Control Arm Calculations (Actual Geometry)

[howeitsdone]

Wondering if there is a math wiz on here.

Firstly, not interested in being pointed to a chart or told "Just do this...". I've read all those forums and posts. I actually want to learn the math. If anyone knows a resource to use that would be nice too. I know there are some smart people in here. My other option is redrawing the parts 1:1 scale digitally and just playing around, but I don't really learn the core equation(s).

 

Clearly control arm length directly correlates to caster and pinion angle since only those can rotate the axle. I have a generic mockup of the whole premise below. The lifted wheelbase is just arbitrary since we are not given the amount of lift. Although, it can be calculated but that's not the point. 

 

It's my understanding the LCAs set the axle position along the X-axis relative to the image. Adding shims or using adjustable control arms would put you back to the target from factory when needed. This applies whether lifted or stock, correct? Meaning that no matter what, 119.9" will always be the target? I'm not talking about what people get by with or runs well. I'm talking about actual targets and baselines.

 

The example image needs to be corrected back to the stock geometry when lifted. Based on the new wheelbase, how would you go about determining the length adjustments for both UCAs and LCAs needed to get back to those original numbers without trial and error methods?

 

I would think starting from stock lengths (15" & 15-3/4") would be a given as well as the Y-axis distance between the UCA and LCA mounting points both axle and frame. Then it becomes fuzzy...

 

 

[howeitsdone]

Would these be the only variables needed to begin with? I would imagine there would be another variable of adjustment needed for the LCA. Which based on my above assumption, would just be the distance to put back to target WB length. Then, effectively we would solve for 'a' and be done?

 

 

[DirtyComanche]

If you're trying to be 100% correct from the get go, you need the Z-axis (horizontal separation) between the mounts as well.  The LCAs are fairly straight, but I don't believe 100%, I do not have my notebook here to say exactly though.  The UCAs have a significantly narrower separation on the axle side versus the frame, as in they're angled quite a bit, maybe 20 degrees or so.

 

Conveniently what you need already exists, you just have to plug in the variables.  You can find it here: https://www.patooyee.com/calculators/4BarLinkV3.1d.xlsx (Ignore any warnings about their unsigned security certificate, I can personally vouch for the person who holds that domain)

 

There is a newer version of that calculator (6.something) but it doesn't run on OpenOffice, so I haven't used it.  It's available from Irate4x4.

[howeitsdone]

I played around with versions 3 & 4 and while it helps visualize, I can't seem to figure out how to get the output link length in travel(2) correct. What is the 'x' Frame End measurement? Shouldn't it be the current link length? I assumed the Axle End was the offset to the front axle centerline and it visualizes correctly. If I put the Frame End as my current arm length it also visualizes correctly, but the output of what the link lengths should be are very wacky.

 

 

Given that the horizontal separation never changes (on stock-style setup) I can't see where that number would have an effect. I could be completely wrong, but it's a constant no matter what. For reference though, I have the actual measurements below that I took from my truck:

 

UCA @ Frame - 23.50"

UCA @ Axle - 24.50"

LCA @ Frame - 30.50"

LCA @ Axle - 33.00"

 

Someone solved the formula for the LCA calculation regarding the chart floating around:

 

a = Amount of Lift + 0.30427
b = 15.7471 (stock length)
Length Needed = √(a² + b²)

 

However, I doubt engineers came up with this to calculate it themselves. I'm sure the actual geometry of the suspension is in the equation. '0.30427' means nothing lol It's just a correction to get the equation to work essentially.

[boxyjeep]

There is a chart online for control arm lengths at various lift heights to meet the stock caster.  Keep in mind that you also have to balance front driveshaft pinion angle.

[89 MJ]

Keep in mind that your wheelbase gets shorter as you lift it (unless going SOA) because with increased travel, the rear wheels must be pushed ahead so they won't come back into the bedside when flexed out. At least that's the reasoning for it that I heard.

[howeitsdone]

Thanks guys. If you read my first post you'll see both your comments addressed. 

 

Was hoping there was someone here with the math knowledge to help me understand. I want to learn the math itself as I understand most of it pretty well. Another skill I'd like to add to the pile.

[AZJeff]

In any XJ/MJ front suspension, pinion angle takes precident over caster angle.  ALWAYS.  It is stated plainly in the shop manual,.

 

That said, I have to ask:   As I understand it, you want to do this theoretical calculation, and use that to set up your arms to match those calculated results.  Your premise is that, by doing so, you remove any of the "trial and error" arm length adjustments, correct?

 

Aside from the fact that adjusting arms is not as difficult as you are implying, there is another factor:   Your vehicle is 30+ years old.  I would not bet that the locator holes in the axle, nor the ones on the frame, and guaranteed to be at factory dimensions.   Wallowing of holes, combined with possible bending of chassis and axle locating brackets might change the dimensions from the factory settings.

 

Better yet, the fact that Jeep included lower control arm adjustments tells me that the dimensional consistency on the location of the control arm brackets, either on the axle end, or the chassis end, might not be very tight to begin with.

 

In other words, doing all these theoretical calculations might still not prevent the use of trial and error control arm length adjustments.

[howeitsdone]

I can see that in my manual. But that's not what this post is about. I know how to adjust the arms and get my angles, but that's not the point of this post. The math should work with anyone's actual measurements; not just factory. I'm interested in the math.

 

Maybe not the forum to ask such a question. No problem 

 

[AZJeff]

On 4/22/2022 at 11:54 PM, PocketsEmptied said:

I can see that in my manual. But that's not what this post is about. I know how to adjust the arms and get my angles, but that's not the point of this post. The math should work with anyone's actual measurements; not just factory. I'm interested in the math.

 

Maybe not the forum to ask such a question. No problem 

 

So you are doing this as an exercise in geometry.  OK, I can buy that.  
 

I know life is quiet in Vernal, but have you run out of other projects for your MJ?  How about stuff to fix around the house?😆😜

[Pete M]

I love geometry!   but unfortunately the last class I had was a couple decades ago and my brain now sucks and doesn't remember most of it.   being a 3 dimensional system that moves in several different arcs and rotations is why I love computers.   

[zomeizter]

I think you're overthinking this Pete...carry on.

[Pete M]

'tis the curse of being me.   

[DirtyComanche]

On 4/19/2022 at 3:34 PM, PocketsEmptied said:

I played around with versions 3 & 4 and while it helps visualize, I can't seem to figure out how to get the output link length in travel(2) correct. What is the 'x' Frame End measurement? Shouldn't it be the current link length?

 

No.

 

That calculator is meant for designing suspension, and while you can use it as a comparative tool, the primary function is design.  In design the link length is rarely a starting dimension, instead it is the attachment points.  Thus the link length is an output rather than an input, and the attachment points would be moved as needed if one is trying to produce a specific length.

 

I don't have the 4-link calc open or a current setup loaded into it, but the 3-link is the same and here is a screen grab.  Note that the "weird" 4-link with panhard (AKA 5-link) setup Jeep uses is probably better actually modeled in the 3-link calculator IF you're only interested in the geometry summary.  THIS IS NOT THE DIMENSIONS OF A STOCK JEEP, I don't know them and am not likely to go out and measure.

 

To explain the numbers in the input box:

Upper link Frame End X dimension (29.25") is the distance from the axle centerline on the X axis the link end is away from the axle, in this case back from the axle.  So if you were to measure straight back from the axle centerline with the tape measure flat and parallel to the centerline of the truck, my upper link end would be attached 29.25" back from it.  The link calculator is actually meant to model the rear suspension, but we're talking front, so just roll with the fact that a dimension farther back is positive rather than negative.

Upper link Frame End Y dimension (11") is the distance from the truck centerline that the upper link end is outwards from, as in it is 11" offset to the passenger (in this case, again, it's backwards because the link calculator is for the rear) side from the center of the truck.

Upper link Frame End Z dimension (22") is how far from the ground (with the truck on the tires) the upper link is.  This one is easy to measure, if the truck is on flat ground with the tires aired up, you can just measure from the ground to the center of this attachment point.  So, 22" above the ground.

Upper link Axle End X dimension (0") is how far forwards or backwards the upper link attachment is from the axle centerline.  This is 0" in my case, meaning the upper link attachment point is dead center vertically above the axle tube, and would be similar on a Jeep with stock suspension.

Upper link Axle End Y dimension (10") is distance from the truck centerline (or axle, whatever, your axle should be centered in the truck) that the upper link attachment is from side to side.  So, in my case it's 10" outward.  This means the upper link(s) are closer together at the axle than the frame.

Upper link Axle End Z dimension (22.5") is how high from the ground, again tires on and aired up, the upper link attachment point on the axle is.  In this case my attachment point is slightly higher than on the frame.

 

 

Going to the Material tab gives me an upper link length of 29.27" for this link.

 

If you are using the 4-link calculator everything works exactly the same, it will just draw in the second upper link as a mirror image of the first.

 

The lower link numbers all mean the exact same thing, it's just the lowers, not the uppers.

 

I'll explain the panhard bar inputs if somebody wants, but it's fairly obvious if you figure out the other ones.

 

To use this tool to give you the comparative link lengths needed, after you input all the correct points for a stock Jeep, simply adjust the Z axis frame dimensions for both the upper and lower links by the amount of lift (add to them) or lowering (subtract) you intend.  It will adjust the link length in the materials tab to keep the axle in the same location.  This will not change pinion angle.

 

Hope this helps.  I could explain more if needed or screengrab a video of doing it I guess.