Correct functioning of sprockets in a machine depends on the sprocket ratios used. Specifically, these ratios involve the relationship between the teeth running along the sprocket and the places they fit into the chain as the machine is set in motion. If a precise ratio is not taken into account when the sprocket is made, the teeth will not line up with their corresponding links in the chain. In effect, the chain will slip off and the machine will cease to function.
Prior to computers and modern technology, some of the most complex machines operated with a series of sprockets fit together with a chain running through them, which is why they were called sprocket machines. Pulleys, as well as a number of other mechanisms operated with these parts. Today, perhaps the most readily available example of sprockets in action comes with bicycles. The sprocket itself is a flat, rounded wheel circumscribed with pointed notches, or teeth, which fit into and move with the chain wrapped around it. Chain parts include pin links, roller links, and link plate; the construction of a length of chain of this kind is quite different from that of the kind found in hardware stores.
Since sprocket machines require proper socket ratios, determining this measurement takes place prior to manufacture with a few simple mathematical steps. All teeth must be accounted for, so the first step is counting each individual tooth along each sprocket. Next, each link in the chain must be counted. It should be noted that some devices may have multiple chains. For a single sprocket, the total number of links in the chain that wraps around it should be divided by the total number of notches around that sprocket, and then the process is repeated with all additional sprockets and the chains that run through them.
Quotients obtained from such calculations are the sprocket ratios. It may be relevant to note that the same mathematical steps can be applied if gear ratios need to be found. As far as form goes, gears and sprockets are exactly the same, but whereas the sprocket rotates in conjunction with a chain, gears fit together and work off of each other — an example of this can be seen in the inner workings of a clock. In determining gear ratio, the notches in both sprockets are added up individually and then divided into each other; sprocket ratios involve only one sprocket and then the chain. The proper functioning of gears and sprockets in a machine requires precision in determining these gear and sprocket ratios.