Side-View Suspension geometry - interpretation

[Jesse214]

I'm just looking for a second interpretation of Milliken & Millien's side-view drawing depicting the layout of the control arm pivot points (Section 17.5 of Race Car Vehicle Dynamics, Figure 17.20).

I've researched this to death (only major book I've not looked at yet is Tires Suspension and Handling, which I'm trying to get my hands on)... and this exact question was asked before, but not clearly answered:
Reference topic: http://fsae.com/eve/forums/a/t...10201341#14510201341 (http://fsae.com/eve/forums/a/tpc/f/125607348/m/14510201341?r=14510201341#14510201341)

The side-view clearly shows how to layout the pivot points with ZERO caster angle. I understand what is drawn. But what I'm unclear about is how to properly extend the construction of this geometry to include CASTER.

(NOTE: I had some modified versions of Milliken's 17.20 on here, but I'm told I can't actually legally post those, so I'll simply explain instead)

The previous answer to this was to just move points 2 and 12 to account for the new ball joint locations due to caster. However, if you do that, do you not also have to re-draw points 1 and 11, 3 and 13, or do those just remain on the side-view tire vertical center line?

[Jesse214]

I'm just looking for a second interpretation of Milliken & Millien's side-view drawing depicting the layout of the control arm pivot points (Section 17.5 of Race Car Vehicle Dynamics, Figure 17.20).

I've researched this to death (only major book I've not looked at yet is Tires Suspension and Handling, which I'm trying to get my hands on)... and this exact question was asked before, but not clearly answered:
Reference topic: http://fsae.com/eve/forums/a/t...10201341#14510201341 (http://fsae.com/eve/forums/a/tpc/f/125607348/m/14510201341?r=14510201341#14510201341)

The side-view clearly shows how to layout the pivot points with ZERO caster angle. I understand what is drawn. But what I'm unclear about is how to properly extend the construction of this geometry to include CASTER.

(NOTE: I had some modified versions of Milliken's 17.20 on here, but I'm told I can't actually legally post those, so I'll simply explain instead)

The previous answer to this was to just move points 2 and 12 to account for the new ball joint locations due to caster. However, if you do that, do you not also have to re-draw points 1 and 11, 3 and 13, or do those just remain on the side-view tire vertical center line?

[Z]

Jesse,

1. Good to see that you have done some research.

2. RCVD gives a flawed "flatland" analysis of suspension geometry (sorry Doug, but true). So do most other automotive textbooks and suspension software programs. Real 3-D kinematics does NOT have "Instant Axes" (it has "Instantaneous Screw Axes", aka "ISAs" or "Motion Screws", which are very different creatures).

3. I will wait to see what others have to say before carrying on. But in the meantime could you please clarify just what it is that you are trying to find. Eg., are you wondering if anti-dive changes with different castor angles? Or do you just want to find the BJ positions for some given amount of castor and anti-dive?

Z

PS. Figure 17.20 has far too much scrub radius for FSAE!

[Jesse214]

Hi Z,

Thanks for your reply thus far! Right now I'm working on finding the inner pivot locations in the side-view (having already located them in front-view).

Anyways...
I think I've got this figured out. Once I realized the longitudinal position of the pivot axis didn't make a difference, that pretty much cleared up any questions I had.

Although, I'd be interested in hearing specifically any suggestions or improvements upon the "flatland" methods outlined in RCVD and places.

[Z]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by Jesse214:
I'd be interested in hearing specifically any suggestions or improvements upon the "flatland" methods outlined in RCVD... </div></BLOCKQUOTE>
This issue is proof positive of the education system going down the crapper, with the auto industry front and centre, pulling the chain.
~~~o0o~~~

Here is some RCVD on 3-D kinematics.

Page 608.
...any independent suspension allows only one path of motion of the knuckle relative to the body. ... the suspension provides five degrees of restraint (D.O.R)..."

Page 612.
"Instant centers come from the study of kinematics in two dimensions (in a plane).
...
In suspension design it is convenient to break down this three-dimensional problem into two, two-dimensional problems.
...
In true three-dimensional space, instant centers are replaced by instant axes. If we take the instant centers defined in the side view and rear view and connect them together we get a line. This line can be thought of as the instant axis of motion of the knuckle relative to the body..."
~~~o0o~~~

Utter codswallop!

Why? After 20 pages of explaining how this "two by 2-D" kinematics works, we get to page 632;

"The design is now complete except for fine-tuning the tie rod to obtain a linear ride-toe plot..."

Huh???

So we eventually find that the "instant axis" doesn't quite manage to specify the "motion of the knuckle", but it needs some help from the tie rod to control steer angle. What the above RCVD section is describing is NOT the 5 DoR control of the knuckle that is initially discussed (ie. a 1 DoF joint), but rather a 4 DoR (= 2 DoF) joint between knuckle and body (more details below).

I note that I have at least one comment per page written in the margins of RCVD Chapter 17 pointing out either badly explained or completely wrong sections. This whole chapter is kinematics-for-kiddies.
~~~o0o~~~

So how do we correctly specify the motion of the knuckle relative to the body? Or, for that matter, the motion of any body/reference frame relative to any other body/frame? That is, how do we describe this most essential concept of "motion"?

Try googling "Instantaneous Screw Axis". On page 1 I found the concept used by knee doctors, golf coaches (!!!), as well as, err, grown-up engineers working on mechanism design, robotics, etc. Here are the Wikipedia entries on the "Screw Axis" (http://en.wikipedia.org/wiki/Screw_axis), and "Screw Theory" (http://en.wikipedia.org/wiki/Screw_theory) (the latter uses the same concepts for both forces and motions).

Briefly, the ISA is the alpha of the kinematic alphabet (I learnt it on day one of "Theory of Mechanisms" classes). It is a very simple "nut and bolt" concept, although rather poorly explained by Wikipedia (too much algebra, not enough geometry). How else would you describe the motion of a nut screwing onto a bolt?

It was first widely discussed by the Italian Guilo Mozzi in the middle 1700s. The Frenchman Michel Chasles published his "celebrated" (that's the word they use) theorem on it in the early 1800s. By the late 1800s Irishman Robert Ball had published numerous papers and a book that comprehensively explained the interactions of both force and motion screws (ie. "screw theory").

There is absolutely NO EXCUSE for any mechanical engineering student to have not at least heard of these things!
~~~o0o~~~

Is the motion screw (ISA) of any use in understanding suspension kinematics?

Of course! Again briefly, the ISA is the most essential element of kinematics, so it appears everywhere.

The 1 DoF motion of an independent suspension (ie. just up-down) means that at any instant there is only one ISA for the motion of the "knuckle relative to the body". This ISA is easy to find. One glance at the location of the ISA tells whether the wheel has either negligible or excessive bump steer, camber change, and a whole host of other properties. Yes, one glance!

The ISA is also found in every other type of kinematic joint. A beam-axle requires 2 DoF wrt body (up-down for each wheel), so its kinematics are best described with a "cylindroid" (google also "Plucker's conoid"). This is a ruled surface traced out by a single infinity of ISAs, and is again easily found.

The double-A-arms-without-tie-rod described by RCVD above is a 2 DoF joint that has the "instant axis" and the "steer-axis" (king-pin) as the two zero pitch ISAs lying on its cylindroid. There are infinitely more ISAs available on the cylindroid, and the position of the tie rod determines which of these relates to the 1 DoF motion of the knuckle.

Any ISA has a "linear complex" of n-lines associated with it. Find the n-lines from the linkage, and you find the ISA. Know where the ISA is, and you know where the n-lines that pass through the wheelprint and wheel-assembly-CG are. Now, understanding vehicle dynamics becomes very easy.

Like tying shoelaces, all this might sound impossibly difficult to begin with, but with practice it becomes effortless. http://fsae.com/groupee_common/emoticons/icon_smile.gif
~~~o0o~~~

So why, after 30+ years of browsing have I never, ever, ever, found any mention of ISAs in any book, paper, or computer program associated with the auto industry?

I can only speculate. Maybe all auto engineers really are brain-dead morons? More likely is that it is a combination of stupidity, and an arrogance that suggests that they can invent their own version of 3-D kinematics. "Hey, we spent N billion giving this model a face-lift, so we must know what we are doing!" But most likely is that the majority of customers are dumb schmucks who swallow any old rubbish that is served up.

Anyone else want to speculate why the auto industry, including motorsport, continues to get this so wrong? http://fsae.com/groupee_common/emoticons/icon_confused.gif
~~~o0o~~~

BTW, and by coincidence, the movie "Idiocracy" was on the box last night. This under-publicised US satire is, IMO, the most accurate prediction of society's medium term future that I have ever seen. Highly recommended!

Z

[ben]

To be fair Z, if you Google "Instantaneous Screw Axis wishbone suspension" you get a lot of results, but that spoils the self-righteous assertion that only knee joint surgeons are looking at it ;-p

That aside you're not wrong. I guess the reality is that most published books focus on draftsman approaches that can be done on a drawing board without needing to do any calculations.

That's not to excuse it, but that's probably the reason.

Ben

[Z]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by ben:
... the self-righteous assertion that only knee joint surgeons are looking at it ;-p </div></BLOCKQUOTE>
Ben,

... and golf coaches! (Page 1, analysing golf swings!!!) http://fsae.com/groupee_common/emoticons/icon_smile.gif

Granted, there are papers out there discussing motion screws in the context of vehicle suspension design. In the past I haven't looked very hard, just browsing anything I came across, but never finding any ISAs. Interestingly, most of the ones I quickly looked at just now are from Korea (Hyundai, etc.), although also one FSAE related thesis.

My point is that ISAs should be mentioned in any suspension paper, book, whatever, that pretends to be at all technical.

If not, then we are truly headed towards Idiocracy. http://fsae.com/groupee_common/emoticons/icon_frown.gif

Z

PS. It is a geometric concept. Any equations/algebra are of secondary importance.

[BillCobb]

The concept is well known in at least one company (the one with 2 letter abreviation), but to counter the pseudo intellectuals and podium planted self righteous know-it-alls, there is also a well known thing called proprietary intellectual rights. No one in their right mind tells the competition how they do their job or make their product(s) special. That's why papers are NOT written about cool stuff, book writers have to make up facts, and vehicles and their parts don't behave like their artistic creators claim.

Get the properties from a multibody analysis CAD program or a complex number based algebra solution and validate it with a K&C test. When all is said and done, DON'T design a steer axis with nonlinear screw motions. Pairs of tires and drivers hate it.

[exFSAE]

1. I'd say undergraduate engineering education could be done much better in general, now that I look back on it having worked for 5 years professionally. Both more rigorous as well as more tied together through the years and with extra focus on practical application. Then again there is a movement among educators for vastly improved teaching methods.

2. To Bill's point, much of the "good stuff" to learn is locked away as IP within top tier organizations - or just comes with working experience. Not an awful lot in the public domain other than once in a while when a legitimately good book comes out. To a degree though it makes me feel that the growing trend of employees moving around from company to company every so often can be good for cross-pollination.

3. You also don't NEED the most rigorous understanding of everything to be successful, in our case here - to win races. If you CAN, then sure sometimes it helps get the answer quicker. But it's not a strict requirement.

[Z]

Z, lamenting the decline of the education system,
"... we are headed towards Idiocracy."

Bill Cobb, on a 200+ year old concept nowadays openly discussed by knee doctors, golfers, and Korean auto engineers.
"... proprietary intellectual rights. No one ... tells the competition how [to] make their products special."

US Government to "Big Three" when they ask for $50 billion bailout during 2008 global financial crisis.
"Why are you only making pickup trucks??? http://fsae.com/groupee_common/emoticons/icon_confused.gif "
~~~o0o~~~

exFSAE,

You say, "... there is a movement among educators for vastly improved teaching methods."

I made it through primary school just before "The New Math", (a US response to the Sputnik kick in the pants) was introduced throughout large parts of the English speaking world. This was supposed to breed a generation of rocket scientists by emphasising fundamental abstract concepts such as "axiomatic set theory" from an early age.

Within ten years it was recognised as a complete failure, because the kiddies could no longer add or multiply! Unfortunately, the experiment was also the final nail in the coffin for traditional teaching methods, such as Euclid and the rote learning of multiplication tables, that had served well for 2000+ years.

IMO, learning maths is very much like learning sport. Mostly practice, practice, practise. It is simply NOT possible to understand any of it, until AFTER you can actually do it.

Or as Euclid said to the Pharaoh Ptolemy, "There is no royal road to geometry."

So students, start simple, and do lots of exercises. http://fsae.com/groupee_common/emoticons/icon_smile.gif

Z

[BillCobb]

Here's one I slipped through: US Patent 8006550. The math in this is well understood by all the new engineers. It's the 'old' ones who have trouble with it. GM was spending 50 billion on just retiree health care at the time. And, banks killed the ability to get a average car loan, mainly because they were told to give zero down mortgages to unemployable people. Oh, and the Holden Commode was supposed to be a supercar but failed miserably in the US marketplace: required expensive custom special tires, couldn't stop in the legally required distance and sucked fuel like a Cat D8 dozer.

Still playing ice hockey on my OE knees, but 1/2 of my team has had one (OR more) replacements for knees and hips.

Put your Twitter gun down and connect with the real world. Sorry to read that you've been left out of it, mate...

[Z]

Bill,

I agree with your negative assessment of GM's Australian "Commode". I also note that GM's Oz division recently only managed a $275 million handout from the local government, so that part of the business plan is working, but not nearly as well as head office. Can't understand your last line though?
~~~o0o~~~

Anyway, I have received a few PMs from students interested in the "Screw Axis" as it relates to suspension design, so I will try to put a brief description together in the coming weeks (hopefully some rainy days...).

In the meantime I would be interested in hearing if any students are already familiar with this stuff, or know of any good references (ie. ones that are not hidden away as "proprietary intellectual rights").

To start the thinking process, and considering RCVD Figure 17.21;

Do different tie-rod locations, namely different amounts of bump-steer, have any affect on anti-dive or anti-roll behaviour?

The "instant axis" analysis of RCVD suggests not. True or false?

Z

[Moop]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by Z:
Do different tie-rod locations, namely different amounts of bump-steer, have any affect on anti-dive or anti-roll behaviour? </div></BLOCKQUOTE>
I'll bite

I would think it should depend on the orientation of the tie rod. The flatter the tie rod is in the front plane, the less I'd expect it to impact anti-roll since it can't give much of a vertical reaction. Likewise, I wouldn't expect the tie-rod to have much effect on anti-dive unless it had a significant difference in X and Z coordinates between the inboard and outboard tie rod points.

As per your other question, I'm not familiar at all with screw theory and apparently neither is my mechanisms prof, haha. My entire mechanisms course has been a bit of a sad joke unfortunately - we've spent most of our time making hand drawings of 4/6 bars to do some ridiculous task like rock between two given configurations with a timing ratio, drawing involute profiles by hand and drawing cam profiles by hand. I'd be very interested to learn something useful about mechanisms http://fsae.com/groupee_common/emoticons/icon_smile.gif

[Simon Dingle]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">In the meantime I would be interested in hearing if any students are already familiar with this stuff, or know of any good references (ie. ones that are not hidden away as "proprietary intellectual rights"). </div></BLOCKQUOTE>

I'm vagely familiar with the screw axis concept, although it was never taught to me by that name (I had to Google it to find out exactly what you were talking about). It was taught very simply and was just "this is how you deal with objects in 3D space". We never did anything more complicated than a single joint. When we moved on to vehicle dynamics we had a new lecturer and moved to 2D plane analysis and didn't go in to anything more compicated than finding slip-angles from the vehicle heading and steering angle.

Not being a suspension man myself I've never tried to analyse suspension geometry and so don't fully understand the weaknesses that you're trying to point out. However it makes sense to me to apply the screw axis theory to suspension geometry, since it's just a set of 3D linkages that can be analysed like any other set of linkages (to my limited understanding at any rate).

I did find an SAE paper from '91 that clearly walks the reader through from first principles to finding the screw axis of the entire vehicle. I imagine that most people on this forum have legal access to the SAE database and I certainly won't be breaking copyright by uploading it, so please don't ask.

"Suspension Analysis with Instant Screw Axis Theory" by C.H. Suh, University of Colorado. SAE Paper no. 910017

[Tim.Wright]

I'll bite too,

There are many ways of representing a suspensions from a force and displacement point of view. All with variying levels of complexity. Different tools for different jobs. Screw theory is one (also noew to me), roll centres are another, multibody simulation is another.

The reason the screw theory is not as common as you would like to see is that there is extra complexity for possibly little gain in accuracy over calculations using instant axes. This is what is most important.

Classical suspension theory uses instant axes to determine the split of forces between the spings and the links. Since the toe link of a typical axle has a very low force, its effect on the jacking, or anti roll or rch is negligible.

To include extra calculations for little return makes little sense. Especially when the magnitude of your improvement in accuracy will be drowned out by hysteresis and compliance effects.

The concept of instant axes and screw theories are just simplifcations. Nothing more, nothing less. One is not necessarily better than the other. Therefore, I dont see any problem in people using what is explained in RCVD.

Tim

[Z]

Thanks for the replies guys. I wanted to do a brief introduction to Screw Theory here, but that will require some figures so maybe in a few weeks...

In the meantime, here are some comments on the subject to date.
~~~o0o~~~

Many times on this forum I have used the approximation Pi=3. That is good enough for "back-of-envelope" calcs. But the important thing here is that I KNOW that I am WRONG.

So, for example, if I have an equation like Y = X/(Pi-3)..., then I KNOW that I must use a more accurate value for Pi. (Otherwise, regardless of X, Y always "overflows"! http://fsae.com/groupee_common/emoticons/icon_confused.gif )

The very important point is that we should know when we are making approximations, and how big they are. Similarly, that is why we put "tolerances" on engineering dimensions (something quite rare on these pages!).
~~~o0o~~~

Some years ago I was given a "gee-whiz, fully 3-D" suspension program. This gave the RC heights, anti-pitch%s, etc., calculated according to the RCVD method. Interestingly, it also had the option of calculating the knuckle/upright's "derivitives", such as the dx/dz, dy/dz, and rotations of the wheelprint centre. As is usual, all these numbers were given to ~eight significant digits, because, I guess, with idealised kinematics we can expect perfect precision.

The disappointing part was that on the "possible bugs to be fixed list", there was mention that the dx/dz didn't always match the anti-pitch% (the dx/dz gives the longitudinal n-line slope, which gives anti-pitch%). In fact, with quite common layouts there was a discrepancy of ~10%, so all eight of the significant digits of the two answers were different!

The really disappointing part was that the standard output displayed the incorrect RCVD anti-pitch numbers, even though the correct numbers, the dx/dzs, were available! The program's authors did NOT KNOW that they were WRONG, even though they had the right numbers at hand.

(And yet again Z muttered "grrrr ... auto industry ... education system ... going down S-bend... grrrrr... http://fsae.com/groupee_common/emoticons/icon_mad.gif ")
~~~o0o~~~

Briefly for now, and just considering front suspension, if the steering geometry has a large "scrub radius" (ie. wheelprint centre WP offset from steer axis in front view, like RCVD Fig. 17.20), and it has zero bump steer, then the anti-pitch IS as specified by RCVD (ie. longitudinal n-line passes through side view IC, like RCVD Figs. 17.19 & 21).

BUT (!), if there is some bump steer, then the WP has additional longitudinal movement during bump (due to the steer and scrub radius), so the n-line slope, and thus also the anti-pitch, changes. Similarly, if there is castor trail, then the WP has additional lateral movement during bump, and the lateral n-line slope and notional RC height changes.

How big are these errors?

Timo says "the toe link ... has a very low force..." With a layout like Fig 17.20, which is not unusual, the scrub radius is of similar dimension to the steer arm length. So the tie rod force is of similar magnitude to the longitudinal force Fx at the wheelprint during braking, which is a lot!

Moop suggests that if the tie-rod is lateral and horizontal then there should be little effect from its forces. Actually it depends on the slope of the tie rod relative to the wishbones (which I will cover in a few weeks). The bottom line is that with some typical suspensions you can expect none of the above computer program's eight significant digits to be correct.

So maybe 10% error, which is not too bad, but it helps to know that there is an error.
~~~o0o~~~

Timo also suggested that 3-D screw kinematics might be a lot more complicated than the 2-D version, for only little extra accuracy. Looking at the Wikipedia pages and other sites I can see why people might agree (ie. poorly explained, with too much emphasis on algebra).

I now realise how lucky I was to have a good teacher in my early education. (Thanks Jack! Anyone interested might try "Freedom in Machinery" by Jack Phillips. Very deep, long, and wordy, but great figures!) Anyway, these days if I see a 2-D kinematic problem I treat it simply as a slice of the full 3-D problem.

It is worth noting that much of practical engineering only needs 2-D kinematic understanding. For example, the crank/conrod/piston-slider, and the chain and gear drives of IC engines only need 2-D. The two widest engineering fields where 3-D kinematics is necessary are robotics, such as those used on auto production lines, and automotive suspensions. That is why I find it so hard to believe that so little 3-D kinematics is taught to potential automotive engineers.
~~~o0o~~~

Anyway, here are some examples of how 3-D Screw Theory can help you understand suspensions.

1. The Five-Link Suspension.

The RCVD method (2 x 2-D) relies on finding the "Instant Axis", which is the intersection of the planes of the upper and lower wishbones (ie. the planes through the centres of the three ball joints of each wishbone). This method also works with strut and other simple suspensions.

But what about the increasingly popular 5-link suspension? These have been used for some time at the front of Audis, to give an outboard "virtual steer-axis", and at the rear of many other cars.

Since, in general, no planes can be found that contain any two of the 5 links, it is not possible to use the RCVD method to find the instant axis. So likewise it is not possible to determine anti-pitch or anti-roll. Of course, you might be able to find a computer program that gives these numbers, but can you trust it?

I will try in a few weeks to post a general approach to solving this 5-link, and similar, problems. (This will require drawing a few figures (easy) but then a new scanner because of cable-crap problems with perfectly functional old scanner... grrr... hence shopping... more grrrrrr...) http://fsae.com/groupee_common/emoticons/icon_smile.gif
~~~o0o~~~

2. Bump Steer.

The 2 x 2-D method of RCVD allows you to approximately (!) find the pitch and roll antis. It also allows you to estimate, "at a glance", the amount of camber and castor change that occurs with bump. That is, if the Front-View-Instant-Centre is close the the wheel, then there will be a lot of camber change with bump (aka a short FVSA). If the FVIC is far away from the wheel, then negligible camber change.

But what about bump steer? RCVD leaves that for another chapter, where it is dealt with in an ad hoc manner. Importantly, note that an 0.1 degree change in steer angle has a similar effect on lateral tyre force as 1 degree change in camber. So steer angles are more important to control than camber angles.

Now, if we know the position of the knuckle/upright's motion screw (ISA), relative to body, perhaps because a good computer program has drawn it on the screen for us, then we can tell "at a glance" how much bump steer there is, as well as camber and castor change.

Just briefly, if the ISA is far away from the wheel (say &gt;100x bump travel), then bump steer is negligible and NOT a problem. However, if ISA is close (say &lt;10 bump travel), then we definitely have to check the details. So, if ISA is close, longitudinal, and horizontal, then OK. If ISA has a lateral component, but the wheel has negligible camber angle, then still OK. If ISA is close and has a significant vertical component, then there will definitely be bump steer, so potentially a BIG problem.

The above is a bit like knowing where a car's "imaginary" centre of gravity is. If an FSAE car with typical track has a CG that is more than one metre above ground, then I reckon most people will see "at a glance" that it will have problems cornering fast. Likewise, there are many suspension properties that can be seen "at a glance", once we know where the ISA is. But first we have to find the ISA. http://fsae.com/groupee_common/emoticons/icon_smile.gif
~~~o0o~~~

More later (but maybe a few weeks...).

Z

[Kevin Hayward]

Z,

Filtering out the negative stuff this is a really interesting post.

It would be great if you could write a paper on the practical application of Screw Axis theory to automotive suspension design. Your balanced suspension paper was very interesting and certainly got us at UWA looking at alternatives back at the turn of the millenium.

I will freely admit that I have designed by the 2x2D approach, with the add-on of avoiding bump steer and the like. But I see no reason with current software that the ISA could be displayed just as easily. None of the information about the motion is lost in something like OptimumK, and it is surprisingly easy programming to create more outputs.

Kev

[Z]

Kevin,

I am currently trying to get my hands on the paper ref'd by Simon above. The SAE are demanding $20-30+ for this 21 year old paper, which I refuse to pay, so I have to go through the local library... With this sort of suppression of the dissemination of knowledge I wonder if SAE stands for "Society Against Education"! http://fsae.com/groupee_common/emoticons/icon_smile.gif

I hope that putting the information here makes it more accessible to anyone/everyone interested.

Anyway, good to see that yourself and a few others are interested in these old but little taught concepts.

Z

[Jersey Tom]

A suspension-related SAE paper from CU Boulder which predates what we had believed to be of the first real attempts at a FSAE car or anything similar. Surviving records from those days were scarce, save for perhaps a manila folder squirreled away in the back of an old filing cabinet in the stock room.

Feels like an archaeological find.

How things have changed...

[woodsy96]

I agree with Kevin - this is an interesting post, and a paper on it would be interesting to read.

However, if I were to do FSAE over agin with what I know now, I still wouldn't give a damn about screw axis theory - I'd use roll axis to design a car quickly, with some appreciations of it's shortcomings, and find substatially bigger gains by finishing building a car on time without major design balls ups, and by spending my time testing the shit out of the car, training drivers(for the easist gains is performance), testing car setups and finding money for more tyres.

Perhaps this "ignorance" is what you call a failing of the education system or the automotive industry or society in general - but I have a feeling most people have SO much lower hanging fruit to grab first (I know I would).

(Goes back to work trying to get any goods with usable threads and square corners from China http://fsae.com/groupee_common/emoticons/icon_mad.gif )

[Z]

Woodsy,

I agree that "a quick build, and lots of testing/driver training" is the best way to get good FSAE results.

But this Screw Axis stuff is really quite easy. The gist in one sentence, "Any and all instantaneous motions of one body relative to another are like screwing a nut onto a bolt"! http://fsae.com/groupee_common/emoticons/icon_smile.gif A whole lot more can be understood after an hour or so of arm-waving, scribbling on blackboards, etc. (but unfortunately it takes a lot longer on this interweb thingy... mumble, grumble... http://fsae.com/groupee_common/emoticons/icon_frown.gif ).

My main concern with the education system is that I foresee a few years (???) from now someone posting;

"Pls sirs,
need advise suspnesion. we no must cut open chikn and study n-trails closly, and will tell us what do. hav opned chknen but dnt no waht ntrails teling us, pls advice most urgntly!".

Ahh... Eng-Voodoo 1.01! http://fsae.com/groupee_common/emoticons/icon_biggrin.gif

Z

[Z]

Some Comments (and Criticisms http://fsae.com/groupee_common/emoticons/icon_smile.gif) re:
=====================================

"Suspension Analysis with Instant Screw Axis Theory", by C. H. Suh, SAE Paper 910017.
================================================== ================================

Firstly, thanks to Simon for mentioning this, the first suspension paper using Screw Theory that I have seen. Also, thanks to the local library for their persistent efforts to obtain this paper for me (it took ~1 month, so NO thanks to the SAE for making it so difficult).

Secondly, these comments are based on my brief reading of this paper. Many of the details of Suh's method are covered in his earlier works, which I haven't seen. So the following is just a "first impression".
~~~o0o~~~

This paper presents an algebraic approach to finding the "Instant(aneous) Screw Axis" (ISA) for the motion of an independent suspension's upright (knuckle) relative to the car's body. Suh uses a matrix approach to solve six equations in six unknowns to find the ISA.

Suh presents the workings for Wishbone, Strut, and 5-link suspension types. The 5-link is the most general type, so it is the only type you need to know (since both Wishbones and Struts can be modelled as 5-links). Note that any and all one degree-of-freedom joints can be modelled as being constrained by 5 n-lines, and can thus be solved using Suh's 5-link method.

(BTW, in 3-D kinematics an "n-line" has "No" motion ALONG it, and thus the body has motion that is purely "Normal", or at right-angles, to the n-line (so it is sometimes also called a "rightline"). A "ball-ended-rod", or "S-S crank" in Suh's terminology, has an n-line running through its centre. So n-lines = S-S cranks.)
~~~o0o~~~

Suh (in this paper) defines his ISA with seven numbers. Namely, three coordinates for an arbitrary point on the screw axis (x1,y1,z1), three direction cosines of the axis (ux,uy,uz), and the velocity of motion along the screw, called the "Instant Pitch" = S(dot)IP. This is different to the definition of ISAs used by most workers in the field, and it has considerable redundancy, since ONLY five numbers are needed.

That is, only 5 "parameters" are required to specify an ISA for the motion of an upright wrt body. The axis of the ISA can be specified with only 4 numbers, perhaps 2 for the (x,y) coordinates where the axis pierces the z=0 plane, and another 2 for the slope of the axis relative to the z=0 plane. There are countless other ways to do this (eg. google "Plucker's coordinates"), but, as an example, consider the Scrub, Trail, KPI, and Castor, used to completely define the position of a wheels's steer-axis wrt the wheel itself. The fifth ISA parameter is the pitch of the screw thread, given in the usual manner (ie. distance advanced along axis for one complete rotation). Another way of looking at this is that only 5 n-lines, or constraints, are required for a 1 DoF joint.

In the paper Suh arbitrarily sets one of his position coordinates (eg. x1=0) so that he can get the other six parameters from his six equations. However, as my above comments suggest, Suh's method can be further simplified.
~~~o0o~~~

My main criticism of the paper is the suggestion in the last section ("Screw Axis" to Replace "Roll Axis"), that wheelprints are somehow "pin-jointed" to the ground in the 2-D Figure 1, or roll only in the direction of their planes with no lateral "slip" in the 3-D Figures 7 and 8.

It is common knowledge that whenever real rolling tyres are subjected to a lateral force they will have a resulting slip-angle, or side-slip. (Note here that the force is the cause, and the slip is the effect, not the other way around!) Thus the application of the Kennedy-Aronhold Theorem in 2-D, or the Three-Axis Theorem in 3-D, is totally unjustified as a means of finding the IC or ISA for the motion of the car's body wrt ground. Also, the above takes no account of static toe-angles, which inevitably cause relative lateral movements of the wheelprints (think about skiing or roller-skating with feet toed in or out), or body heave and/or pitch on its suspension.

Put simply, the motion screw (ISA) for the body wrt ground can be pretty much anywhere. It depends much more on how much the tyres are sliding on the road, and on their relative loadings, than it does on any kinematic constraints. Furthermore, this obsession with "body roll", and hence with finding the "roll axis", comes at the expense of understanding "body heave/pitch" or "jacking", which in many cases is the more important behaviour to control.
~~~o0o~~~

Other than the above criticisms, it is good to see that there is at least a little interest in 3-D kinematics in the automotive world. http://fsae.com/groupee_common/emoticons/icon_smile.gif

Also I am still trying to find time to post some more info on Screw Theory++ here, but am waiting for some rainy days. For example, the 3-D "Three-Axis Theorem" mentioned above states that any three bodies in relative motion will always have their three respective ISAs (ie. 1-2, 2-3, 3-1) all lying on the same "cylindroid", and thus always with their axes perpendicular to the "spine" of the cylindroid (more later...).

Z