# Steering with non-zero fork offset

How come the wheel centre O shifts to O* instead of O₁ in the case where we have a non-zero fork offset, when turned sideways? Shouldn't it have shifted to O₁, such that the contact point P₁ lies exactly below the centre, as is the case of zero-fork offset? Or maybe, P₁ could've lied directly below O*, if what the author says is true? Can't really wrap my head around the idea. Could anyone explain? These are the assumptions that the author made:

• the roll angle of the motorcycle is zero.
• the wheels have zero thickness.

(Book : Motorcycle Dynamics by Vittore Cossalter)

• Shouldn't it have shifted to O₁, such that the contact point P₁ lies exactly below the center, as is the case of zero-fork offset? No. For nonzero axis angles, the contact point only lies below the wheel center if the steering angle is zero. When you have steering and a nonzero axis, it gets quite complicated. But the offset doesn't change the relationship between the center and the contact point. Commented Jan 6, 2023 at 14:38
• And how did you render the subscript such that it copied into comments. I've never been able to do that. Commented Jan 6, 2023 at 14:40