The chain is advanced by the chainwheel, the number of teeth on this wheel determining the length of chain that is pulled over it in one revolution. The photograph

shows the teeth on a new sprocket (top) and a worn sprocket (bottom) with wear locations indicated by arrows. This wear results from a friction interaction between the chain and the wheel and the work causing the damage comes at the expense of the work available for propulsion. Lubrication is important here as well as proper tooth shape that favors a rolling interaction rather than a sliding interaction between the chain and the chain wheel.

The link-by-link advance of the chain causes a tooth-by-tooth advance of the rear sprocket, and so the ratio of the number of teeth on these two wheels determines the gear ratio associated with power transmission between the pedals and the rear wheel.

From: Sloane, "Sloane's Complete Book of Bicycling," Simon & Schuster (1995)