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Finding the Roll Center for a 3/4 Link Rear


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It has been asked a lot on here and it comes up once every few months "bench" racing somewhere at the deserts, soo here we go... I know for me the answer were not easy to find and to understand but I hope that this info can help some one out in the future when deciding the pros and the cons of which one to use...

Attached are 3 pictures taken from an SAE text I got a long while ago,
In the first one it shows a traditional four link rear suspension, obviously the scale of the parts and angles are not what is "typically" seen on desert cars of today, how ever the concepts are the same! The most common misconception I have come across, and I was guilty of it too, was the the RC of a four bar suspension was located at the convergence point of the Track bars past the rear end.
Here is what you do....

Traditional Four link:

Sketch out your suspension looking at it from the top and from the side, as seen in the diagram, then in the top view find the convergence point or "lateral restraint point" as they describe, of the upper and LOWER links.

Then transfer this point to the side view making sure that each point is on plane with their respected link pair, after doing this you scketch a line from one point to the other. This line represents the ROLL AXIS of the rear suspension.

Where this axis crosses the Wheel Center line in the side view is the true height of the Roll Center!

Now you may ask how does one determine the RC if one of the planes is in Infinity and beyond? Well diagram 2 shows this

Say the lower links are parallel and the uppers have a convergence point. Like before you find the CP of the upper links and transfer it to the side view projection.

Now the Roll Axis line is drawn Parallel to the lower links in the side view plane and right through the CP of the upper links, and where this line intersects the wheel Center line vertical plane is the RC height!

Now for the Three link:

In the diagram it shows an inverted three link, with parallel lower links, but the principles are the same if everything was inverted.

Find the convergence point of the wishbone, hey! it is the center of the rod end!

Same as the aforementioned parallel link four bar, draw a line through the convergence point that is parallel to the lower links in the side view (remember the diagram is inverted so I am talking about a traditional three link) and where this line crosses the wheel center line in the vertical plane is the RC height!

Now with this you can easily tell if you have a Roll Understeer/Oversteer set up. By looking at the Roll Axis in the side view, if the axis is tilting up in the front, then it is Roll Oversteer, and if it is tilted down, well then it is Roll Understeer. Pretty simple? Now how powerful these effects are is based on how much this axis is tilted, if the axis were to be parallel with the ground, then it would be neutral. This is also true with the combined Roll Axis of the whole vehicle when connecting the front and rear RC's but that is a whole other conversation.

Now with all of this you can see how easily you can affect RC and Roll Axis by simple chassis adjustment mounts.

Also if you have ever seen Rick Huesmann(SP)'s Pro-4 rear end, you have noticed the odd arrangement of bars on the axle, he has 5 Links, and it very similar to a inverted three link, how ever the lower "wishbone" does not control the lateral position of the rear end, it is the three parallel upper links by creating a geometric conflict. Kinda hard to understand at first but after drawing it out, the RC in the rear is Really Low!

Hope this helps if not or my info is wrong don't hesitate to correct. Thanks



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Thanks for posting Dave. Can you elaborate on the pros and cons of the three types of roll axis, and how they would change throughout the travel?
I could very well be wrong..... but here goes.... I have been taught the average height of the lateral locating device determines the height of rear roll center (solid axle application). We call the RC the moment center which is the bottom of the moment arm - top being the center of gravity. And so the lengthy discussion could continue. With a triangulated four link, the upper arm and lower arm frame mounting points would be the lateral locating device. I do not have a picture available to illustrate what I'm saying. The diagrams you posted are similar to the methods we use to determine front roll center height and location. We tried the method you have described on the rear suspension of our dirt track car. We never were able to make the RC's and moment arms match and have a neutral handling car. After adopting the lateral locating device method, our roll center calculations matched and our car handled very well - i.e. consistant. We do not calculate the geometry manually. We use a 2d program where we input the physical measurements. But, this subject has been and will always be debated, updated, and refined over and over again. So if it works consistantly - use it.


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Isn't the rear on your dirt car a three link with a Panhard bar? If so then the method for RC is similar but you use the CL of the Panhard bar as the rear lateral locater and then connect that point with convergence point of the lower links. Is that how you were doing it?
Our car is now a three link, but was stock mounting point metric four link (stock except for 9" with adjustable control arms). We were not allowed to use a panhard bar with stock mounted rear. The three link does have a panhard bar. We don't factor in any of the control arm angles when determining roll center height. Only use the average height (CL) of lateral locating device. We only use control arm angles from static to dive and roll to determine rear steer. Are you trying to achieve roll-couple with your method of roll center height? Your method puts the rear roll center height higher than our method. The method you may be using for the front could possibly put the front roll center higher also which would most likely end up with the same over-all results when the two methods are compared. The biggest difference would be our choices in spring rates to control "roll -over" at each end. Do I make any sense here? Also - we do not use the roll-couple theory. We just try to match the moment arm lengths. Also adjust front roll center location from static to dive and roll to compensate for track banking, etc. I am very interested in roll center design for off road. We plan to build a truck over the next few years with a triangulated four link and long travel front end. Transfering our method from left turn only combined with little jounce and rebound compared to desert racing is a challenge (for the inexperienced). (P.S. -stock GM metric is a four link triangulated set-up - no panhard bar)
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So this past week we were setting up a factory metric four link for first practice of the year. For kicks and giggles, I used your method as well as ours and compared roll centers. Low and behold with both methods we arived at the same roll centers. After comparison, I feel like an idiot. I could not seem to wrap my brain around your diagrams. Now it is all so perfectly clear. I did not understand the math behind our method. But, now I see the calculations we are using determine the intersections of the control arm angles without physically maping them out for us to see. And, the panhard bar on our present car is centered within 2" of the spring base. Chassis designers I have talked to seem to agree for all intense purposes this will not affect roll center location enough to cause an issue. Roll center location should still be "felt" halfway between the rear springs. If we were to use a short bar with lots of offset, roll center location would be greatly affected. As for my last statement, I now question it's accuracy. More input please ACID-RAIN.


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Thanks Acid Rain. This cleared thing up some for me. Of course I have no idea what the proper Off- Road setup is...I'm sure everyone has and opinion. Like you said...build in some adjustable mounts and play with it.


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It is always at the builders discretion, now at least with this you can see what you have and maybe what others have and draw your own conclusions as to what you think you want and what works. I have been lucky enough to have come across info from a G-Bros, two similar porter/Gordon, Corr, our independent truck, Vortec and so on, Rivi/Norman, and SPD chassis, as well as been able to talk to and ride in some of them to figure what I think I would like to see.


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Hmmm.... I have been reading up a lot recently and all I have achieved is to confuse myself more and more.
Now in the Pro 2 design I looked at on the Lucas Oil rules I noticed that the top links are apart on the axle and angle towards the center on the chassis. And when looking at the calculator it brings the roll axis lower than when compared to having the top links apart on chassis and close on the Axle.
Then when I look at setting up a link system with the triangle on the lower side of the axle and the straight links on the top side of the axle it brings the roll axis even closer to the ground, not to mention what it does to the Anti Squat.
So my questions are,
Is a Low roll axis more desirable than a Higher roll Axis?
Anti Squat, is 100% neutral? meaning when at 100% the rear will not lift or squat down?
When under power, is the more desired effect to to have the rear squat down or lift up in order for best traction. (There seams to be quite a few different opinions on what gets power to the ground better)


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There are other effects of having the "pro 2 " arrangement of parts it also plays into how the roll axis is oriented under braking an acceleration either promoting over/under steering depending on where the positions are set on the chassis better suited for short course where traction is at a premium. By doing a simple sketch and comparing "pro2/desert" you can see how the roll axis moves in relation to the CG and which end of the vehicle has the increase in leverage on the CG

100% anti squat is neutral
A pro 2 in its "softest" setting is about 95% if I remember correctly and 140% at its highest. There are of course no free lunches. In a perfect world you would say I want max bite and traction. But drivability may suffer depending on the track conditions. Because the higher the percentage the quicker it gets to max traction so if its a sloppy track it will be much harder to moderate wheel spin.
Now desert a high anti will result in great traction and straight line speed but desert is not a groomed track and produces a high degree of instability at higher speeds. You will also suffer a high amount of roll steer and the rear of the truck moving the chassis on single wheel bumps. So a neutral setup would be desired.