need to allow 16 inches per side for those 8" bumpers, you get a maximum of 12 inches wide (narrow side). I’ll let you figure out the wide side.

As for depth… well, you could go all the way through the robot, but I don’t think that’ll help you much…