Car Steering with a Trapezoidal Mechanism

Car

track length

4.5

wheelbase

10

Trapezoidal Linkage

offset arm length

0.75

offset angle

15°

steering wheel angle

L

R

Ackermann condition

trapezoidal mechanism

This Demonstration simulates a classical trapezoidal steering linkage of a car with front-wheel steering.

In order for the inner and outer front wheels of a car to turn without slipping in a curve, the steering angles have to comply with the Ackermann condition. This condition ensures that the turning circles of both wheels have their center on the same horizontal line defined by the rear axle.

If the inner and outer steering angles are

δ

i

and

δ

o

, the Ackermann condition states:

cot

δ

0

-cot

δ

i

=

w

ℓ

, where

w

is the track and

ℓ

is the wheelbase of the car [1].

A plot shows how close a trapezoidal linkage can approximate the Ackermann ideal, given the right geometry of the car and the linkage [2].