Tribot swerve

[Aren Siekmeier]

Originally Posted by Andrew Schreiber

One thing to be aware of is that you DO have a smaller contact patch.

This sort of depends on what you mean by "smaller." Turns out the the forward back or side to side direction (versus diagonally) is actually less stable than any direction for 3 wheels. I crunched some numbers on this a bit ago: suppose you have a unit circlecircle of diameter 1 available as your frame perimeter, and you need to fit your contact points on this circle. To simplify things (and because it's almost always at least approximately true), the contacts are evenly spaced around the circle. How many do you want? We start by quantifying "stability," as you have, by the distance across the contact polygon in a given direction. In some directions this will be maximized (corner to corner) and in others it will be minimized (side to side). Below is a plot of these maximum and minimum moments for 3 wheels all the way up to 10 (could easily go higher, but honestly?).



The odd numbers have the smallest spread between max and min, so they are maybe more stable when looking at all directions combined. But the even numbers actually achieve the max in a particular direction, since you can actually go from corner to corner on a diameter. So while in certain directions, 4 wheels is less stable (side to side), in others it is the most stable (corner to corner). But when do you ever push or accelerate in the corner to corner direction?

Remember that this is comparing 3 vs. 4 vs 5 wheels (etc.) on the same circle (for the sake of having some sort of control). You could possibly get more out of a 3 wheel since you can make a triangle with longer legs instead of keeping the entire frame inside the circle, but then the shape of the frame is getting more awkward.