I see nothing in the rules that suggests an orientation that the sizing cube must be relative to parts of a robot or to the field.
Typically we would try to only respond to the specific questions being asked, but in this case, all of the specific questions are based upon this initial assumption, which is incorrect.
The full text of R5 reads as follows, with a few portions bolded for emphasis:
<R5> Robots must fit in a sizing box. Robots must be able to satisfy <G4>, and begin each Match in a volume smaller than 18” (457.2 mm) long by 18” (457.2 mm) wide by 18” (457.2 mm) tall.
a. Compliance with this rule must be checked using the official VEX Robotics On-Field Robot Expansion Sizing Tool: https://www.vexrobotics.com/276-5942.html.
b. Any restraints used to maintain starting size (i.e., zip ties, rubber bands, etc.) must remain attached to the Robot for the duration of the Match, per <G5>.
c. For the purposes of this rule, it can be assumed that Robots will be inspected and begin each Match on a flat standard foam field tile.
The full text of G4 reads as follows, with a few portions bolded for emphasis:
<G4> Robots begin the Match in the starting volume. At the beginning of a Match, each Robot must be smaller than a volume of 18” (457.2 mm) long by 18” (457.2 mm) wide by 18” (457.2 mm) tall. Using Field Elements, such as the field perimeter wall, to maintain starting size is only acceptable if the Robot would still satisfy the constraints of <R5> and pass inspection without the Field Elements.
A common-sense interpretation (G3) of the words "long", "wide", and "tall" make it clear to any reasonably astute inspector / Head Referee that the sizing "cube" in question is resting flat on a foam tile.
- Given that it fits within an 18” cube and does not violate the 24” “virtual ceiling”, is it legal to use a robot with the dimensions of the robot in the attached images as-is with all 4 wheels contacting the ground?
With that common-sense interpretation of the sizing rule in mind, the two parts of this question are in conflict with each other. The depicted Robot, with all four wheels contacting the ground, would not fit within a cube which is 18" wide.
- If the answer to part 1 is no, would this robot be legal to use if it started the match in a different orientation? Would there be any constraints on how the robot could move or orient itself once a match starts?
Yes. If the Robot started on its side, as depicted in the third attached image (assuming that the image is from a top-down angle), it would satisfy the constraints of G4. However, as pictured, it would likely be unable to move once the Match has begun without violating SG4 or SG5.
- Regardless of how it is used or not used during actual matches, should a robot with the dimensions of the robot in the attached images pass inspection?
This would depend on if the inspector was only strictly following the technical interpretation of R5, in which case the Robot would likely pass if inspected while resting on its side. However, a secondary purpose of the inspection process is to help Teams identify potential problems with their Robots before reaching the field and committing an illegal action. We would hope that this inspector would notice that the Robot would immediately violate G4 when it is placed with all four wheels on the ground, and advise the Team to modify their design.