[GeeTwo]

And in case it isn't obvious, for most robots you want the drop to be as small as possible while achieving a short wheelbase for turning. The greater the drop, the more the robot will pitch up as you accelerate and down as you brake, resulting in manipulators moving along with the chassis.

If your manipulators are relatively insensitive to pitching or you have sensors that reduce this sensitivity, and the maneuverability is essential, you may opt to add a bit more drop as a safety margin.

On the other hand, if you have a long arm that reaches forward and back to pick things off the floor, you probably want to minimize the drop. With that long arm, you may want to consider an 8 wheel configuration so that while you're doing low speed/acceleration pickup/placement maneuvers, your chassis will be horizontal. Another solution would be to put your CoG intentionally ahead or behind your center axle so that you're at least at a known attitude.

Note also that "stiffness" in this sense is primarily in the plate/bar/channel in which each track of wheels runs; the required drop is not nearly as dependent on flexibility in other axes. Using pneumatic wheels also counts as reduced stiffness for this purpose.

Another alternative to actually dropping the center is to turn down the corner wheels on a lathe. This is not usually the best solution, because the wheels are usually constrained by chain or belt to rotate at the same angular speed, which does not result in the same linear speed with uneven wheel sizes. However, if you scaled the number of teeth on the sprockets to be proportional to the diameter, this would not be a problem. (E.g. 14 teeth on a 3 1/2" wheel and 16 teeth on a 4" wheel, and with holes on the same level, you'd have a 1/4" drop).