Ackermann Steering

Ackermann Steering

  • A steering technique used in car-like vehicles
  • Invented by Rudolph Ackermann in 1818. Before this point, wheels always rolled with slip unless traveling straight ahead
  • As the car travels along a curved paths, all tyres follow unique trajectories around a shared centre
  • To avoid sliding, the geometry must steer the inside front tyre at a larger angle than the outside front
  • Its premise is based on low-speed turning which applies to sedans. Sports cars tend to be configured toward parallel steer.

Equations

  • Let w  be the track width, l  the wheel base, \phi_i  the relative steering angle of the inner wheel, \phi_o  the relative steering angle of the outer wheel, and r  the distance between ICC (instantaneous center of curvature) and the center of the car, we can write the following:
  • \tan{\phi} = \frac l r
  • \tan{\phi_i} = \frac l {r-w/2}
  • \tan{\phi_o} = \frac l {r+w/2}
  • By subtracting the reciprocal of these equations, and
    considering the fact that \cot{x}= \frac {\cos{x}} {\sin{x}} , we can deduce:
  • \phi_i = \tan^{-1} (\frac {2l\cdot\sin{\phi}} {2l\cdot\cos{\phi-w} \sin{\phi}})
  • \phi_o = \tan^{-1} (\frac {2l\cdot\sin{\phi}} {2l\cdot\cos{\phi+w} \sin{\phi}})

Playable Demo

Ackermann Simple

Ackermann Advanced