Spherical wheels

[Ciro Pabón]

These are more questions than answers, feel free to comment.

Let the work speak for itself.

On-thread:

* Jhon Hopkins sphere: (long and difficult paper here)



* US Patent. Clever guy: he could have patented the wheel.

* Halfbakery's Orb-it:



In a related thread at Halfbakery there was a really good idea: why four wheels? why not use a lot of smaller ball-wheels? Then you can put a hamster in each one to propel the car.

* Halbach array: this is a really cool link. Sort of "the monopole of engineers".



* Inductrak: a train over a Halbach array. You could look at the image, invert it, and think of the cart taking the role of the wheel of a vehicle (not flat, of course).



* SKF's magnetic bearings:



* Tribolo robot:



* Magnetic levitated haptic interface: Cool device that allows you to "feel" the surface texture of virtual objects through a levitated magnetic ball controlled by a computer.



* Dynamically-Stable Mobile Robots: (a.k.a. Ballbot)



Vaguely related:

* iBot:



* Ilon wheel: You might like the Airtrax site (with videos of forklifts moving diagonally).



* Steel belted radials already produce magnetic fields

* Spìraculum and Radiaculum (2 Mb video on this link): Nice example of the intelligent use of gyroscopic effect that could be exploited on a car.



Well, thanks, ginsu. Nice questions and answers, I guess.

P.S. How do you change the tires of the Audi car? You use a robot, of course. Imagine removing the hub caps by hand... Besides, they are the only ones able to inflate the tire with air saturated with magnetic nanoparticles.

[tf1]

I understand the mechanisms necessary, I don't understand where the advantage is. Ok fine, mobility. But the mechanisms required to give that mobility are going to be incredibly complex or heavy depending on the implementation. Take something as "relatively" simple as the tilt rotor (V22 osprey). It has two engines on the tips of the wings that rotate to give reasonable helicopter like capabilities. The way that the harrier does it is not really reasonable as it can carry very little payload and has very little time on station in vstol mode. Anyways, the osprey is required to have a mechanisms that links the two rotors because in the case of an engine failure you need to have both powered. This is a fairly simple idea but a heinous engineering problem in real life. And that is with something that only has to turn a few thousand times in its life cycle. Your theoretical mechanism would have to take many many times that. It would be cool as hell and would be extremely useful to have that capability but it doesn't seem to be very economically feasible even if it becomes techincal feasible. I'd look for the military to be working on stuff that does these kinds of things. Although F1 may be high tech, it is nothing compared to what goes on under classified programs. That stuff would blow most peoples' minds.

[NickT]

Excellent post Ciro, will try and digest all of this later. I had an idea about a car using in a single sperical drive in the centre and supported with air bearings in the corners. Then, thought of what might happen in an accident if someone else his one corner of the car, knocking it int a spin, the passangers would feel like they were in a centrifuge

[Scuderia_Russ]

http://video.google.com/videoplay?docid ... 1928430302

[Ciro Pabón]

I understand the mechanisms necessary, I don't understand where the advantage is.

I'll try again:

A normal wheel goes naturally in a straight line, because it is a cylinder. When you turn a normal wheel, you are "scrubbing" it against the pavement to deliver lateral force. The angle of "scrubbing" is what is called (roughly speaking) the slip angle.

This kind of friction degrades the tire quickly, as opposed to the non-slipping friction you get when you are in a straight line.

As I see it, a spherical wheel does not have to slip to be able to change the direction of the car.

For example, imagine you are going 10 kph and you want a lateral speed of, let's say, 2 kph, to turn your car into a curve. You can make the ball turn 10 times longitudinally and 2 times laterally, without slipping at all.

Spheres can turn around two axes at the same time, while cilinders cannot.

I hope that you can understand why I say that this eliminates most of the "scrubbing" effect of curves on tires.

This would be a revolution for the dynamic of the car. We should throw all equations about movement and get a new set. This is what I tried to explain with those weird posts about "holonomic" systems.

With spherical wheels, the dynamic of a car (I think) would be more like the dynamic of a rocket.

I am starting to believe that either I am wrong, or the concept is hard to grasp because we never see spheres propelling themselves, we just see them roll.

The last example I give, I swear...

Imagine you replace the normal wheels of a supermarket trolley with spherical wheels. Now you grab it by the handle and push the thing to move it.

Allright, your first curve: you turn the handle and the trolley rotates, but it continues to move in a straight line. It does not behave like a normal trolley.

One way to make the trolley turn around is for a friend to push it laterally. The wheels are moving smoothly all the time, instead of dancing like crazy, like in normal supermarket trolleys... they do not slip at all.

With a magnetic sphere, you replace yourself and your friend for a set of magnets.

[West]

So would the car be looking in one direction all the time if it took a lap around Monaco?

[Ciro Pabón]

So would the car be looking in one direction all the time if it took a lap around Monaco?

Of course not, you silly. You can vary the counter torque on the four wheels... the attitude of the body depends on the sum of the torque of the four wheels.

You could even go around Monaco doing doughnuts all the time, without burning the tires... and waving at the same time.

The guys at Jhon Hopkins did a serious job on the equations that relate the electrical waves on the electromagnets and the desired movement of the ball. You can take from there to deduce the movement of the body.

Now that I think of it, you could rotate the body to get the G-force on your back only... if the body was simmetrical.

[Crabbia]

looks like this would go hand in hand with electricity as a power source in cars. Further its essentially a 'motor in each corner' of the car.

I think one down side to driving a car like this is the totally new dinamic it bring with it, that being a third degree of freedom, being able to rotate whilst still moving at 120.

If your going to look far into the future you'd have to say tht this rotation will be handled by a cpu which will most likely be of super computer status in our terms.

now bearing those two things in mind, it couldhave benefits in collision avoidance. Example:

Youre driving down the highway at 160 with no1 in the passenger seat. There is a car crash infornt of you. ther is no way of missing it and no way of going round it. Your gonna plow into it. Where a technology like this could come in handy is, when in an accident the car will pick a point which will cause the slowest deceleration and hit that, moving laterally while breaking to make sure it does. Further it could rotate the car so that the impact will occur on the passengers side, keeping the collision as far away from the lone driver as possible.

Well looking at it another way, side impacts could be a thing of the past since the cpu could rotate the car to ensure that all impacts happen head on, and crach tests need only be calculated for head on collisions.

[Saribro]

Spherical wheels would definitly rock for parking :D, driving backwards at 100+ km/h. The driftscene probably won't like it though :).
btw: In 'I, Robot', all cars/trucks/... are on spherical wheels.

[theSuit]

Hmmm... spherical wheels, not sure about it, not from an F1 point of view... after all, circular wheels are a bit too hi-tech and push costs up what with all that non-rectaliniar geometry. No, I think square wheels in 2012.

[Guest]

As I see it, a spherical wheel does not have to slip to be able to change the direction of the car.

Ciro, I think your reasoning is not correct. As you said, a conventional tire requires a slip angle in order to generate any lateral force. This lateral force is a function of the tire's cornering (sidewall) stiffness. One thing you failed to mention however was that in order for a tire to generate a longitudinal force, the tire itself must slip. The amount of longitudinal force a tire can deliver can be described in terms of a Slip Ratio. Essentially what I am getting at is that it is impossible for any tire, cylindrical or spherical, to deliver any sort of force, lateral or longitudinal, without slipping.

Spheres can turn around two axes at the same time, while cilinders cannot.

Spheres cannot turn around two axes at the same time. A sphere can only turn around one axis (which may happen to be the resultant axis of two other axes of rotation).

For example, imagine you are going 10 kph and you want a lateral speed of, let's say, 2 kph, to turn your car into a curve. You can make the ball turn 10 times longitudinally and 2 times laterally, without slipping at all.

Accelerating the vehicle from 0 to 2 kph laterally would require a slip ratio of the tire normal (perpendicular) to the current direction of the tire, aka a slip angle. Also, once this acceleration was acheived, the result would be another straight heading of the vehicle which would just be the resultant of the lateral and longitudinal velocities. In order to turn the vehicle, lateral velocity would need to be steadily increasing while longitudinal velocity decreased. This again would require slipping of the spherical tire. The dynamics of a spherical tire are essentially identical to that of a cylindrical tire.

The only difference is that parallel parking would be easy with a spherical tire. Hope this clears things up.

[Mikey_s]

I may be about to deminstrate my ignorance (again!) here, but I think that two issues are being confused (and I'm uncertain that I am able to articulate what is in my head, but here goes);

The ability of the spherical wheel to change direction easily is only the first part of the problem, but the second, and possibly more important, is the wheels (tyres) are used to transfer the force required to turn the vehicle. In Ciro's shopping trolley example the wheels are easliy able to accomodate the change of direction whilst the force to overcome inertia is applied via the shopping trollwey handle. However, in a vehicle the tyres are required to overcome the inertia of the vehicle via the application of the force in a different direction, induced by turning the wheel against the direction of travel. In other words, it does not overcome the inertia of the vehicle just because it is able to turn through any angle. Does that make sense to anyone else?

... and another thing, the contact patch is extremely small.

[Ciro Pabón]

First of all, welcome to the forum, LifeSpitter. Only Mikey_s has tried to show the problems here... Let me try to argument against the necessity of slip ratios.

Ciro, I think your reasoning is not correct. As you said, a conventional tire requires a slip angle in order to generate any lateral force. This lateral force is a function of the tire's cornering (sidewall) stiffness. One thing you failed to mention however was that in order for a tire to generate a longitudinal force, the tire itself must slip. The amount of longitudinal force a tire can deliver can be described in terms of a Slip Ratio. Essentially what I am getting at is that it is impossible for any tire, cylindrical or spherical, to deliver any sort of force, lateral or longitudinal, without slipping.

This is not true for a maglev wheel: with it, you have a "new way" to produce force, because you can displace the wheel laterally or longitudinally: the "flat spot" or contact patch does not have to be located under the axis of the weight forces of the car. If the wheel moves "backwards" it will generate longitudinal force without having to resort to a "differential spinning velocity" (slip ratio). It is the same thing with a bycicle: you can incline your weight to move laterally, if you follow my drift.

Spheres cannot turn around two axes at the same time. A sphere can only turn around one axis (which may happen to be the resultant axis of two other axes of rotation).

I was pointing to the fact that the rotation axis can be inclined with respect to horizontal and has two spin axes or principal rotations, originating the displacement that allows to turn. Anyway, a sphere can precesse and can rotate around a point external to itself in an "arbitrary way".

Accelerating the vehicle from 0 to 2 kph laterally would require a slip ratio of the tire normal (perpendicular) to the current direction of the tire, aka a slip angle. Also, once this acceleration was acheived, the result would be another straight heading of the vehicle which would just be the resultant of the lateral and longitudinal velocities. In order to turn the vehicle, lateral velocity would need to be steadily increasing while longitudinal velocity decreased. This again would require slipping of the spherical tire. The dynamics of a spherical tire are essentially identical to that of a cylindrical tire.

The only difference is that parallel parking would be easy with a spherical tire. Hope this clears things up.

Look, this is the best I can do about why I think an spherical tire can develop lateral forces without sliping:



In essence, this wheel can develop its own sideslope. Or, if you wish, it can change its camber angle (and caster angle, for longitudinal forces). I fail to see why the wheel can be located at the opposite end of the force exerted on it by the vehicle, in such a way that is "normal" to it.

There is an essential difference between holonomic vehicles and non-holonomic vehicles I already pointed out.

I can understand the remark about parking, I spend a lot of time plotting vehicle trajectories: this is the reason I started to think about all that spherical wheels thing. The fundamental constraints to the trajectory are the same if you calculate them with the car moving at parking speeds or at road speeds. This is why I suggested watching the behaviour of the Audi in the chases depicted in "I Robot".

There are other implications, as the ability to "move your weight around", that is, spinning the vehicle in any direction you choose while moving "ahead".

As for Mikey_s argument about the smaller patch, I think the size of the patch depends on the pressure inside the tire, nothing else. Of course, at the same pressure an spherical wheel has a patch that is smaller than a cylindrical one, but all you have to do to reach the same patch size is decrease the pressure.

Anyway, thanks for the refutation, LifeSpitter. I believe now that even if you could move laterally, like a bycicle, some slipping has to occur, as you and Mikey_s state, but I am not totally sure, after devising these "counter-arguments". Could you try to explain again, specially in view of the ability of the maglev wheel of moving around its socket?

[Carlos]

I believe I sent a PM to Lifespitter welcoming him to the forum and commenting positively about his comments, and specifically mentioning---------------

" Contact Patch " as a limiting factor of slip angle and adhesion. A rubber or polymer tire will always have to contend with the problem of adhesion.

We could " expand " the contact patch of a spherical tire by filling it with a light liquid polymer foam that would respond in density to an electrostatic charge generated by electrodes in the spherical tires carcass, under sensor and computer control to " expand " the contact patch -- on the fly.

As a first primitive experiment---although it will not duplicate all the conditions we have discussed--- I will consider removing the wheels from my '85 Mazda RX7 and installing soccerballs instead.

[Carlos]

Sorry--- I did not intend to detract attention from the technical depth of the conversation--up too early and just too many cups of strong coffee--and too much time on my hands. Thank you all for your indulgence.