Calculations for the Anti Ackermann Steering Mechanism

let me qualitative describe anti-Ackermann steering. In order to do this I will start with a description of Ackerman steering which forms the basis for Anti-Ackermann steering.

In 1818, Rudolf Ackerman  patented a design of Georg Lankensperger that provided a steering system for carriages that eliminated the angle scrub and subsequent wear of the wheels on the front axle. While not intellectually right to Mr. Lankensperger, I rather glad we don’t call this system Lankensperger steering!  The assumption was made that a carriage would rotate in a turn by a center somewhere along the line of the rear axle, that the outer front wheel had to turn faster and at a greater angle than inner front wheel and that the plane of  front wheels would perpendicular to the radial axis to center of the turn. The assumptions made in Ackermann steering are:

• No lateral forces
• No wheel compliance
• No body roll
• Only front wheels contribute to steering
• No suspension effects
• No longitudinal weight transfers
• Constant speed

Ackerman steering is normally computed using  a Jeantaud diagram (Charles Jeantaud in 1878 created a geometrical method to arrive at Ackerman steering) where the equal length steerings arms are placed on a line connecting the wheel center and the center of the rear axle:

What this is a special case of trapezoidal steer which is a four bar linkage:

Solving this for the the condition of the outer front wheel we get

Then we can ask, what are the requirements for Ackermann angle:

As you can see, we can only approximate true Ackermann steer to within a small steer. Normally, in Vehicle Dynamics, where computational accuracy can be sacrificed for simplicity, the Ackermann steer angle is computed by

Anti-Ackermann was devised, mainly for race cars to gain a steering advantage in tight turn race courses where increased outer wheel steering angles are needed. Anti-Ackermann steer is usually computed using the a “horizontally flipped Jeantaud diagram:

(borrowed from

http://www.mae.ncsu.edu/klang/co…
)

The computation are essentially the same as above.