How is an unstable object balanced?

[Jordi Heguilor]

TL;DR Summary

Keeping balanced over an unstable object.

The other day I was watching a trials rider balancing a stationary motorcycle and apparently they can do it pretty much indefinitely. I don't understand how they can do it. Say the motorcycle (and rider) starts tipping left. So the rider moves their body to the right to compensate. But this transferring mass to the right moves the bike further to the left. So once the bike starts tipping it should be impossible to stop. Obviously that is not what happens. I would appreciate an explanation.

 

[.Scott]

If you tip to the North and respond to moving your arms or upper torso South, then to preserve angular momentum, your feet will try to push the floor (or pavement) South. Of cource your feet don't move anywhere, but the effect is to apply a force to your feet that creates the angular push to correct your tipping.

 

[Jordi Heguilor]

You talk about a stable object (the Earth). I don't see that applying to an unstable one (i.e. a bike) that is affected by my moves.

 

[.Scott]

You can still make locked tires on the bike push against the pavement. You need to hold the bike firmly enough so that you are a single flexing object.

It takes a little arm and leg muscle, but anything you can do with your legs, you can do on with a bike with locked wheels. You can hop, pivot one tire at a time up, walk the bike sideways.

 

[Jordi Heguilor]

Thank you.

 

[.Scott]

That same basic idea of apply lateral force to the pavement to recover balance is what keeps the iBot standing.

BTW: For me, this is job-related. The development and manufacturing is happening in the same campus where I work by related companies.

 

[Lnewqban]

So once the bike starts tipping it should be impossible to stop. Obviously that is not what happens. I would appreciate an explanation.

Welcome, Jordi!

None of the masses, rider or bike, are rigid bodies.
Therefore, each center of mass can be relocated by modifying the geometry.
For the rider, the main tools are the knees and hips.
For the bike, the steering mechanism.

We are talking about very small amounts of tipping over moments, which are kept small by the quick movement of the rider, who is following its sense of balance.
If he/she is too slow, the COM moves too far from the balance point for recovery.

A running engine helps in slowing the tipping movement of the bike via gyroscopic effect, which gives a greater margin of reaction to the rider.

 

[Jordi Heguilor]

That same basic idea of apply lateral force to the pavement to recover balance is what keeps the iBot standing.
View attachment 328674

BTW: For me, this is job-related. The development and manufacturing is happening in the same campus where I work by related companies.

I have no problem understanding this situation, but the non-moving bike seems different to me. The action of the rider moving their body right seems to me would produce a left force on the pegs, so the bike would continue tipping left. But I trust you are right.

 

[.Scott]

Looking for articles on this is a bit tricky. It's a form of "inverted pendulum".
In a lot of articles most of the equations are just assumed.
But here's one that shows some of them: Stabilizing an inverted pendulum
You'll notice that there are a lot of "dt"s in there. Timing is everything.

Conceptually, if you start with a "perfectly" balanced inverted pendulum - one that's basically rotating reaction masses on the top of a stick - as that article describes. Then if you can see how spinning those masses can topple the pendulum, then you should be able to see how the opposite procedure can re-balance it.
So if you spin the reaction mass at the top, then to conserve angular momentum, the post that supports the reaction mass must rotate in the opposite direction. Once it starts tipping, the mass of the post will make it tip faster. So, to correct the tipping, you will need more reverse angular momentum than you put in originally. By the time you have the device righted, the reaction mass will be spinning opposite the to the direction of that first maneuver.

To balance, basically, all you need to do is over-correct by cranking in enough angular momentum to force the center of gravity not only to the point where it is directly over the balance point, but a little further so you can zero out the angular momentum perfectly as you restore the vertical position.

Hope that makes sense to you.

 

[jbriggs444]

A tight rope walker is a good analogy.

If you are falling right, you push your feet rightward. You bend right at the waist. Waist left, head right, feet right. Naturally, this results in a clockwise torque on your body, increasing your rotation rate. That part is working against you. However, it also results in a leftward push on the walker, so your center of mass is deflected leftward, so that you are centered over the rope... and a little bit past on the other side.

It is important to do the correcting push quickly enough so that you can get your center of mass over on the side opposite to the fall. With enough time to let gravity provide the torque to cancel your rotation rate. Holding a long pole as an angular momentum sink can help give you that time. Like this.

A unicyclist does a similar thing in the fore and aft direction. The unicycle takes more skill. You have three axes (roll, pitch and yaw) to control and one primary input (fore and aft on the pedals) to control them. So you accept a sideways lean and then use fore and aft input during the lean to produce a right or left yaw. The result is that what had been an uncontrollable roll becomes a controllable pitch.

That skill took a couple hours to learn on my parent's driveway. No teacher. Just us three children taking turns and trying to see if we could do it. Consciously, I saw what needed to be done. But it was down to repetition and muscle memory to actually do it in real time.

[A unicyclist also has some available yaw input (twisting the hips) and some roll input (bending at the hips), so the mechanics are not always as pure as what I've described above].

 

[Baluncore]

Even when not moving forward, the act of turning the steering moves the balance point on the ground sideways, back under the centre of mass, which corrects the fall. The magnitude of that movement is determined by the steering geometry and the curve in the front forks.

Turning the steering while leaning the bike, can change the height of the combined centre of mass, as is done by sitting up or leaning forward. The combination of those moves seems to maintain balance, most of the time.

Notice how, to turn right, you first steer left, then begin to fall right, until you are going in the right direction. The rider is forever falling, and correcting their fall, towards their destination.

 

[Lnewqban]

 

[DaveC426913]

The action of the rider moving their body right seems to me would produce a left force on the pegs,

Consider what the rider-and-bike wants to do when this happens. It wants to pivot about its centre-of mass. And it could - if it were in free fall.

But because the wheels are in contact with the ground, it actually pushes the whole object to the left, which is what puts the wheel back under the CoM.

 

[Lnewqban]

Please, see how the trails allow the rider to move the COM of the chassis over the line between both contact patches, which is the imaginary line vertically over which the combined bike-rider COM should remain:

https://motochassis.com/Articles/Balance/BALANCE.htm

 

[DaveC426913]

View attachment 328687

Please, see how the trails allow the rider to move the COM of the chassis over the line between both contact patches, which is the imaginary line vertically over which the combined bike-rider COM should remain:

https://motochassis.com/Articles/Balance/BALANCE.htm

This assumes the rider is turning the wheel to stay balanced. I'm not sure that's necessary. A rider can balance on a bike - with the handlebars and front wheel straight - and still balance indefinitely. (I think!)

 

[jbriggs444]

Consider what the rider-and-bike wants to do when this happens. It wants to pivot about its centre-of mass. And it could - if it were in free fall.

But because the wheels are in contact with the ground, it actually pushes the whole object to the left, which is what puts the wheel back under the CoM.

View attachment 328690

The latter diagram seems to be backward. The rightward push by the feet on the ground yields a leftward impulse on the body by the ground. That drives the center of mass even farther left.

If you are falling left you want to bend to the left.

Watch a person falling off an edge. They will windmill their arms in the direction of the fall. Because that is the correct thing to do. You want to sink as much angular momentum as you can into your arms while you work on getting your body back on the safe side of the edge.

If you think in terms of the angular momentum of the falling body about its feet then no amount of pushing left or right can change the body's angular momentum. The moment arm is zero. No torque.

The point of pushing left or right against the ground is to manipulate the position of the body's center of mass. Then gravity can provide an external torque that will cancel and then reverse the angular momentum of the fall.