The trigger mechanism looks complicated but is actually pretty simple. There are a few parts: the sling attachment, a rod that holds the sling during throwing, and a hook trigger. One end of the sling is shown on the side of the arm, tied to a screw eye. The other is tied to a "quick link" that goes over the rod.
The rod coming out of the end of the arm was made from a "L" shaped screw-hook. It was straightened with heavy pliers after being screwed into the arm. Some experimentation was required to get a good angle that allowed the sling to slide off and throw at a good time. It comes mostly straight out of the end of the arm.
The trigger is made from a hook and eye set. The eye part was used to hold one end of the sling. The screw end of the hook was set into the base so that it snaps over the rod snugly, pulling back at an angle that won't slide off the end. A cord is tied to the back of the hook, and the loose tail of this cord is frayed in these pictures.
To load and set the trigger, the arm is pulled down and the sling's quick link is slid over the rod. The trigger hook is passed over the rod, holding down the end of the arm and preventing the quick link from sliding off.
The other end of the trigger cord is attached to a short piece of dowling. This allows someone to give it a tug, pulling the hook off the rod and releasing the arm for it's swing.