Beam Axles - Front, Rear or both.

[Z]

Jay and MCoach,

Given that FSAE students are known throughout the universe as the "Masters of Floppy Linkages", I must assume that you are kidding with your above comments. This assumption supported by Jay's humorous question "Do you intend to hammer the locating pin in so it's a nice fit with zero compliance?", and MCoach's suggestion that my brake system has "two 30" ... [pull-]rods" when quite clearly they are closer to 10" in length. Also MC's acknowledgement of his prior mastery of floppiness.
~o0o~

Bill,

You suggest that students, such as above, should get busy FEMing when they want to determine which linkages are floppier (or stiffer?) than others. Sadly, I suspect that it is the FEM itself that is the root cause of this problem.

Two generations ago all students were given "calculators", and now hardly any can do simple sums.

One generation ago all students were given word-processors with "spell-checkers", and now hardly any can spell simple words.

Today all engineering students have access to structural-analysis programs (eg. FEM), and now hardly any can analyse simple structures.

The problem seems to be that the young-engineer thinks that their job is simply to give an "executive level" description of the structure (ie. its rough topology), and the computer-minions will then go away and optimise it. Unfortunately, not even the cleverest computer-minion can turn a sow's ear into a silk purse, or make the major topological changes needed to turn a bad structure into a good one.

(Edit: And since the young-engineer has lost the ability to analyse simple structural topologies, they cannot distinguish the good ones from the bad ones. So we all end up with highly optimised sow's ears...)
~o0o~

Goost,

Thanks for the reference. I will look it up. Given that it is 1904, it should be good! :)

(Edit: The example shows that efficient cantilever beams are NOT triangular structures, as sometimes assumed, but rather are somewhat fatter in the middle...)
~o0o~

Finally, any students pondering the above issue of "stiffness of brake-linkages" might compare the FBDs I mentioned in previous post with those of an "almost vertical M/Cs" linkage. Keep in mind that my last sketch has the "pedal motion-ratio" at about 2:1 (foot : pullrod motions), whereas most FSAE brakes are typically at higher ratios (roughly 3:1 -> 5+:1).

Then explain how a linkage that converts the driver's NECESSARILY ~horizontal foot-force, of, say, 2 kN maximum, into TWO almost vertical forces of 6 -> 10 kN, can ever be more structurally efficient than a linkage that keeps all forces close to in-line, and at low magnitude (ie. with 2 kN foot-force my linkage has each pullrod at 2 kN tension, and the pedal-tray longitudinal member at 2 kN compression, with negligible chassis stresses/strains forward of FRH, etc...).

PLEASE SHOW ALL FBDS!!!

Or, to put it another way, I will happily wager your first year of real wages that my pedal-tray is stiffer, stronger, and lighter than yours! :)

Z

[Jay Lawrence]

Z,

Not sure if you're intentionally ignoring my question or you actually think I was being 'humorous' (I wasn't). I'm truly interested to know your intended idea for securing your brake system. I completely agree with the overall concept (and as I mentioned earlier I understand that it is much more structurally sensible (assuming mounting rigidity) than the near vertical m/c's), but I plainly don't understand the secure location of such a device. What sort of tolerances do you envisage on the square hole to the locating arm? On the locating arm to the pin (and the top/bottom of the square hole)? Is there other hardware that you would add in a more detailed design?

[Z]

Jay,

A key point here is that the driver only ever PUSHES on the pedals. Mostly they push very hard on the brake-pedal, and somewhat more softly on the accelerator-pedal. They never PULL on the pedals (well, not unless throttle stuck!).

In the main post covering this I mentioned that the front of the pedal-tray is constrained left-right and up-down by some "slide-rails". These would be extremely simple in my version, and I am aware of many FSAE teams doing similar slides, albeit in a more complicated way. Anyway, these slides would have a simple, springy, "friction pad" incorporated that suppresses any "rattling" of the tray. The rear locating-pin slide, at base of FRH, may also have something similar.

So, while the driver is not pushing on the brake pedal, the whole pedal tray just stays where it is. It follows that the locating-pin can have very loose tolerances. Any "slop" is taken up the first time the driver pushes the pedal, after which NO MORE MOVEMENT.

Furthermore, a practical locating-pin hole tolerance is about 0.5 mm. This translates to maximum fore-aft movement of the brake-pedal of ... 0.5 mm! So even if the pedal tray rattles around and moves fully backward after each brake application, there is still only 0.5 mm of slop at the pedal. I doubt it is possible to adjust brake-M/Cs so that the necessary pedal movement to close the "refill-hole" is less than 1 mm. So the lesser locating-pin slop is really a non-issue.

Can anyone who is really proud of their rock-hard brake-pedal post how much pedal movement they have, measured at the foot-pad and wrt the seat-back, between zero foot-force and 2 kN?

This is a number that all Teams SHOULD have!

Z

[MCoach]

My 30" length was based on me sitting in our car and what I'd be able to reach as a driver belted in. If it were to be 10" I don't think even our lankiest, orangutan-armed driver would be able to reach it based on the Percy requirements of seating distance from pedal face. I think the 2:1 ratio is not achievable without significantly affecting the weight of the rest of the system, either much larger calipers, rotors, etc. and that, to me, would take greater precedence over putting the pedal is less bending based on our system engineering requirements. FSAE usually has a high pedal gain because the rest of the components are sized for the likes of a mountain bike to minimize overall mass. If your human can reliably interact with his environment with X deflection of Y part in the overall goal of putting the damn car across the line the fastest, then mass be damned, that car will be built to minimize mass and live with the consequences. Considering our pedal already weighs on the order of .1 to .2lbs, I think it's a moot point to wager and becomes a freshmen level lower member swinging contest of "my part is more optimized than yours." ...And there are much larger fish to fry.

I chose to study our '09 car because I knew it had problems and wanted to understand the extent of the problems. It left a lot of room to dig as it was well documented. I wanted to understand it to understand how to basically rewrite our design process for this system this year. It wasn't like I had any design input on that so I can't quite speak for the evaluation process used for the design. Oh my, has this year been fun.


As to the sliding pin joint, could a linear motion bearing assembly be used? As in something like this? I think a full metal version may be more equipped for the job.
http://m4.sourcingmap.com/photo_new/20130703/g/ux_a13070300ux0120_ux_g03.jpg

[Mitchell]

we use 3/4 x .049 SHS sliding on 5/8 x .049 SHS rails (thats ~.6mm of play), both 4130. The pins were made from some 6mm bar and the holes were hand marked and drilled with a 6.5mm drill. We added some springs to the pins to allow quick adjustment. You never notice the (small) play in the assembly because, as Z says, you only ever load it in 1 direction.

[Z]

What is often considered the seminal paper on structural optimization gives a fascinating introduction to how to think about these concepts.

A.G.M. Michell. The Limits of Economy of Material in Frame-structures. Philosophical Magazine Vol 8. 1904.

Attached an excerpt. I think this can be found on Google Books. Short story - make everything parallel/perpendicular between loads and constraints. Where curvature is needed to 'connect-the-dots', replace parallel/perpendicular with tangent/normal (in a circle or a logarithmic spiral).

Doesn't only apply to frames either - in many practical circumstances applying topological optimization to a 'smooth' shape (e.g. monocoque) will result in a frame-like 'optimal' anyway (e.g. space-frame-like strips of reinforcement within the monocoque wall).

So assuming you have access to water-jet, maybe the ideal beam axle looks something like this [attached] cantilever...

Goost,

Thank you very much!

I am putting this reference up again because it is a VERY GOOD paper! HIGHLY RECOMMENDED!

Students who get the gist of this paper will go on to be very good structural engineers. One specific example of this "gist" is that the triangles in spaceframes should be as "compact" as possible. Put the other way around, the very long and narrow triangles found in many FS spaceframes (eg. SISs with triangles ~0.8m wide by ~0.3m high) are BAD DESIGN! Also, Michell's last section on minimal structures to resist torsional loads should be very helpful to Frame-Guy.
~o0o~

When trying to download the above paper (which, as per modern practice, was mostly hidden behind numerous "pay-walls"), I came across this paper (also good, because also very short).

"What was wrong in Michell’s paper of 1904?", Mariano Vazquez Espi, Jaime Cervera Bravo, v2.0: January 19, 2012.

I mention this paper because it gives an interesting insight into the modern academic system (ie. YOUR educations, and the "spiral down the S-bend to Idiocracy" rants you may have noticed hereabouts :)). The answer to the title question is given here.

"4. CONCLUSION - The Writers conclude giving an answer to the title question: nothing is wrong in Michell’s paper - or at least, the errors pointed out by Rozvany do not exist. One of the Writers warned time ago (see Cervera Bravo, 1982: note 90) against the careless rewrite of old texts, ...
...
Perhaps the main moral of this story is that the peer-review method - that was so useful during XVIII and XIX centuries with Royal Society’s format - performs somehow bad nowadays..."

Z

[Mitchell]

Looks like the 2015 Aus comp is going to have a few beam axle cars attending.

- ECU (assuming they stay beam)
- UWA (assuming they attend)
- ADFA
- Uni SA
- UQ

Maybe more?

http://www.scienceagogo.com/news/20110627031219data_trunc_sys.shtml

We are well past the 10% point, at least in the Australian competition. Wonder when we will start too see this concept internationally.

[Will M]

Mitchell,

Besides UWA I'm not familiar with those teams.
Do you have links to photos?

-William

[Mitchell]

ECU - https://www.facebook.com/ECU.Motorsport
UQ - https://www.facebook.com/UQRacing
ADFA - https://www.facebook.com/academyracing
Uni SA - https://www.facebook.com/UniversityOfSouthAustraliaFormulaSae


As far as pics of the beams go, there are none for this year yet. I can share this though. We are using a triangulated 4 link de dion.

502

[Pete Marsh]

Will that be with mechanical interconnection again Mitchell?

Anyone other than UWA using a beam at the front as well?

Pete

[Will M]

That disassembled ECU photo is great.
Thanks!

William

[Mitchell]

Will that be with mechanical interconnection again Mitchell?

Anyone other than UWA using a beam at the front as well?

Pete

I have not yet seen another front beam. Everyone seems to be sticking with wishbones there.

We are building a 4 corner spring car this year. The change is due to an overall concept decision and tight manufacturing timeline, we are already machining parts for this year.

[Mitchell]

Thought I would share the 2015 UQR beam. Triangulated 4 link with roll centre and antisquat adjustment. Whole assembly including all links and brand new tyres (exactly what you see here besides driveshafts) weighs in at 20kg. Main tube is 2.5x0.065" 4130.

Would like to thank Kev and Z for their excellent input into this thread. There are a few pages from ~20-23 that are absolutely gold if you're interested in 4 link design.

[Jay Lawrence]

Thanks for sharing that Mitchell, looks really tidy!

Couple of queries:
-your upper trailing arms appear to be non-nodal. Problem?
-does this configuration have adequate lateral restraint or am I missing something?

[Mitchell]

Good spotting Jay. The upper link on the chassis is not triangulated. The attached picture shows more clearly. To put it in perspective the whole length of that tube is ~150mm. It is primarily due to packaging and the goal to have a certain amount of antisquat adjustment without changing the length of the link.

Lateral restraint is fine. The links are as far apart as packaging would allow on the beam with the uppers nearly inside the wheel and the lowers with ~5mm of clearance to the sump. This puts them nearly perpendicular in top view.

[Jay Lawrence]

That makes more sense, cheers

[mech5496]

Totally unrelated, but wow that car is small!

[Jay Lawrence]

Yeah they mostly look great before subjecting them to the nose cone atrocity haha

[Ahmad Rezq]

Erik,
Back to page 22 there was a discussion about Inertial Forces.
I think nothing can describe what I've learnt and wanted to discuss better than this video about Inertial Frame Of Reference

https://www.youtube.com/watch?v=aRDOqiqBUQY

Better to watch it starting from 13:00.

[Z]

Ahmad,


Back to page 22 there was a discussion about Inertial Forces.
...
https://www.youtube.com/watch?v=aRDOqiqBUQY


I liked the first few minutes of the video where the first presenter showed real commitment to his belief that his "frame of reference" was the right one. Or, at least, that his frame was just as good as the second presenter's. Even though, on a practical level, it obviously wasn't!

Unfortunately, the rest of the lesson repeats the same old ideological claptrap that claims "Inertial forces are fictitious".

This nonsense starts with the ASSUMPTION, at ~10:15 of the video, that "... the "Law of Inertia" [states] An object moves with a constant velocity unless an UNBALANCED force acts on it". (<- My emphasis.)

Then, when strange motions are observed in accelerating frames that seem to contradict their assumed version of the Law of Inertia, they argue "... our belief in the Law of Inertia is so strong that when we see [this strange motion] we think there is a force causing it, so we make up a fiction that there is a force, and ... call this a fictitious force..." (<- at ~16:25+).

In other words, they start with a flawed assumption, and then when the facts get in the way they call these observably real facts "a fiction". But, as all small boys who fall out of their billy-carts as they try to take the corner at the bottom of the hill too sharply know, the (fictitious?!) "centrifugal" forces are very, very, real!

Claiming that Inertial forces are "UNreal", "fictitious", etc., just because they contradict a faulty assumption, does not make them so.

Much more that can be said, but I will keep it to the following two points.
~o0o~

Newton explained all this much better and more reasonably in his "... Principia...". Quotes below are taken from Motte's English translation.

In Axiom 1 (or Assumption/Law...1), Newton uses the words "... forces impressed upon [the body]", rather than the modern corruption used in the video of "...unbalanced force". The video version (and other comments in the video) make it clear that they consider there is a net (or "unbalanced") EXTERNAL force acting on the accelerating body, but NO equal and opposite ("balancing") INTERNAL "Inertial reaction force".

By contrast, Newton makes it very clear in his Definition III (right at the front of book!) that all massive bodies have a "... 'vis insita' or innate force of matter, ... [that may] be called inertia (vis inertiae) or force of inactivity..." (<- my emboldening). Furthermore, Definition IV makes clear that "An impressed force is an action exerted upon a body...", and Newton stresses the difference between these (external) "impressed" forces and the (internal) "Inertial" forces.

The reason for the above corruption of Newton's version of Mechanics is that early 20th century science had no good explanation for how "Inertial" forces work, so they simply got rid of them at the "axiomatic" stage (ie. at the ~10:15 quote from video).

This was also done because in the late 1800s the "Relativists" (a sort of scientific/religous cult founded by Ernst Mach) were trying to abolish any notion of preferred reference frames, such as the Absolute Space that Newton discussed in the Scholium at the end of his Definitions. It was also partly because of the speed-of-light experiments that were being done at that time, that the Relativists wanted all reference frames to be equally valid (a bit like modern teachers preaching that "all opinions are equally valid"). So anything that depended on "the rest frame of the universe", such as "Inertial" forces, had to go.

Of course, the recently conceived Higgs Field may give a reasonable explanation (?) of Inertial forces, with the HF acting as the universe's "rest frame", or N's Absolute Space. But before "HF=Inertia=real" can be accepted and widely taught, the science teachers will have to admit they have been peddling bulldust for a hundred years. So we might have to wait quite some time for an update (or apology?).
~o0o~

Modern science teaches that in any NON-accelerating frame it is perfectly acceptable for all the usually acknowledged "real" forces acting on a body to sum to zero, or be "balanced".

For example, a book sitting on a table has a downward gravitational force acting on it, and an exactly "balancing" (ie. zero-sum) upward E-M force acting on it. Both these forces are the result of the relative POSITIONS of the various stuff. Position of book-CG and Earth-CG for the gravity forces, position of lower-book-atoms and upper-table-atoms for the E-M forces.

Similarly, "Magnetic" forces are the result of charged particles moving at a relative VELOCITY to other stuff, and these forces can also be in perfect "balance" with other real forces. In a looser sense, a winged-racecar travelling along a racetrack has VELOCITY dependant aero-downforce that can also be in perfect "balance" with the upward road-to-wheel E-M/atomic forces. And there are many other examples of bodies in various states of "motion" that have perfectly "balanced" systems of forces acting on them.

So the big question is: Why should ACCELERATING bodies be the ONLY CASES where there MUST BE an "unbalanced" system of forces in action?

Is it not simpler to always have all the forces acting on the body as "balanced"?

(That is, you determine the balanced system of forces necessary for a body's given position, velocity, and acceleration relative to other stuff around it, and thus predict the subsequent behaviour of the body. Too easy?)

All that is needed here is to acknowledge the reality of Inertial forces. (Which is something all small boys already know! :))

Well, ... also needed is that apology from the Scientific Establishment (sort of like the Vatican) for peddling such nonsense. Could take some time...

Z

[Ahmad Rezq]

Erik,
Well Said. I must say that i haven't read the "Principia" before. Now I have a copy and I'am reading it in my free time (Tough English).

In DEFINITION III
" Upon which account, this vis insita, may, by a most significant name, be called vis inertice, or force of inactivity.But a body exerts this force only, when another force, impressed upon it, endeavours to change its condition ; and the exercise of this force may be
considered both as resistance and impulse ; "



The reason for the above corruption of Newton's version of Mechanics is that early 20th century science had no good explanation for how "Inertial" forces work, so they simply got rid of them at the "axiomatic" stage (ie. at the ~10:15 quote from video).


I didn't go on reading Principia, Had Sir Newton explained how a body exerts the inertia force.

How does a body exert inertia force, Erik ?
How can we classify the inertia force ?
What's meant by (Force) ?

[BillCobb]

A Higgs boson goes into a church and the priest says "Hey, you can't come in here".
"Oh, yeah?", says the Higgs. "Well without me, you can't have Mass."

[Z]

Ahmad,


Had Sir Newton explained how a body exerts the inertia force ... ?
How can we classify the inertia force ?
What's meant by (Force) ?

Those are very difficult questions to answer, indeed.

Many thousands of years, and many clever people have tried, but still no clear-cut answers.

Important to note that Newton made no attempt to explain the "how" or "why" of Inertial forces. Instead he simply took them as "a given" and included them as such in the Definitions section of "... Principia...".

As I have noted before, Newton's book (which in English is "The MATHEMATICAL Principles of Natural Philosophy") was written in the same "Definitions + Axioms => Deductions" style as Euclid's Elements. As such, neither of these books belongs in "science", nor do they claim to be explanations of "how/why" the real world works. Rather, they are an idealised, though rigorous, mathematical model, which may be, within limitations, used to solve real world problems. (Eg. Euclid - How do you evenly subdivide your circular farm for your five children? Newton - How do you build a winning FS/FSAE car?)

Also worth noting here that Newton never gave any sort of "how it works" explanation for gravity, as is often claimed these days (eg. the much repeated phrase "...Newton's Universal Law of Gravitation"). In fact, he did just the opposite by very clearly and publicly stating "I frame no hypotheses!". Instead, Newton calculated the motions of bodies, or orbits of planets, as they would be under numerous different types of attractive force. For example, a force that is constant, or a force that varies inversely with distance, or a force that varies inversely with the square of distance, or the cube, or higher order..., and so on. He then simply noted that the observed motions of bodies and planets, of which there was much empirical data available at the time, best fits the "inverse square" model. But to restress the important point, he never claimed to explain the detailed "how" of gravity.

Not much has changed since. There is no really good, "deep and meaningful", explanation today for "how" gravity works. The General Relativity explanation is circular gibberish. Namely, "... mass bends space-time, and curved space-time tells mass how to move...". Err..., yes..., but which did the "bending" or "telling" first? And, more importantly, HOW do they do it???

Similarly, all the other "real forces" are today explained in terms of "field theories". (Edit: Indeed, the property of "Mass/Inertia" is lately being explained as due to the Higgs-Field, as Bill so succinctly put it! :D). But there is never any deep explanation of "how" these fields themselves work, namely what they are made of, or where they came from, and so on. The "explanation via fields" is really just a convenient calculating device, and quite similar to the approach used in the Elements and Principia. They are very useful in helping you figure out what will happen in certain real-world situations, but they give no deeper explanation than their "assumptive" base.

Furthermore, with these "aether"-like field theories taking over on the explanation front (...ah, yes, the aether is back! ... Newton's Absolute Space is reborn!), the old fashioned notion of "force" has pretty much been eliminated from modern Science teaching. Nowadays it is more fashionable to talk only of the "Symmetries of Natural Laws", which in turn generate "Conservation Laws". For example, we assume Nature behaves the same "now" as "then", ... so Energy is conserved. We assume stuff happens the same "here" as "there", ... so Linear Momentum is conserved. Assume stuff happens the same in "this-direction" as "that-direction", ... so Angular Momentum is conserved. (Or something like that...)

The Conservation Laws then lead to a slightly different approach to solving Mechanical problems. Here you can google Lagrangian and Hamiltonian Mechanics, vs Newtonian Mechanics. Same fundamentals, but different approaches to finding the solution. In short, L&H deal with the "energy" in the system. Since this energy is a directionless "scalar", it can sometimes be easier to keep track of it than those damned difficult force and momentum "vectors" in N-Mechanics, which keep changing their directions. On the other hand, L&H-M requires you to know (or assume you know?) the values of some things at ALL times (ie. the amount of energy), whereas N-M deals only with the "right now" and how it will change in the next infinitesimal time-step.

The big disadvantage of L&H-M is that they have difficulty dealing with "NON-conservative" forces (although sometimes there are work-arounds). Typically, non-conservative forces come out of engines (which turn "heat-energy" into mechanical-energy) and friction (which, in a mechanical sense, destroys energy). But (!!!) these non-conservative forces are almost the majority of what you deal with in Vehicle Dynamics. So, IMO, while L&H-M can be useful as a short-cut when dealing with some problems that are relatively "frictionless", for most of VD it is better to stick with the old fashioned Newtonian "forces".

Newton gave a reasonably good "practical" description of these forces in the commentary just after "Axiom/LoM III - To every action there is always opposed an equal reaction...". Namely;
"Whatever draws or presses...
If you press a stone with your finger...
If a horse draws a stone tied to a rope, the horse ... will be equally drawn back towards the stone...".

So, in everyday language, forces are just the "pushing" or "pulling" of one thing against another. This notion of "what is a force" was commonly understood, and widely used, for at least a century prior to Principia, with the many developments in the field of Statics in 1500-1600s (... google Simon Stevin/Stevinus...). Hence, I guess, Newton did not think it necessary to give a more detailed definition of such.
~~~o0o~~~

Summary 1. - You are hurtling down that long straight towards the sharpest hairpin on the FS/FSAE track. Wouldn't it be wonderful if you could just spin the steering-wheel and have your car zip around the hairpin, with NO FORCE AT ALL required from the tyres? That would indeed be the case if there was NO such thing as "Inertia", or its damned annoying forces. Sadly, it is because of those damned Inertia-forces that your tyres have to work so hard to get the car around the corner. And the greater the "quantity of motion" of your car (ie. "momentum" = Mass x Velocity), the harder your tyres have to work. In fact, too much M x V and your tyres say "We give up... You win Inertia!!!"

Conclusion 1 - You score more points by having high V, so try to reduce your M as much as possible. And increase your aero-DF...
~o0o~

Summary 2 - In the above battle between Tyre-forces and Gravity/Aero-DF+Inertial-forces, your suspension is the meat-in-the-sandwich. If you want to have a good understanding of what happens to your suspension during said battle, then it is easiest to picture it getting squashed between the upward-and-centripetal Tyre-forces, and the downward-and-centrifugal Gravity/Aero-DF+Inertial-forces.

Conclusion 2.1 - From above picture, you should clearly see that high Roll-Centres are BAD on independent-suspensions (see "Jacking force..." thread), but high RCs are acceptable on beam-axle-suspensions (draw the FBDs, which show NO similar jacking effect...).

Conclusion 2.2 - Picturing Inertial-forces as being VERY REAL makes Mechanics much easier to understand! :)
~o0o~

Hope above helps in some way... Back to enforced holidaying...

Z

[Ahmad Rezq]

Erik,
"I like to read what you write. Your writings are very structured."
Some search keys which I will look at them after the exams.
-----

An example from the Egyptian street
951

Turning over a swing is a normal thing in Egypt specially in festivals.
This person may not be an Engineer or a physicist but he trusts the Centrifugal Force.

[Ahmad Rezq]

- I was thinking about the steering with the front beam axle, i know that there are some ideas posted by Z and others about the steering and how to reduce bump/roll steer.
but i was wondering has any team run a front beam axle with the traditional rack and pinion/or any other steering system mounted on the sprung mass. i didn't design any beam axle before but i can make rough calculations to calculate the steer in case of bumps and rolling.
IMO this can save alot of pain in the steering design for front beam axles.

[BillCobb]

Regardless of what kinematics you arrive at, the compliance(s) are the most difficult to minimize for your body mounted gear. There WILL be relative motion between them because that's what the unsprung mass's job is. The steering shaft can no longer be a fixed length, so the sliding element is the usual culprit in wear, durability, flexure, lash and compliance. Then there is the issue of resolving the steering effort reaction torques from SWA inputs, braking and cornering.

[Z]

... has any team run a front beam axle with the traditional rack and pinion/or any other steering system mounted on the sprung mass.

Ahmad,

The most common arrangement for the steering of front-beam-axles is, indeed, to mount a steering-box on the "sprung-mass", namely on the "body" or "chassis". Bump-steer and roll-steer are then minimised by having the steering-tie-rods run close and parallel to the beam-axle-constraining-links that go from chassis to beam. See countless trucks/buses/tractors today, and most every passenger car prior to WWII, for examples of such. This is essentially the same problem as with independent suspensions, where the steering-tie-rods should be parallel to their upright's "n-lines" in that area of space (ie. ~parallel to the wishbone or other control-arm links).

Mounting the steering-box or R&P on the beam itself can also work (and has been done...), but now you just change the problem to one of providing a flexibly jointed shaft going from body-mounted-steering-handwheel to beam-mounted-R&P, as mentioned by Bill.

But all things considered, bump/roll-steer of the front-wheels is NOT A BIG PROBLEM in FS/FSAE, because:
1. There are NO bumps in FS/FSAE (at least none big enough to cause big problems)!
2. There is very little body-roll, because of the small +/- 25 mm mandated suspension travel, and the typically very stiff springing that often results in NO body-roll at all (other than from tyre-squash).
3. The driver can easily correct for small steer-changes of the front-wheels.

Note that any unexpected steering of the rear-wheels, either from bump, roll, or compliance-steer (= slop + flex!), is much worse than at the front, because the driver only senses rear-steer after the whole car has changed direction significantly, by which time it may be too late for correction. By comparison, small bump-steers at the front during hard cornering are no different to crossing some lower or higher grip sections of track, which the driver constantly corrects for anyway (if they are anywhere near "the limit").

More important things to get right with your steering-linkage are:
1. Minimise slop (ie. "backlash"). You can live with some flex, but too much slop is downright annoying.
2. Minimise stiction. A smooth, low-friction steering makes fast driving much easier (see Pete Marsh's post somewhere...). A steering system with high levels of stiction + slop is near impossible to drive fast.
3. Get Ackermann right. To get good lateral forces (Fy) from BOTH front-tyres when going through tight corners, the two front-wheels need quite a few degrees of "dynamic toe-out". More than 10 degrees for the tightest hairpin. Typical worst-case levels of bump/roll-steer should be much less than this, perhaps ~1 degree, so they can be 10 x lower down your priority list.

Fix the big problems first!

Minimise slop (=compliance) and stiction, and get Ackermann (over full range) and RELIABILITY right first... (I recall one potentially fast Team that only just managed to finish Enduro after their R&P decided to become "fully-floating"!!!)

Z