The principles underlying the design of gears may be best understood by considering the historical development of the gear. Originally transmission of power in machines was carried out by two smooth cylinders placed close together, as in Fig. 146, the revolution and friction of one causing the revolution of the other. Smooth cylinders, however, tend to slip when under a load, so projections or notches were placed on their surfaces, as in Fig. 147. Here the diameters D and d are the same size as on the rollers in Fig. 146. Teeth were simply added to gear A and corresponding notches cut in gear B. These two gears did roll together without slipping, but as the teeth were short their points soon wore off. To overcome such troubles, the teeth on gear B were made twice as long and the corresponding grooves or recesses in gear A were cut twice as deep, as in Fig. 147. Today this is the design of the teeth. Gears are made by casting a blank wheel and then cutting the teeth in the gear according to the above design.

335 The Principle Of Gearing 262

Fig. 146.

335 The Principle Of Gearing 263

Fig. 147.

335 The Principle Of Gearing 264

Fig. 148.

Note that the inside dotted circles in Fig. 148 are exactly the same size as the rollers in Fig. 146 and are called pitch circles. When the gears turn together they simply roll together on the dotted circles just as they would do if they had no teeth.

Two gears represent the mechanical principle of the wheel and axle. The large gear represents the wheel and the small gear the axle. The most important part of gearing is the relative movements of the gears and the ratios between their diameters, their teeth, and their speeds.

When a small gear drives a larger one, the latter will make fewer revolutions in a minute. Just the reverse is true if a large gear drives a smaller one; i.e., the smaller one will make fewer revolutions in a minute. The rate at which a gear revolves is always proportional to the number of its teeth.

As there are driver and driven pulleys, so there are driver and driven gears. The driver gear and the driven gear may be distinguished by the following characteristics: The teeth of the former are bright or worn on the front side - that is, the side which faces in the direction of the motion of the gear; the teeth of the latter are worn on the side opposite from the direction of motion.

Since gears are simply pulleys with teeth on them, the principles underlying pulleys apply to gears. When the teeth of two gears interlock they are said to mesh.