# Centripetal Force v. Torque

1. Jan 16, 2012

### physicsofme

Hi guys and gals, I have a robotics related engineering problem I need help with.

So, for our robot we are building, it has a centripetal arm that launches a foam basketball. The arm is 2 foot in diameter rotating from the center with 3 pounds on each side (including projectile and counterweight). It is also shooting up to 60 feet away and 6 foot high. So that comes out to needing 468 RPM with 19 ft/sec acceleration, 15 N force, a required torque of 684 oz-in with 10 spin up rotations that releases after 2.5 seconds.

So basically the centripetal force is 232.449 N and the centripetal acceleration is 732.089 M/s^2.

So for our claw design, it's three different welded chain links to form fit the ball with a urethane fingertip to add friction between the urethane ball. But how can we calculate the required torque of the three servos (one on each chain piece) that's needed to hold the ball in place against the centripetal force? It also needs to be able to release fast enough. Is the centripetal force too much for any servo? or what? We're very confused. Please help :(

2. Jan 16, 2012

### Simon Bridge

looks like centrifugal force to me - the servo is not seeing an inertial reference frame - by your calcs you need the servos to be able to hold on to 75kgs ... which seems a bit excessive to me. Mind you, I've never had to throw a 3lb ball 60ft.

Last edited: Jan 16, 2012
3. Jan 16, 2012

### Simon Bridge

Aside: have you considered putting the ball in a cup with the opening perpendicular to the arm so the acceleration holds the ball in place - releasing the ball involves stopping the arm abruptly ... say your servo pushes a barrier of some sort in the way, at the correct angle, as the arm comes around on the tenth turn? (You'll probably want the same action to disconnect the motor driving the arm too.) This way the servo does not have to be strong enough to hold the ball.

Of course this assumes that throwing the ball is all the robot has to do.
If you must have a hand, then you only need one servo-finger... and only that one needs to form-fit the ball.

4. Jan 16, 2012

### physicsofme

Well it does have to have a hand to receive the ball from another hand, and we went over the abrupt release but we fear damaging our robot, which is a high probability with such speeds. The ball is actually 11.2 ounces and the rest of the arm is a little more than 2 pounds if that helps. And that's just one side of the arm, the other side has the same counterweight as the first side with the ball.

So also, is there a way to create a claw piece that would be able to act as a normal force for the ball while spinning because the centripetal force would also push it towards the outside so if it were balanced correctly, it would still remain towards the outside? Then would it still need 75 kg force to open up?

5. Jan 16, 2012

### Simon Bridge

Yes. Hard to describe ... consider: on release, the ball wants to fly perpendicular to the arm.

Make two stiff fingers in a kind of claw so they curl over the ball stopping it from moving radially. You'll need to experiment a bit so the ball will still slip out tangentially if it is not restrained. Then you just need a servo thumb to hold the ball in place. Should require almost nothing to hold it in place.

If you were sitting on the hand holding the ball, it would feel like you were holding a grown man against gravity. I suspect this is the reason machines for throwing balls are usually a flywheel and a hopper.

note: centripetal force pulls everything towards the center.