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Car Steering with a Trapezoidal Mechanism

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

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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 and , the Ackermann condition states: , where is the track and 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].

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Contributed by: Erik Mahieu (October 2014)
Open content licensed under CC BY-NC-SA

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Details

The Freudenstein equation gives an analytical solution for the geometry of a four-bar linkage. The steering mechanism in this Demonstration has two four-bar linkages:

1. the trapezoidal steering linkage between the two wheel steering arms

2. the linkage between the steering wheel shaft and the steering linkage

References

[1] The Institute for Dynamic Systems and Control. "Steering Dynamics." (Oct 15, 2014) www.idsc.ethz.ch/Courses/vehicle_dynamics_and _design/11_ 0_ 0_Steering _Theroy.pdf.

[2] D. Askins-Gast. "Approximating Ackermann Steering Geometry with a Trapezoidal Linkage." from the Wolfram Demonstrations Project—A Wolfram Web Resource. demonstrations.wolfram.com/ApproximatingAckermannSteeringGeometryWithATrapezoidalLinkag.

[3] A. Ghosal, "The Freudenstein Equation: Design of Four-Link Mechanisms," Resonance, 15, 2010 pp. 699–710. www.mecheng.iisc.ernet.in/~asitava/resonance10.pdf.

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