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

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

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", and "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.
~~~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?
~~~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!!!)

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.

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??? "
~~~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.

Z