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Consider a four-wheel steering vehicle in which:

  • The front wheels follow Ackerman condition
  • The rear wheel are rotated with a fixed angle (dir == dor in the picture below, and such angles do not change if the driver moves the steering wheel)

Actually, this is similar to a classic front wheel steering vehicle, but the rear wheels are not "straight", they are angled.

What kind of trajectory would this vehicle follow? Is there any closed-form equation to describe it?

enter image description here

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  • $\begingroup$ There are trucks using rear wheel steering on many more than 2 axles... As for trajectory, it means that long trucks can deal with tighter bends etc $\endgroup$ – Solar Mike Dec 3 '19 at 16:51
  • $\begingroup$ Extend the axles of each wheel and see where the (don't) meet. Then figure out the average direction and how long the tyres will last. $\endgroup$ – Transistor Dec 3 '19 at 18:57
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It means there is still some side slipping and dragging of the wheels if the rear tires and front tires are not all aligned to track circles around one common center.

In your case, the rear wheels axis are parallel and never meet.

If a vehicle needs for steering at both the rear axle as well as the front, then the geometry of the steering linkage both at the front and the rear axle should direct inner wheels to turn more so that all the wheels axis meet at the center of rotation of the vehicle.

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