The ackerman arms move round in circles. What makes the car steer is basically how much you rotate them.
So the rotation is determined by the horizontal movement imposed by the steering rack.
This picture looks like an ackerman arm.The left one, lets sayhttp://media.photobucket.com/image/cos%20circle/Nautth/sin.jpg
Our steering rack will produce an horizontal movement. Let's put a number of 1cm. You can see in the picture that to move horizontally 1 cm to the left(car steering to the right) since we are in the horizontal part of the circle, that would produce a small angle variation(hence small steering). Meanwhile, to produce 1cm to the right(car steering to the left) the ackerman needs to turn a whole deal of degrees.
You're interested in how many degrees of rotation are needed for a given horizontal displacement. If we put the arms in 90° position, we're symetrical, it's the same going to the left or to the right. But if we put them in an angle we can achieve ackerman, or anti ackerman.
If we look at the image of the cosine we can see that to have a given horizontal deflection(change cosine magnitude) we need to move a greater angle if we are near 0 degree, than if we are near 90 degree. This is because cosine changes as -sin.
This is talking ideally since the steering arm would angle as the uprighr rotates-