Quote:
Originally Posted by cmrnpizzo14
Out of curiosity, is there really that much usable space created by using a round robot as opposed to the standard polygon shape?
|
Let's assume a circular robot and a rectangular robot with the maximum allowed frame perimiter (112 inches).
For the circular robot C = 2πr. Since C = 112, the radius of the circle is 56/π or approximately 17.825 inches, and it's area is πr^2, which is 3161/π or approximately 998.220 square inches.
For a rectangular robot, we have 112 = 2l + 2w, and A = lw, or A = l(56 - l). With some calculus, we can find that the maximum area occurs when the robot is a 28x28 square, with an internal area of 784 square inches. In other words, a circular robot can have up to about 28.339% more usable area inside it's frame perimeter than a rectangular one.
You could run the numbers for any other polygon, if you really wanted to, but I'll leave that up to you (I'm too lazy). You'll find that as you increase the number of sides on your polygon, the maximum area will approach, but never reach, that of a circle with the same perimeter.
As for how useful this extra internal area is, that can only really be answered on a case-by-case basis by each time based on how much space their subsystems use.