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Below is a picture 4-wheel vehicle steering linkage. I figured that in order to steer correctly $(W+D)tan\theta_1=Dtan\theta_2$ where $\theta_1$ is the angle of the outside front wheel, $\theta_2$ is the angle of the inside front wheel, $W$ is the distance between the two front wheels, and $D$ is the radius of curvature of the arc the rear inside wheel follows. The front wheels are the ones at the bottom of the picture. How can I figure out what lengths of the segments of the linkage will satisfy the equation for all values of $\theta_1$, $\theta_2$, and $D$?

enter image description here

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To find the lengths of the components of the linkage mechanism you are going to have to use trigonometry. I'd envisage doing so for the case when both $\small\sf\theta_1$ and $\small\sf\theta_2$ are zero.

Assuming the lengths of the components of the linkage on each side of the vehicle are the same do the calculations for one side of the vehicle and use the overall distance of $\small{W/2}$. For that however, you will need to know the angles between the linkage components for when $\small\sf\theta_1$ and $\small\sf\theta_2$ are zero.

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  • $\begingroup$ I didn't check that. Let me check my math and I'll get back to you. $\endgroup$
    – IOWF
    Mar 3 '16 at 1:17
  • $\begingroup$ My equation is wrong. I'll edit my question. Also, the equation wouldn't apply when the vehicle is going straight because D would be undefined. $\endgroup$
    – IOWF
    Mar 3 '16 at 1:23
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This is called Ackerman Steering. In an ideal case a line drawn through the wheel pivot point and steering arm pivot point will cross the centre point of the rear axle when the steering is centered. In practice other dynamic effects like roll etc may mean that the best position for this point will vary a bit.

As long as the steering arms are the right angle to the hub you can still have toe in or out by having adjustable length track rods.

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