Bible Linked Suspensions Bible

While rereading the best 4x4 suspension thread written by a suspension god over on PBB, somebody (Blackjack post 227) mentioned something that may be worth discussing. The balance of the suspension was brought up. I think he was discussing the amount of flex of each end and using an anti roll bar to balance the roll.

I saw someone in another thread from the same era mention something about the balance as well. I am struggling to find the post again. It was said that a 50/50 balance was unpredictable when going down a hill and a tire drops into a hole. Whereas if its 30% front, the tire would drop in but the sprung mass was more predictable in which end of the vehicle it followed.

Thoughts anyone on balancing flex and roll stiffness at each end?
 
About two weeks ago, gt1guy and I had a brief discussion about roll centers in another thread. A few days before that I had started gathering the below data, but had not gotten around to posting it. And then forgot to post it for another 2 weeks.



I wanted to look at the roll center, and the roll center envelope, of the axle in 3d. Previously I had looked at the orbit point of the axle, but I do not fully trust how I do that. And roll centers are a bit easier to explain and understand. The difficulty in solving roll centers is for a dependent suspension is how to go about doing it. The traditional method involves looking at the intersection of the links, drawing a line, and finding where it intersects the wheel plane. But this only works for symmetric travel. So I got the inspiration from the independent suspension world. Get the IC of a wheels, draw lines to the contact point, and find the line intersection. The problem was finding the ICs. The solution I took was to move the wheel up and down one step while holding the opposite wheel at a constant height. This gave the 3 points that define a circle, providing an IC.

I also rotate and translate the line intersect point so that the result is relative to the axle, not to the chassis. The 2d 4 link calculator does something similar.

First up is a pretty standard double triangulated 4 link. All of the plots have a travel step size of 0.32 inches.
1733614048862.png



Straight uppers with the lowers getting the angle.
1733614684788.png


Straight lowers and wider at axle uppers.
1733614990102.png
 
About two weeks ago, gt1guy and I had a brief discussion about roll centers in another thread. A few days before that I had started gathering the below data, but had not gotten around to posting it. And then forgot to post it for another 2 weeks.



I wanted to look at the roll center, and the roll center envelope, of the axle in 3d. Previously I had looked at the orbit point of the axle, but I do not fully trust how I do that. And roll centers are a bit easier to explain and understand. The difficulty in solving roll centers is for a dependent suspension is how to go about doing it. The traditional method involves looking at the intersection of the links, drawing a line, and finding where it intersects the wheel plane. But this only works for symmetric travel. So I got the inspiration from the independent suspension world. Get the IC of a wheels, draw lines to the contact point, and find the line intersection. The problem was finding the ICs. The solution I took was to move the wheel up and down one step while holding the opposite wheel at a constant height. This gave the 3 points that define a circle, providing an IC.

I also rotate and translate the line intersect point so that the result is relative to the axle, not to the chassis. The 2d 4 link calculator does something similar.

First up is a pretty standard double triangulated 4 link. All of the plots have a travel step size of 0.32 inches.
1733614048862.png



Straight uppers with the lowers getting the angle.
1733614684788.png


Straight lowers and wider at axle uppers.
1733614990102.png
Based on this findings. Which link configuration would you recommend as the most stable/best handling ?
 
Based on this findings. Which link configuration would you recommend as the most stable/best handling ?
Based on my current understanding and logic, it depends on the application and the overall setup. But also in what sense are we talking stablity and handling? High speed, low speed, street manners?

Ideally you want to minimize flex/roll steering. I think roll stability comes from the side to side movement of body relative to the axle.. If the body moves towards the extended side, then it has to fight the force that is causing the compression to do so. I think this may be what causes what is typically known as the results of a high roll center, calculated through the normal approach of link intersections.
 
Based on my current understanding and logic, it depends on the application and the overall setup. But also in what sense are we talking stablity and handling? High speed, low speed, street manners?

Ideally you want to minimize flex/roll steering. I think roll stability comes from the side to side movement of body relative to the axle.. If the body moves towards the extended side, then it has to fight the force that is causing the compression to do so. I think this may be what causes what is typically known as the results of a high roll center, calculated through the normal approach of link intersectionsl
I had in mind Ultra4 style racing.. I know there are a lot of things that make a good handling buggy, but If we talk about the prefered roll center behaviour in theory , is it optimal to look for as constant roll center through travel as possible, such as double triangulated system provides (if I can read you graphs correctly)
or should in theory be better that the roll center gets higher on the extended side and lower on the compressed side while cornering, as the ‘’wider at axle uppers’’ graph shows.
Or vice versa ( lower RC on extended side and higher for compressed side) for straight uppers.
 
I had in mind Ultra4 style racing.. I know there are a lot of things that make a good handling buggy, but If we talk about the prefered roll center behaviour in theory , is it optimal to look for as constant roll center through travel as possible, such as double triangulated system provides (if I can read you graphs correctly)
or should in theory be better that the roll center gets higher on the extended side and lower on the compressed side while cornering, as the ‘’wider at axle uppers’’ graph shows.
Or vice versa ( lower RC on extended side and higher for compressed side) for straight uppers.
I do not know. I would refer to the previous page and compare ground contact shift to flex steer. I am not a huge believer in roll center being what we think it is.

But what I think would be preferred rear behavior for an solid front axle would be different than that for an IFS
 
Force based roll centers. I have no clue how they go about getting it but, it's what is being used these days.
A quick search says it involves adding the force vector from the tie rod to the force vector from the intersected A arms. Flipping that vector and putting it at the tire contact. Where the line along that vector crosses under the CG is the force based roll center. Typically they are very close for most street and race cars.

But that all comes from the independent world. I do not think it would change things for a non-steering solid axle. And finding derivations or proofs for anything regarding solid axles is a chore that I have never had much luck in.
 
Based on this findings. Which link configuration would you recommend as the most stable/best handling ?

There are many other forces involved that make this hard to answer.


But that all comes from the independent world. I do not think it would change things for a non-steering solid axle. And finding derivations or proofs for anything regarding solid axles is a chore that I have never had much luck in.

^^^This^^^

But we do need to look at spring and shock location, that will also affect how the body reacts around the suspension.
 
Due to some of the recent questions regarding link angles, I decided to do a broad sweep of angle changes looking at flex steering, wheel contact center movement, and the physical roll center. The physical roll center being the point of intersection of a lines from the tire contact patch to the IC of that side being moved up and down. In this data, the only thing that was changed was the side to side spacing at one end of one pair of links.

First is the side view image showing the suspension geometry. It was selected because it is a generic 4 link setup.
1736661144113.png

Here is a top view of all the links. Naming scheme is link point and how it is moved with negative being inboard. EG: UA-10 is Upper axle 10 inches in. "Base" is the generic setup from which movement occurs. Due to current tool limitations, I had to limit outboarding of the lower links.

Top row is moving the upper axle, 2nd row is upper frame, 3rd row is lower axle, and 4th row is lower frame. Base is shown in each row.
top view links.png


The first result up is flex steer. All suspensions were solved as travel of the center of the wheel. All flex steer plots share the same color scale.
flex steer.png


And here is the side to side movement of the axle under the chassis. This is the center point between the wheel contact patches with the chassis being held fixed. All contact movement plots share the same color scale. It is my belief that more shift means more resistance to body roll because the body must move against the force.
contact shift.png


Here is the physical roll centers as if the were solved the way that independent suspension roll centers would be found.
physical roll centers zoomed.png

And here they are on the same axis limits.
physical roll centers same scale.png
 
Hope no one minds me bring this conversation over here. I want to help Boomtacoma keep his thread on the tracks.
My thought was to use the Subi motor in a rear-mid 2-seat application, not front engine.
Figured the width would matter less. But with rear-steer it'd matter just the same I guess.
The width issue is no different than using a Subi engine in the front.
Uppers straight back, lowers get triangulated still, so still no need for panhard. The uppers being straight allow for lots more room in between them. Have even seen some where the uppers are a reverse triangulated where the axle side is wider than chassis side with relatively straight lowers, for even more room. But yeah, none of that is conducive to clearing 40"+ tires at any appreciable steering angle.
Any straight links are difficult with large turning angles. It is why they are rare in the front.
triton/armada like doing that on their 6100 trucks. i think some of lolo's cars are setup that way
UFO Fabrication's 4400 cars and some short core trucks as well. I only know of a few rigs that did it with a solid front axle. And none of them newer than 2009.
so do you get the 40 degrees of angle that's always talked about?
Yes. The strength in side loading does not care if it is in the upper or lower links.


This setup is known as the Satchel link in the pavement world. There is some analysis of it in the last 2-3 pages. It is characterized by a low roll center, low side to side movement, and low roll steer.
 
Hope no one minds me bring this conversation over here. I want to help Boomtacoma keep his thread on the tracks.

The width issue is no different than using a Subi engine in the front.

Any straight links are difficult with large turning angles. It is why they are rare in the front.

UFO Fabrication's 4400 cars and some short core trucks as well. I only know of a few rigs that did it with a solid front axle. And none of them newer than 2009.

Yes. The strength in side loading does not care if it is in the upper or lower links.


This setup is known as the Satchel link in the pavement world. There is some analysis of it in the last 2-3 pages. It is characterized by a low roll center, low side to side movement, and low roll steer.
thanks again for helping us understand the link system.
 
This setup is known as the Satchel link in the pavement world. There is some analysis of it in the last 2-3 pages. It is characterized by a low roll center, low side to side movement, and low roll steer.
You sure thats low roll center? From playing around with it in CAD it looks like it has a high roll center vs standard triangulated 4 link. It is nice and flat though.
 
You sure thats low roll center? From playing around with it in CAD it looks like it has a high roll center vs standard triangulated 4 link. It is nice and flat though.
Yes. When one pair of links is parallel, the roll axis goes through the intersection of the other parallel to the parallel links.

With relatively flat links, this would put the RC at the height of the lowers. With normally triangulated uppers, the RC is about upper height. Inverse uppers can be all over the place depending on the lowers
 
Copied to here from the How's My Numbers? thread for discussion. Most of this will involve antis with the historical understanding of antis and not the force analysis understanding.
Hi Treefrog, been doing more reading up and thinking about AS/AD and would appreciate some input on my line of thinking here.

You recommended AS/AD be in the 30-40% ish range for my use type (Highway capable moderate rock crawler on 37s).

Please correct any of my thinking that may be wrong here, but having a below neutral AD (<50% at 50/50 drive bias) in the front will cause the suspension to tend to unload and move the wheels down under traction. So, when trying to climb up a rock or ledge, the suspension will have a tendency to push the wheels down into the rock and move the body up in the front. In some ways this seems like a good idea because it may give the tire more traction, and try keep the tires pushing into the ground on steep climbs, but in other ways opposite of what one would want when rock crawling.
Anti = bias is not neutral. It is no movement. 0% is neutral.

I do not think the front moves the wheels down. What I think happens is the side view (SV) torque from the front axle pulling and load transfer causes the nose to rotate away from the axle. Where as in the rear, the links push the wheels down.

When pushing into a rock or ledge to get the front end up, we want to push as much force forward into the surface. More AD/AL comes from a higher IC by definition. A higher IC means that the axle wants to push under the vehicle more instead of moving up and down.

Moving the body up has the downside of raising the CG that plays a part in flipping over.
In my mind, especially if I an climbing one side and not the other, I would think that I would prefer >50% AD in the front so that the side of the suspension hitting the rock will tend to squat, making use of the uptravel available and allowing the wheel to move up the obstacle without having to push the whole body up right away, which I feel would allow the wheel to roll up stuff more easily and comfortably.
I do not know if we want the suspension to compress while driving up a ledge. On one hand lowering the CG will help, On the other, the momentum from the inevitable unloading may cause the cage to be tested. We also want less weight on the front when driving up a ledge, but more weight on it once it is up. I also think that we may want the weight to go up early when we have more traction to push into the obstacle with. And we do not want the vehicle trying to drive over the axle, something that typically comes with a high AL.

The root cause of antis is a moment about the CG caused by the forces in the links. On straight flat ground, our links pass under the CG, causing a nose up moment (pushing rear, pulling front). But when you push the front up against a rock, it creates a nose down moment canceling out the rear's nose up. The torque from the tire climbing a vertical wall predominantly loads the upper link in compression for most offroad setups, though this can not reliably be used to compress it more.
I am also aware that >50% AD makes for better braking performance, and that may just be one of the compromises to make when building a streetable rig.
In theory, yes. But in reality, probably not. The primary function of suspension is to keep the tires in contact with the ground. If you are not touching the ground, you are not braking or accelerating. If it is too stiff it can chatter and hop as you brake. This is more likely the rough the road is.
As for the rear, I would also think having >50% AS would be desirable because on steep climbs or obstacles, the rear wheels pushing down under traction will shift weight onto the front wheels giving them traction, rather than the rear squatting down shifting weight off the front.
The problem that rigs with high anti-squat experienced was the axle kept try to drive under the vehicle. Another issue in hindsight might have been the the rear extending causing the CG to move away from the surface, increasing flip over risk. The IC being higher up means that the point on the travel arc ends up with a larger horizontal component than is desirable. The more the travel is not perpendicular to the surface, the more the force of going over a bump is transferred to the chassis in an uncontrolled manner instead of in a controlled manner through the springs and damper.
I was also wondering more about AS/AD slopes and how opposite sides may interact. You suggest having antis rise with compression, which makes sense to reduce squat and dive more as you approach max compression. But what about drooping out? The way I see it, if you are in a situation such as the video I linked below where you have one side stuffed up and the other side drooped out and you get traction, and your AS curve is such that you have more AS higher up in the suspension travel vs drooped out, the stuffed tire AS will overcome the dropped side AS and push the stuffed tire down as well as the dropped tire up, forcing the body to roll over.



If my thinking there is true, then I would think you would want to make sure the AS curve looks something like this (ignore %, just looking at cure shape):

1741647024881.png


Where the drooped tire AS will overcome the stuffed tire AS until it has reached a more stable point. If the curve is more of a straight line like " \ " or doesn't curve back over, then the lower tire will always have more AS than the higher one, which may help even more with stability. Maybe?

I think you are overlooking the part where traction results in antis. A drooped out wheel has no weight and therefore no traction. The lack of force means that any pitch resistance it may generate could be considered negligible. As such I do not believe that antis on a drooped out tire are worth much effort in targeting behavior.

One thing to keep in mind is that those plots only show symmetric antis. As an axle flexes, the projected to side view links change their relative end points.
The same sort of logic applies if we are going with <50% AS in the rear, but with the graph going the opposite way like " / ". If the drooped side has a lower AS then the stuffed side in this situation, then it will want to do the same thing and roll the body over, just that it will moreso be the dropped side pulling it over vs the stuffed side pushing it over. Having the graph go like " \ " in this situation would counteract that, but that is the way people's curves seem to go when building <50% AS anyways. So the main thing there is making sure the AS curve looks like " \ " regardless of whether you are running more or less than 50% AS.

But, what about AS crossing over that 50% mark at some point in the curve? If the curve looks something like this:

1741650594094.png
The same thing as above about weight -> traction -> reaction. I think that you would want the compressed side to have less anti since it will tend to compress the high side more.
then the stuffed and dropped wheels will act oppositely under traction, with the stuffed trying to squat more, and the drooped trying to droop more, which seems to me would be kinda unstable.
That sound like it would be more stable with it trying to lean towards the uphill side. Copied from my shorter response: "The reason to not design near anti = bias is that in theory small changes in traction and travel cause crossover of between anti-squat and pro-rise. This generally results in hopping. Similar can happen with antis over anti = bias where the instantaneous force from acceleration wears off and with it the pro-rise, causing cyclic traction spikes and hopping."
However, with a more vertical curve that doesn't cross over the 50% line, then the stuffed and drooped sides wont have too different of AS values and wont be counteracting each other as much. This may be something to shoot for? A relatively vertical AS curve, whether it is more or less than 50%?

1741651101587.png
I may be starting to sound like a broken record, but weight -> traction -> reaction. However, I do think that for a trail rig, a steady anti is a good thing. But flex does change the antis.
I could be seriously overthinking all of this though, as I know a lot of this behavior can be addressed with coilover tuning and sway bars. But seeing videos like this makes me think it can have a pretty big effect.
Try not to think yourself into design paralysis. Are you overthinking or are others underthinking? :stirthepot:

Again copying from my previous response "The second video is a really good example of something that was prevalent in the early linked days but has generally been designed against. The rear is trying to drive under the vehicle as the front applies resistive force, braking in this case."
 
Part 2 cause 10,000 character limit:

Sorry if I may have followed a wandering path with my response. The thinking that this resulted in lead to some interesting considerations and changes in thought. I also kept switching my thoughts between anti and force analyses. I think I will have to look into doing some FBD analysis for pushing into something. Some initial results are showing a much lower pitching moment than acceleration with a normal looking 4-link.
I think I briefly touched on it when talking about pushing into a rock, but antis are a derived prediction. When you look at the forces from a typical 4-link suspension under driving load, you will find that the upper links are mostly reacting to the torque and the lower links are countering the uppers' force and taking the driving force. When the forces are applied to the chassis, the torque created about the CG by the lowers is larger than the torque in the other direction from the upper. Thus pitching the chassis nose up. Something we do not generally see at ride height is the upper or lower forces passing above the CG.
Something that muddies the water with antis, is that there is some independence between antis and the IC. A high anti with a close IC is going to be very different than a high anti with a far IC. This relative perpendicular distances from the axle centerline to the links has a similar problem. The entire response has been assuming that the lower is close to the centerline. If balance is more even or the lower is farther, it changes things.
 
Your welcome.

But I feel way lost looking at this.

I sometimes forget I stare at this too much.

Short version: more red or blue is more flex steer. In this case + (red) values cause steering to the left.

Left side travel is the axis on the left and right side is on the right. Travel is measured as +- from ride at the contact patch. I keep the plot rotated so that straight up is both sides up. Side to side is roll.

More explanation:
In reality, roll tends to be be more /\ shaped than --- since we tend to use dual rate setups.

Flat suspensions tend to have lower overall values than those that go up towards the frame.

Of the suspensions shown, parallel lowers are tied for peak flex steer and have the most along the roll line. Parallel lowers have the lowest peak, and are best for symmetrical roll. And the way it is designed ties for peak but has the lowest along the likely roll line.
 
My head exploded 6 pages ago. Thank you for putting this together. I plan to read and reread because there's a ton of great knowledge shared.
 
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