I would create a shape layer that is the shape of a single link in the chain. I would then create a mask path around the outside of the chain bar. I would then copy the mask path then paste to a motion path for the link.
Once you have the link moving around chain bar where you want it, pre-compose this layer and then apply echo the pre-comp to adjust the spacing and the number of echoes.
Another way to do that would be to draw chain for the top bottom straight portions of the bar plus enough to have chain the move distance of one link. Animate top and bottom straight pieces of chain so they travel one link, use a loop out expression to make it appear as if a chain is continually moving. Create a chain Circle for the nose of the chain bar, animate the rotation of Circle, and then adjust timing of the animations so it appears as if the chain is moving.
There are lots of fairly easy ways to do this if you just break it down. You also have to be aware of stroboscopic effects that are caused by the speed of the chain and the frame rate. You don't want your chain moving the wrong direction, that would be very easy to do.
What you should do is cut out a single piece of chain, make that a layer, animate it moving along the saw blade, then duplicate that layer to fill the chain, offsetting each duplicates' time so that they're spaced out correctly.
EDIT: Bah, Rick beat me to it.
Animation of this kind is known as a cycle. It only takes three or four frames of movement, repeating in a loop, to create the illusion.
Here's a little project to get you started. Took me about 15 minutes.
Chain Bar layer
in a 12 frame comp using Echo and CC Force Motion blur
Dropped in a 30 second comp, time remapped with a loop out expression.
Here you go, a CS6 Chainsaw project.
This is fantastic, thank you very much Rick. I'm trying to recreate what you've done in that Chainsaw project, and i'm struggling with creating eliptical motion sketch - how do i connect the first and the last points of a motion sketch? i did watch creative cow's ae basics tutorials about shape layers/mask paths and read this article http://helpx.adobe.com/after-effects/using/creating-shapes-masks.html, but still cannot "close" the motion path the way i want. Am i supposed to press and hold some additional key while motion sketching?
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I did not use motion sketch, I just selected the mask path for the chain. By then selected the position property of the link, set a keyframe and executed a paste.
As long as your anchor point is in the right spot the link should follow right around the outside edge of the chain bar.
I'm posting from a mobile device so this is going to be a little funky, but here's a link to a video that shows you how to copy a mask path and turn it into a motion path. The tutorial shows you how to do it for a camera, but you could figure out how to do it for a shape layer.
ahh, now i got it! this is very cool trick and i think i'm gonna use it pretty often Appreciate your time Rick, it was excellent support