Collision of Ball with Table Tennis Playing Robot 2D Elastic Collision

[Zeeshan86]

Hi !

I am working on a table tennis playing robot. The picture of the robot is attached.

I have few questions.

1) Can I consider the collision between Ball and the plate as the two dimensional collision ? ? (At this time I am not considering z-axis)

2) If I am considering the 2-Dimensional collision (neglecting z-axis) and the mass of the Ball is considered as Mass-2, then should I consider the whole mass of the Robot as Mass-1 OR only the mass of the hitting plate is considered as Mass-1 ?

I am confused about the Mass-1 ... Either the whole robot is considered as Mass-1 or only the hitting plate is considered as Mass-1.

Can anyone help me in this ?

Regards,
Zeeshan

 

[haruspex]

2) depends on the stiffness of the connection between the robot and the paddle, and how that relates to the duration of contact. Imagine, in tennis, relaxing your grip on the racket at the instant of contact. This would take almost all of the power out of the shot. How much that carries over to table tennis I'm not sure, but I would think it's significant.
And it's not just the mass of the robot. The robot, presumably, has some grip on the ground. I'd think you could effectively take the mass of the paddle as infinite.

 

[Zeeshan86]

What would be the case, if the ball is collided with the plate. Just like the table tennis.
Can we also consider the collision between the table tennis racket and ball as the 2D collision like collision between two ball ? ?
Will the shape of the plate will effect the equations ?

 

[haruspex]

If you ignore spin, yes you could get away with two dimensions. Taking the plate as the frame of reference (assuming it's moving with constant velocity at impact), the ball strikes the plate at some angle to the normal. The plane containing the line of strike and the normal is the only plane you have to care about.
But spin is rather a major consideration in table tennis, no?

 

[Zeeshan86]

Yes, spin is also very important. But at this time I am neglecting the spin of the ball.
I am doing some simulations and at this time I am neglecting spin of ball.
Yes, in my case the racket will strike the ball with the constant speed.
What would be the mass of the tennis ? ? Either the complete mass of the robot or just the mass of the hitting plate should be considered ? ?

 

[haruspex]

What would be the mass of the tennis ? ? Either the complete mass of the robot or just the mass of the hitting plate should be considered ? ?

I answered that already. In table tennis, you can take the mass of the paddle as effectively infinite because it and the arm wielding it are so much more massive than the ball.
In lawn tennis it will be a little different.

 

[Zeeshan86]

Thank you very much for the help.
I am only using it for table tennis.

 

[Zeeshan86]

Can I consider the whole robot as a Big Ball having infinitive mass as compare to the mass of the Small Ball ? ?
Can I consider the plate in the circular shape ?
It will simplify the problem as the two Balls have oblique collision ...

 

[haruspex]

Can I consider the whole robot as a Big Ball having infinitive mass as compare to the mass of the Small Ball ? ?
Can I consider the plate in the circular shape ?
It will simplify the problem as the two Balls have oblique collision ...

I'm saying you can treat the plate as having infinite mass. It will be like a ball bouncing off the ground. The error from making that approximation will be much less important than that from ignoring spin.

 

[Zeeshan86]

Will the velocity of the plate effect or not ?
Should I consider the velocity of the Plate ? (This velocity of the plate will be constant).
Is there any article/equation that shows the relationship of the velocity of the plate on the final velocity of the Ball ? ?

 

[haruspex]

Will the velocity of the plate effect or not ?

Of course! Easiest way is to take the plate as the frame of reference, i.e. consider the ball's motion relative to the plate. So now it just looks like a ball bouncing on hard ground.