[ToddF]

There are ways to mechanically reduce the play, like pinning the connection, shimming, and the like. However, one thing that works rather well is preloading the connection with a counterbalance spring. We do this quite often by using surgical tubing to partially support the weight of various arms. It has the added benefit of often reducing the size of the actuator needed to provide the motion.

But, if you really want to do it mechanically, use a couple #4-40 screws and attach a hex shaft collar to the face of your sprocket. Position the sprocket with the collar loose, then tighten it up. (Disclaimer: never actually done this, but seems like it ought to work.)