Where's the roll axis?.... Triangulated 4-link

[-DA]

The roll axis of a triangulated 4-link (in plan view: one set of triangulated links, one set of parallel links) is created by drawing a line through the intersection point of the triangulated links with the slope equaling that of the parallel links in the side view. But...

How would you determine the roll axis if the slopes of the triangulated links varied from side to side? i.e. they technically never intersect in 3 dimensions, only the plan view. Do you simply use the plan-view intersection point projected into the the side view? You'd still have to pick a vertical point in the side view between the projected slopes of the links though.

Or let's say you built a Satchel Link but the upper links (parallel in plan view) have different slopes in the side view. Which slope from the parallel links becomes the slope of your roll axis? Perhaps you just split the difference...?

An inverted example of this is Billy Shope's triangulated 4-link being set up to dynamically cancel driveshaft torque by differing the slopes of the lower parallel links and, therefore, changing the anti-squat from side to side.

-Dave

[David Pozzi]

Look in a "Chevrolet Power" catalog. In the back they have a great Vehicle Dynamics section. It shows how to find the roll axis of various suspensions, Satchell link or Chevelle rear suspension is included.

Found it online.
http://www.race-dezert.com/forum/attachment.php?attachmentid=55139&d=1236028954

http://www.race-dezert.com/forum/attachment.php?attachmentid=55140&d=1236028972

[BillyShope]

Careful, David! Those illustrations are from the Millikens' Race Car Vehicle Dynamics and the publisher wants a lot of money for using them. This is the publisher, mind you, and NOT Bill and Doug. I talked to Doug about using an illustration in a post and he couldn't have cared less, BUT he went on to point out that he no longer had control over such matters and that the publisher was not so liberal. I had already posted a copyrighted photograph and...so far...I have not received any letters from lawyers. Perhaps I worry too much, but, when you're living on Social Security, you tend to be very protective of those savings.

As for asymmetric linkage arrangements, I would point out that...in the final analysis...it's the forces carried by the links that are important and not their location. Yeah, that sounds like a lot of double-talk, but here's an example: The conventional 3link has a pair of symmetrically positioned links and a third more centrally located. This makes it very easy to determine the antisquat. Okay, but what if no 2 links are at the same angle in side view? This would be like a 3 legged stool where the holes were drilled without a fixture. Actually, any one of the 3 links could be considered the "odd" link. Once you fix the location and angle of the odd link and the locations of the other two links, there would be two sets of angles for those remaining links which would provide the desired antisquat and the desired degree of cancellation of the driveshaft torque. Carrying this a bit further, it can be seen that there exists an infinite number of 3link combinations which will yield the same performance.

I recently added a page (Page 40) at my site which includes a spreadsheet which allows the user to select any 3 points along the axle housing (providing, of course, sufficient spread in Y and Z directions to satisfy strength considerations) and the percent antisquat. The results include the link angles which satisfy the input and also completely cancel the driveshaft torque effect.
http://www.racetec.cc/shope

[David Pozzi]

Billy,
Thanks, I found them on the net and they are not hosted on this forum's computer or on my computer. I had them set to appear here but changed them so they are just links to the images.
David

[-DA]

hmm... Thanks for the input guys. Ironically, last night I had my copy of Race Car Vehicle Dynamics sitting in front of me while I was playing with Billy's Page 40 calculator when my question came to mind. I was working out the math by hand and comparing it with a solidworks drawing to see if I could get the same results as Billy's calculator. Apparently, my late-night math skills have already deteriorated since college as I wasn't getting the same dimensions...

Billy- I understand how the resulting forces are what matter; however, as link geometry determines the location of force distribution in all respects, if I want to drive around turns on all 4 tires I need to control more than just the anti-squat and driveshaft torque. Of the infinite positions available to meet the prior two specs not all will attribute quality roll characteristics. This is where my question derived as I found my links differing in angle according to both my math and your Page 40 calculator. Hence, I've lost my roll axis (or my mind) and am trying to locate it. :jump:

I've got another question about using your Page 40 calc but I can't think of it right now.... maybe later tonight it'll come back to me.

-Dave

[BillyShope]

...to see if I could get the same results as Billy's calculator.
You can view the page source, but, unfortunately, it is not at all documented so you'd have to fight your way through it. Briefly, the three horizontal force components can be found directly. (There are enough equations.) I then "pointed" the links at the desired antisquat and found the vertical components. (Actually, I only needed to do this for one link.) Using two equations (one for the percentage of weight transfer carried through the links as dictated by the desired antisquat and the other the moment balance for the cancellation of the driveshaft torque), I solved for the "delta" vertical at two of the links and adjusted the angles to correspond.


...I need to control more than just the anti-squat and driveshaft torque. Of the infinite positions available to meet the prior two specs not all will attribute quality roll characteristics.

Of course. Specifically, you're concerned about roll steer characteristics. As I point out on the home page, my site is primarily devoted to dragrace suspensions and...as a group of us at Chrysler found out when we got involved in the fifties..., "expert" advice was restricted almost entirely to references to what seemed to work for the other guy. So long as the car can safely make its run, little concern is expressed regarding other handling aspects.

I'm convinced that roll steer is dependent upon more than the roll axis angle. In other words, I believe I could build a car with a horizontal roll axis and give it either roll understeer or roll oversteer. Whether that's true or not, you have the tool (SolidWorks) to determine whether one wheel advances (or retreats) more than its companion...during roll...and that's what you need to know. So, I would suggest that you forget about finding the roll axis (and I wouldn't have a clue when you've got 3 different link angles) and rely instead on the results from the SolidWorks assembly.
http://www.racetec.cc/shope

[-DA]

So, I would suggest that you forget about finding the roll axis... and rely instead on the results from the SolidWorks assembly.

That's not a bad idea. I'm not sure why I've only been using it statically to show the locations of links and the resulting values (anti-squat, roll axis location, etc.). I could easily enough animate the entire thing and project all those values throughout bump, droop and roll. Too bad I can't afford and/or don't have access to ADAMS/Car, Optimum G, or another nice suspension design software... of course, at that point I'd start wanting tire slip angle data and it'll get out of hand for a street car with street tires. lol


I'm convinced that roll steer is dependent upon more than the roll axis angle. In other words, I believe I could build a car with a horizontal roll axis and give it either roll understeer or roll oversteer.

How so? Just curious...


-Dave

[BillyShope]

How so?
Maurice Olley, in his notes as reproduced in Chassis Design, describes the steering effect when the pivot is above or below the wheel center, but, when he develops the defining equations, he uses only the effect of an angled rear suspension roll axis.

If you take your RCVD and consider the examples pictured, I believe you can visualize a situation where the roll axis is horizontal, but the pivot point is above or below the wheel center.
http://www.racetec.cc/shope