Open gears_1.skp, a model with two 3D gears. Click the "Create Circle Path" button on the SU Animate toolbar, or "New... -> Arc/Circle Path Animation" in the SU Animate dialog.
Mouse over the center point of the larger gear until the cursor snaps to "Center in Group". It may help to mouse over the nearest circular edge first. Click and drag a circle of any convenient size.
The Path Animation dialog appears for animation named "Circle1". Click "Save".
The new animation appears in the SU Animate dialog. At this point, no objects are animated. Right-click on "Circle1", and select "Add/Remove". The non-modal "Select Objects" dialog appears, inviting you to select the objects to be animated. Select the big gear in SketchUp and click "OK" in the dialog. Back in the SU Animate dialog once again, double-click on the name of the new animation "Circle1", and change it to "big gear".
You can save a couple steps by pre-selecting the object to be animated. Select the smaller gear, then click "New... -> Arc/Circle Path Animation" in the SU Animate dialog. Again, mouse over the center point of the smaller gear until the cursor snaps to "Center in Group", and click and drag a circle of any convenient size.
This time we don't have to use "Add/Remove", because the animation automatically animates the objects that were already selected. Also, notice that the new animation is named after the selected group; this is the default behavior if a single named object is selected for animation.
Since the little gear has to turn in the opposite direction of the big gear, click "Reverse Direction". Then "Save".
If you click "Play" in the animation dialog, the animations both play, and you can see that the gears do not mesh well. We need to set the number of frames proportional to the number of teeth. The gears have 17 and 9 teeth respectively, so set the frame values in proportion, say 10x those numbers. But since the paths are closed (last frame is the same as first frame), and an extra frame to each: big gear 171, little gear 91.
The gears mesh beautifully now. The repeat option lets the little gear keep going until the animation is done. Your model should resemble gears_2.skp.