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If the scrub is zero, the scrubbing action of the contact patch is equal on either side of the pivot point causing the tire to act like a car with a welded differential, inducing a condition called 'squirm'. In a straight line the tire tends to be stable and tracks well. As you turn though, the portion of the contact patch on the outside of the pivot point moves faster than the portion on the inside of the contact patch. Since the scrubbing area is equal on each side of the pivot point, yet the forces are different, the tire tends to fight itself and it becomes 'grabby' causing tire wear to increase and the steering to become unstable.
Positive and negative scrub radii have benefits in different types of suspension. A MacPherson strut assembly typically performs well with a lot of SAI and caster, a system negative scrub works well in. Because both SAI and caster increase the amount of camber on the outside wheel when steering, the fulcrum pivot point is at a point that has more leverage, requiring less steering effort. Negative scrub also helps reduce torque steer in front wheel drive cars. Positive scrub radius works well with suspensions that use dual control arms that use less caster and SAI to optimize geometry.