A while back I was interested in the geometry of draw leaf tables. I was curious about how they work and how one would go about getting the action to work. I drew a simple table and by using the Move tool set up a linear array to show where the leaf would be at the stowed and extended positions along with a couple of intermediate points along the way. I also used the Rotate tool on the top component to show where the top would be at each stage of the leaf's extension. The copies of the leaf and the corresponding copies of the top were shifted to their own layers. Then, by setting different layers on or off for different scenes, I was able to animate the action. The attached link shows a short clip of that animation.

Note, the Pro version of SketchUp allows one to export the animation as either a series of JPGs or as an AVI file. The free version doesn't have this export option but you can still watch an animation in SketchUp by choosing Play under the View menu. The Settings option right below Play lets you choose transition and delay times.