A bicycle's chain runs between the crank set in the center of the bike and the rear cassette attached to the rear hub. The pedal is attached to a crank arm that is part of the crankset. Cranksets typically have multiple chainrings. Shifting to a different front ring has a major effect on pedaling effort and is used for coarse gearing adjustments. Most bikes have two or three front chainrings. Cranksets with two chainrings are called "doubles," and three chainrings are called "triples."
Fine gearing adjustments are made by shifting the chain between the sprockets in the rear cassette. Bikes typically have anywhere between 7 to 10 sprockets available in the cassette. The total number of speeds a bike has is the product of the number of chainrings and the number of sprockets in the rear cassette. For example, a bike with a triple front chainring and a nine-sprocket cassette has a total of 27 "speeds."
The front derailleur moves the chain between the rings on the crank set, while the rear derailleur moves in between the sprockets on the rear cassette. Each derailleur is controlled by a shifter, one for each derailleur.
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