Forces acting when we squeeze a ball?

[Mohanlalfan]

I have few doubts to clear. I would like to know the forces acting when we squeeze a foam ball. Mode of squeeze will be by placing the ball between the palm of the hand and the four fingers.

What will be the force acting at the center of the ball when we squeeze? Is the force same through out the ball and only the stress is different at different points inside the ball? If not, how do we find out the force? I would like to know about the forces and stresses acting.

Any help would be appreciated.

 

[paisiello2]

When you say "the force acting at the center of the ball" do you mean the force acting on a cross section perpendicular to the direction of the applied force?

Or do you mean the internal force acting in the ball?

 

[Mohanlalfan]

When you say "the force acting at the center of the ball" do you mean the force acting on a cross section perpendicular to the direction of the applied force?

Or do you mean the internal force acting in the ball?

Suppose we have a sensor at the center of the ball. What would be the force acting on the sensor when we squeeze the ball? How do we calculate it?

 

[paisiello2]

The sensor would be some sort of strain gauge so you would technically be measuring stress not force.

From the definition of stress:
σ = dF/dA
⇒ F = ∫ σ dA over some arbitrary area A

So I think you have to define specifically what area A you are talking about. And because the area is arbitrary it is somewhat meaningless to talk about the "force" inside the ball at any point. Rather it is better to talk about the stress at any point inside the ball.

 

[Mohanlalfan]

The sensor would be some sort of strain gauge so you would technically be measuring stress not force.

From the definition of stress:
σ = dF/dA
⇒ F = ∫ σ dA over some arbitrary area A

So I think you have to define specifically what area A you are talking about. And because the area is arbitrary it is somewhat meaningless to talk about the "force" inside the ball at any point. Rather it is better to talk about the stress at any point inside the ball.

Thanks a lot for the reply. Could you please explain me what do you mean by "because the area is arbitrary it is somewhat meaningless to talk about the "force" inside the ball at any point" ? I understood about stress part. Stress would be maximum towards the surface as the surface area is less. But I am not understanding why force should not be considered here. Any help would be appreciated.

 

[paisiello2]

Well I am saying you shouldn't consider force simply by itself because you need to know also the area this force is acting on.

I don't agree with the stress being maximum because the area is less (which it isn't). In your example, the stress is greatest where you are directly squeezing the ball and gradually smooths out to be close to uniform at the ball center.

 

[Mohanlalfan]

Well I am saying you shouldn't consider force simply by itself because you need to know also the area this force is acting on.

I don't agree with the stress being maximum because the area is less (which it isn't). In your example, the stress is greatest where you are directly squeezing the ball and gradually smooths out to be close to uniform at the ball center.

So when I squeeze the ball, greatest stress will be under the finger tips and hence it will be better to place the sensors there if I need to convert the force applied to an signal.

 

[paisiello2]

Yes, the greatest stress will be under the fingertips.

I am not sure why you think placing a sensor there would make any difference to placing it anywhere else to just get a signal unless the goal is to get just the largest signal possible?

 

[Mohanlalfan]

Yes, the greatest stress will be under the fingertips.

I am not sure why you think placing a sensor there would make any difference to placing it anywhere else to just get a signal unless the goal is to get just the largest signal possible?

Our goal is to place the sensors at maximum stress points so that squeezing force is efficiently converted to signals. Am I wrong to think like this?

For example, we have a foam ball and we have few sensors. We need to place the sensors(doesn't matter how many) inside the foam ball so that squeeze force is converted in the best possible way. So I am looking for locations for sensors to be placed and also the number of sensors required.

 

[paisiello2]

What is it are you ultimately trying to do? Once you get this info from the sensors what are you going to do with this info?

 

[Mohanlalfan]

What is it are you ultimately trying to do? Once you get this info from the sensors what are you going to do with this info?

We are planning to use the signal as an input to games that we will develop. So we want the largest possible signal and if we need some modifications we can do that in software. But the initial signal should the largest. So could you please let me know what's your opinion on this?

 

[paisiello2]

Ok, there might be technical reasons that I am not aware of why this might not work, but if you simply want to measure the largest amount of strain with the minimal amount of force applied then as close to the finger tips as possible is what I would think.

 

[Mohanlalfan]

Ok, there might be technical reasons that I am not aware of why this might not work, but if you simply want to measure the largest amount of strain with the minimal amount of force applied then as close to the finger tips as possible is what I would think.

Thanks. This is what I also feel. But how do I show it theoretically? May be by writing some equations. I know stress is force by area and if we take cross-sectional areas, it will be less towards the surface and hence we can say that stress is maximum there. Is there any other way?

 

[paisiello2]

1) You could use the theory of elasticity (with a simplifying approximation) to show this.

2) You could create a finite element computer model to show this.

3) You could build a photo elastic model and test this.

4) You could do a literature search to see if someone else has created a mathematical model or tested for a similar loading condition.

 

[Mohanlalfan]

1) You could use the theory of elasticity (with a simplifying approximation) to show this.

2) You could create a finite element computer model to show this.

3) You could build a photo elastic model and test this.

4) You could do a literature search to see if someone else has created a mathematical model or tested for a similar loading condition.

Thanks a lot. If possible could you please elaborate your first point?

 

[paisiello2]

By theory of elasticity I mean applying the relevant equations of solid mechanics to create a mathematical model that you can then solve for.