View Full Version : semi OT: steering geometry and mechanism

09-08-2006, 01:49 PM
So I'm looking on eBay for go kart stuff, and I stumbled across this one. Check out the question submitted at the bottom of the page.

http://cgi.ebay.com/ebaymotors/GO-KART-110CC_W0QQitemZ200023248212QQihZ010QQcategoryZ4609 2QQrdZ1QQcmdZViewItem

But seriously -

Those who have studied the mechanics of steering a vehicle may have noticed this - when the steering wheel is turned all the way to the left or right lock, you can see that the inside wheel is at a sharper angle than the outside wheel. This is because the inside wheel will travel a circle of smaller radius than the outside wheel. Makes sense?

I'm trying to understand (visualize) how this is accomplished mechanically. It would be great if someone here could explain it or post a diagram, but that may be asking too much. Can anyone recommend a link or other source so I can get a handle on this?

For simplicity, assume a car with no suspension, like a go kart. (This is why I want to know.) It may not matter too much with a kart, and I may not be able to pursue it, but I'd like to understand. I know it has something to do with the fact that the axis that a car's front wheels will pivot on is not vertical - normally it's tilted back somewhat.

Below is a basic diagram of one system I saw. In this diagram, the axis of the wheel pivot is, in fact, vertical, but despite appearance, the steering column is not. Can someone explain how a linkage like this could "pull" more disance than "push", allowing the inner wheel to turn a smaller radius?


Failing that, if anyone knows of one of those cool "educational" links that explains it, I'd be grateful. Thanks.


09-08-2006, 01:53 PM
Google for Ackerman Angle, look at the RC car links...

09-08-2006, 01:54 PM

09-08-2006, 02:38 PM
Mark...with a kart...you may want to build it as a rear steer outfit(tie rods, SA's behind the axle).
If they are in front you have to build a longer spindle to clear the arms as they will point in towards the tire at the front.
The same steering setup can be used with a rear steer but the arms will angle away from the tire to get the same Ackerman effect. This allows you to run a shorter spindle.
A rule of thumb that I use....for the Ackerman angle...use the center of the rear axle as the measuring point. Run a string or straight edge from that point out to the corner of the front axle(just inside of the front of the inside tires) and that will ball park your Ackerman angle.
Don't forget about king pin inclination and caster...it all makes for a better handling cart. I built quite a few off road karts and all this made them handle much better than my early ones that didn't have any of the proper steering design.

09-08-2006, 03:00 PM
Mark, on a vehicle used on the highway, the toe in or toe out on turns is controlled with the steering arms(from tierodto spindle). The arms are bent to control this difference in turning radius, diferent bends and lengths depending on wheel base length. JIM

09-08-2006, 04:01 PM
Sorry but that 'point the arms at the centre of the rear axle' thing just isn't really valid and I'm surprised it's repeated on Wikipedia.

OK, maybe it's worth a try if you have nothing better but if it actually gives proper steering geometry then that's down to luck rather than any real method. It's obvious that e.g the length of the steering arms, not accounted for at all in that method, will affect the geometry.

It's not rocket science to do the maths and analyse the linkage. In fact I wrote some spreadsheets to do just that (the second link you get on google for Ackermann steering geometry, yay!)


Originally wrote it for human powered trikes but it's been used for all sorts from solar and mileage marathon vehicles to some specialist off-road thing with six wheels :-).

Basically the spreadsheets work out the error compared to ideal Ackermann for various angles of turn, once you've entered the geometry. Just a 2D approximation but that's usually good enough for starters. Then you just tweak the linkage until you get the errors to be small. I've modelled most of the common linkages including the one Mark pictured.

I'm a crap programmer so they're not pretty but they do work. Free. There are loads of free software spreadsheets around which will run them if you don't have Excel.

I've also never got round to writing the 'how the spreadsheets work' page but basically they do some co-ordinate geometry and solve a quadratic equation to find the 'moving' pivot points in the linkage. The rest is just graphs etc.

I guess on a car with horsepower to burn it doesn't matter much if it's wrong which is why that old wives' tale about the rear axle has persisted, but if you want it to be right or you have limited horsepower as with a human-powered vehicle or solar vehicle (I get lots of student groups using the spreadsheets) then any tyre scrub is a significant loss of power.



09-08-2006, 04:17 PM
Click on the photo below:

http://www.kartbuilding.net/racingkart/Old_Racing_Kart/ackerman2.jpg (http://www.kartbuilding.net/racingkart/Old_Racing_Kart/ackerman.htm)

09-08-2006, 04:26 PM
It's obvious that e.g the length of the steering arms, not accounted for at all in that method, will affect the geometry.

Not exactly. The center of the rear axle method takes into account both the wheelbase and the track of the vehicle. The length of the steering arms doesn't change the geometry in terms of steering angle. If the same steering angle is applied to a short arm as a long arm the relationship between the front wheels and the turn radius remains the same. Angles are angles regardless of the size of the triangle.

What it does do is change the steering rate. The shorter the arm the higher the rate for the same amount of linear movement of the end of the arm.

09-08-2006, 04:42 PM
I don't think the triangles we're talking about are similar. Imagine very long steering arms with a short horizontal bar connecting them. Turn one wheel and very quickly the connecting bar will have swivelled through 90 degrees and beyond, making a nonsense of any triangles you may once have had. It's not a linear geometry type system. As the angles of steering arms and the connecting rod between then get to be more than 'small' you can't play similar triangles - you have to work it out.

Also, the rear axle method takes no account of different linkage types e.g the one posted in the first message, compared to one where the two steering arms are linked directly.

ON EDIT - that wasn't put too well. You're right that the arm length has no effect - BUT only for very small turn angles. As the angle increases the geometry moves away from the initial condition as the linkage operates, and it's the subsequent geometry that needs to be worked out properly to see if it's giving the proper angles to achieve Ackermann at all required turn radii.

And indeed to check that the linkage can give you the turning circle you require without running out of movement. And also to check that you don't end up with the connecting rod in line with one of the steering arms at full lock (it'll get 'stuck' and the wheel won't be positively positioned).

09-08-2006, 05:00 PM
Yes, that is the case if you use one solid arm to both steering arms. If you use individual control rods to each arm as in the drawing then it's a different matter. As long as the control rods are at the same angle in relation to the ends of the arms only the rate changes for the same change in steering angle.

Making the arms longer reduces the amount of steering angle available while making them too short can increase it too much.
Heh. missed your edit.

09-09-2006, 12:24 PM
Wow - thanks, all. This is why I like this board.

Of course the answer had to be something beautifully simple that everyone but me seems to already know about. :D

Thanks again, especially bikepete for the spreadsheets. I'll give them a whirl.