Step 1:
Use acetone (nail polish remover--available in most grocery and drug stores) to "weld" the pieces together. I "paint" the pieces with a small brush then put them together.

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Gone to my Blog.
http://faz-voce-mesmo.blogspot.pt/2013/02/fablab-ras-e-reprap-magazine.html
Have you thought about using pneumatics to make the ride go up and down?
Just a piece of pipe shaped like a tiara ===|\ so the arm can go up and down it. Hope these images help describe what I mean.
Yellow is the new part required.
You would need to modify the part that attaches to the motor (let's call this part Fred) by making it slightly less wide than the distance from the motor spindle to the edge of the motor so it can rotate freely inside the pipe.
You would also need to mount the crossbeam using a pivot and cutting a channel inside Fred so the crossbeam can move up and down on the pivot.
Still with me?
Here are my 5 minutes in gimp images that hopefully show what I mean
By the what's the speed?
And what would happen if like went 20 times the speed?
Since it's unbalanced (the red and blue frogs are larger), something would quickly come undone at 20 times the speed.
Stay tuned--I may sling some around in swings at a much higher speed :)