Slings: How do they work?
One of the most often asked questions deals with how a sling works and how it's connected to the throwing arm.  See if this graphic explains it for you.
 

At the moment of release, the payload is still on the ground or trough, if your have one.  The sling lines get tight and start pulling the payload along. The green sling line is fastened, in some manner, to stay with the beam.  The red sling line is fastened to the slip ring, which is over the release pin.  The pouch (not shown) is fastened to both lines at the other end.

As the throwing arm rotates around, the pouch is picked up from the ground.  Please note that the red ring is not quit where it should be, poor graphics on my part.  But it is seated at the bottom of the pin, where it should be.

Now the beam as gone past horizontal and the sling is getting some good velocity going.  If the pin was straight, you might start getting a release at this point.  Since it's not, we don't.

Okay, we've reached a critical point here.  The beam is still rotating but the sling is now at right angles to the pin.  This is the point where the greatest stress on the pin is.  If it survives this, it will probably survive the rest.

Depending on your design, the beam will be rotated to some angle at which point the sling, rotating around the pin, will reach a critical angle with respect to the pin.  Depending on the forces involved, design criteria and the friction between the pin and the slip ring, this is the point where the slip ring will start to slide off the end of the pin.

Fine tuneing your machine will produce the optimum launch angle.  Once the slip ring is clear of the pin, it will begin to move towards the pouch/payload.  This action allows he pouch to 'unroll' from the payload, releasing it.  After that the sling will usually reach its full length and simply fly around.  So be careful because getting hit in the head with that ring can hurt!  (See my 'Stuff' page for a safety tip about this problem.)

Sling and pouches can be make out of a large selection of materials.  Sling lines can be clothes line, hemp, manila, thread, leather, steel cable, nylon...  Whatever you use should be strong enough to carry the load and be light weight. Cost, your ability to work with it, weather resistance, etc. are other choices for you to make.
 Slip Rings follow the same guidelines, strength and light weight.  Many people use split key rings on table top models, only to discover that the forces are enough, even when throwing golf balls, to spread open the ring!  In other cases a simple loop tied in the end of the sling line works fine.  Keep in mind that the friction between the slip ring and the release pin will effect the timing of the release, the more friction the later the release. Pin length will have timing affects as well, but the pin angle is the usually adjusted for release angle.
 Consistency is a valuable consideration especially when trying to fine tune your machine.  Steel on steel with a touch of grease is very popular as it has a very low drag coefficient (it slides easily).  So much depends on what scale your building at.  Some table top models use paper clips only to find that the little ribs on the paper clips are holding the ring much too well!  Some very large machines use a simple manila or hemp sling, tied with a loop in the end and fitted on the end of the throwing arm which has a simply tapered end for a release pin.  Lots of friction but it can work well.
  I mention light weight materials as a design factor, here's why;  The end of the throwing arm is what your trying to 'get up to speed', which takes energy.  It's this energy that we're trying to 'give up' to the payload, the more the better.  Anything that hangs on to this energy is a loss, including that energy required to move the sling and pouch!  So, the lighter they are the less energy needed to get them up to speed, saving said energy for other things, like distance!