What are the forces acting while squeezing a ball?

[Anuroop]

Hi,

I am new to this forum. I am currently working on a project in the field of tangible user interface. I am developing a game in which a pressure sensor squeezable ball is the input controller. I am done with the game. Now I need to design a squeeze ball.

My next aim is to find out the number of sensors required, their ideal locations in the ball so that user's fingers are utilized to the maximum while playing the game & maximum forces are applied to the sensor locations.

So I would like to find out theoretically the points where maximum forces are applied when we squeeze a ball. Also I want to know the forces acting & displacements occurring while squeezing a ball.

Any input to this will be highly appreciated. Thanks in advance.

Regards,
Anuroop

 

[Astronuc]

At points of contact, the stress into the ball and in the interior would be compressive. Either side of the point of contact, the stress would be shear in the ball, and near the surface, away from the points of contact, the stress would be tensile in the circumferential directions.

At the point of contact, the material is being 'pushed' toward the interior. At the surface, the material is being pulled toward the depression where contact is made. The magnitude of stress depends on the stiffness.

A very stiff ball, like a cricket ball will have very little distortion, while a nerf ball could have a substantial deformation.

 

[Anuroop]

At points of contact, the stress into the ball and in the interior would be compressive. Either side of the point of contact, the stress would be shear in the ball, and near the surface, away from the points of contact, the stress would be tensile in the circumferential directions.

At the point of contact, the material is being 'pushed' toward the interior. At the surface, the material is being pulled toward the depression where contact is made. The magnitude of stress depends on the stiffness.

A very stiff ball, like a cricket ball will have very little distortion, while a nerf ball could have a substantial deformation.

Hi Astronuc,

Thanks for the reply. I would like to know how to find out the areas where maximum force/pressure is felt while squeezing. Let's take an example of a stress ball. So for a spherical ball, when we squeeze, which are the areas where maximum force is felt? How do i theoretically find out? Could you please advise?

 

[256bits]

The pressure areas would be a result of how one holds the ball. One could squeeze the ball between the fingers and the palm of the hand; or one could use just the thumb and a finger or two. Some users might want to try squeezing the ball down and rolling it around on a flat table surface, and see what that does.

I suppose it is up to you to provide the method the user will use, or perhaps all three, if not more.

 

[Anuroop]

The pressure areas would be a result of how one holds the ball. One could squeeze the ball between the fingers and the palm of the hand; or one could use just the thumb and a finger or two. Some users might want to try squeezing the ball down and rolling it around on a flat table surface, and see what that does.

I suppose it is up to you to provide the method the user will use, or perhaps all three, if not more.

Hi,

Sorry. I missed it. Thanks. We are mainly interested in the above mentioned first method of squeezing i.e. squeezing the ball between the fingers & palm of the hand. So in this method, where could be the pressure area?

 

[256bits]

Astronuc gave a pretty good answer - compression under the contact with the fingers etc. That might be the most adequate that you will receive since several variables would come into play, such as size of hand, size of ball, type of grip, flexibility of fingers. You might have to do some testing so that your input controller would work just as well with a large hand from a lumberjack as with the small hand of a six year old child.

 

[Anuroop]

Astronuc gave a pretty good answer - compression under the contact with the fingers etc. That might be the most adequate that you will receive since several variables would come into play, such as size of hand, size of ball, type of grip, flexibility of fingers. You might have to do some testing so that your input controller would work just as well with a large hand from a lumberjack as with the small hand of a six year old child.

Hi,

Thanks a lot for the advise. I am planning to do such testings in future. But right now I am looking for some equations & theoretical knowledge regarding the force distribution when a ball is pressed. Once I can figure out theoretically the locations, I will test it by placing sensors & compare both the results. This way I believe I will get a strong base to claim the squeeze ball design. I am stuck at writing equations wrt force & displacement.

 

[A.T.]

their ideal locations in the ball so that user's fingers are utilized to the maximum

How about under the fingers? That is usually where the sensors on a controller.are

 

[256bits]

Ok. A 3D stress problem.

This may help you out, to get started.
http://www.mech.utah.edu/~me7960/lectures/Topic7-ContactStressesAndDeformations.pdf

 

[Anuroop]

Ok. A 3D stress problem.

This may help you out, to get started.
http://www.mech.utah.edu/~me7960/lectures/Topic7-ContactStressesAndDeformations.pdf

Hi,

Thanks a lot. Let me go through it.

 

[Anuroop]

How about under the fingers? That is usually where the sensors on a controller.are

it could be under the fingers or may be at the center. But I am thinking about how to theoretically prove by writing equations of force & displacement & get the locations of maximum force.

 

[A.T.]

But I am thinking about how to theoretically prove by writing equations

For some arbitrary distribution of external forces you need FE-software. How many degrees of freedom are you trying to squeeze out of that controller?

 

[Anuroop]

Ok. A 3D stress problem.

This may help you out, to get started.
http://www.mech.utah.edu/~me7960/lectures/Topic7-ContactStressesAndDeformations.pdf

Hi,

Is there a way to prove that the maximum force is felt under the finger tips(which I believe is correct) while squeezing a foam ball? I would like to write equations to support my point. As mentioned before, the ball will be squeezed using the fingers & palm of the hand.

 

[256bits]

You should begin thinking of the distinction between force and stress.

For example, if you squeeze the ball between flat plates, both plates apply the same force. If you take sections of the ball perpendicular to the normal of the plates and do a FBD ( free body diagram ), the sectional areas also have the same force. So from this perspective, there is not a place within the object that can be labeled as having the maximum force.

On the other hand, there are places that have maximum stress (or pressure, but that is not the usual descriptive term used for material bodies ). If you look at the PDF, Figures 7-5, 7-6 and 7-9, it shows the deformation of the contact areas, for a sphere and a cylinder on several surfaces of different curvature. The contact area is the region where, or somewhere around there, ( see Figure 7-8 and 7-12 ), where the stress should be the greatest, since the area is the smallest and we know that P=F/A. Figure 7-5 gives Pmax = 3F/ 2 (pi)a^2.

At the centre of the ball, we can, probably with confidence, assume the stress is constant across the whole sectional area, and calculate the compressive stress P(r=0) as being the force F divided by the sectional circular area at the centre of the ball, which is just A=pi R^2, if R is the radius of the ball. P(r=0) < than Pmax. As we increase r, the circular sectional area decreases, and with it, as the same force is being applied, the compressive stress will increase. At some r, though, the stress will not be the same across the whole circular area, but will be greater at the centre-line of the area and decrease, possibly to zero at the perimeter. As r is increased more to the final radius of the ball, we come to what is described in the preceeding paragraph, or as described in the PDF. You can see this from Figure 7-8 and looking at the curve of σz, noting the decrease as the depth below the contact area increases. Similar pattern as we move away from directly underneath the contact point.

Note that the other stresses are part of what, I repeat, Astronuc was alluding to in his post, where there are shear and tension components.

So perhaps it is not the maximum force that you are really should be asking or worrying about, but perhaps rather the maximum stress and accompanying deformation of the ball, as it is squeezed, and how to convert that into an electronic signal for processing.

 

[Anuroop]

You should begin thinking of the distinction between force and stress.

For example, if you squeeze the ball between flat plates, both plates apply the same force. If you take sections of the ball perpendicular to the normal of the plates and do a FBD ( free body diagram ), the sectional areas also have the same force. So from this perspective, there is not a place within the object that can be labeled as having the maximum force.

On the other hand, there are places that have maximum stress (or pressure, but that is not the usual descriptive term used for material bodies ). If you look at the PDF, Figures 7-5, 7-6 and 7-9, it shows the deformation of the contact areas, for a sphere and a cylinder on several surfaces of different curvature. The contact area is the region where, or somewhere around there, ( see Figure 7-8 and 7-12 ), where the stress should be the greatest, since the area is the smallest and we know that P=F/A. Figure 7-5 gives Pmax = 3F/ 2 (pi)a^2.

At the centre of the ball, we can, probably with confidence, assume the stress is constant across the whole sectional area, and calculate the compressive stress P(r=0) as being the force F divided by the sectional circular area at the centre of the ball, which is just A=pi R^2, if R is the radius of the ball. P(r=0) < than Pmax. As we increase r, the circular sectional area decreases, and with it, as the same force is being applied, the compressive stress will increase. At some r, though, the stress will not be the same across the whole circular area, but will be greater at the centre-line of the area and decrease, possibly to zero at the perimeter. As r is increased more to the final radius of the ball, we come to what is described in the preceeding paragraph, or as described in the PDF. You can see this from Figure 7-8 and looking at the curve of σz, noting the decrease as the depth below the contact area increases. Similar pattern as we move away from directly underneath the contact point.

Note that the other stresses are part of what, I repeat, Astronuc was alluding to in his post, where there are shear and tension components.

So perhaps it is not the maximum force that you are really should be asking or worrying about, but perhaps rather the maximum stress and accompanying deformation of the ball, as it is squeezed, and how to convert that into an electronic signal for processing.

Hi,

Thanks a ton for the reply. Now I have got some idea to start.

 

[A.T.]

Thanks a ton for the reply. Now I have got some idea to start.

I was wondering for what kind of computer game squeezing the controller would be the appropriate control method?

 

[Anuroop]

I was wondering for what kind of computer game squeezing the controller would be the appropriate control method?

It's a small left to right obstacle avoiding game( we will be improving the game in the future). Our main focus is its application which is to help people by making their rehabilitation from hand injuries much more entertaining. Patient's hand must be utilized to the maximum while playing the game. Hence the need to place the sensors at the correct locations & detect the squeezing.

 

[Anuroop]

You should begin thinking of the distinction between force and stress.

For example, if you squeeze the ball between flat plates, both plates apply the same force. If you take sections of the ball perpendicular to the normal of the plates and do a FBD ( free body diagram ), the sectional areas also have the same force. So from this perspective, there is not a place within the object that can be labeled as having the maximum force.

On the other hand, there are places that have maximum stress (or pressure, but that is not the usual descriptive term used for material bodies ). If you look at the PDF, Figures 7-5, 7-6 and 7-9, it shows the deformation of the contact areas, for a sphere and a cylinder on several surfaces of different curvature. The contact area is the region where, or somewhere around there, ( see Figure 7-8 and 7-12 ), where the stress should be the greatest, since the area is the smallest and we know that P=F/A. Figure 7-5 gives Pmax = 3F/ 2 (pi)a^2.

At the centre of the ball, we can, probably with confidence, assume the stress is constant across the whole sectional area, and calculate the compressive stress P(r=0) as being the force F divided by the sectional circular area at the centre of the ball, which is just A=pi R^2, if R is the radius of the ball. P(r=0) < than Pmax. As we increase r, the circular sectional area decreases, and with it, as the same force is being applied, the compressive stress will increase. At some r, though, the stress will not be the same across the whole circular area, but will be greater at the centre-line of the area and decrease, possibly to zero at the perimeter. As r is increased more to the final radius of the ball, we come to what is described in the preceeding paragraph, or as described in the PDF. You can see this from Figure 7-8 and looking at the curve of σz, noting the decrease as the depth below the contact area increases. Similar pattern as we move away from directly underneath the contact point.

Note that the other stresses are part of what, I repeat, Astronuc was alluding to in his post, where there are shear and tension components.

So perhaps it is not the maximum force that you are really should be asking or worrying about, but perhaps rather the maximum stress and accompanying deformation of the ball, as it is squeezed, and how to convert that into an electronic signal for processing.

Hi,

After reading your post, I read few other articles. Now I have a better idea about the topic. Thanks a lot for patiently replying to my posts. The only part I am unclear now is regarding the forces acting. I know, as u said, I need to think about the stress & not force. But still I would like to know few more things.

When we squeeze the ball using fingers & palm, there will be two opposite forces acting on the ball. So is it correct to say that the resultant force of these two forces will be the force acting on a sensor kept at the centre? Apart from these forces, are there any other forces acting on the ball? I mean if I need to draw a FBD, what are the forces that I need to consider?

 

[A.T.]

Apart from these forces, are there any other forces acting on the ball? I mean if I need to draw a FBD, what are the forces that I need to consider?

Contact forces from the hand and gravity.