Wheel and axle principle. Gears

Wheel and axle principle. Gears

Fig. 8.14 opposite shows some examples of devices using the wheel and axle principle. The steering-wheel of a car is another obvious example, but on” of the main applications of the principle in modern engineering is found in gear-boxes where
toothed wheels of different diameters engage to give turning forces at low speed (large mechanical advantage), or high speed (small mechanical advantage), according to which gear is the “driver” and which the “driven” (Fig. 8.13). In the laboratory, the velocity ratio and mechanical advantage of the wheel and axle may be investigated by using two wheels or different diameters rigidly fixed on the same axle. Fig. 8.15 shows how the effort is applied J.y a string attached to the rim of the larger wheel while the load is raised by a string wound round the axle or smaller wheel. For one complete turn, the load and effort move through distances equal to the circumferences of the wheel and axle respectively. The velocity ratio is therefore given by,

Wheel and axle principle. Gears
Wheel and axle principle. Gears

The mechanical advantage for a “perfect” wheel and axle may be found, as in previous cases, by applying the principle of work. Otherwise it may be found by taking moments of the load and effort about the axis of rotation. Using the latter method (see Fig. 8.15) Note. For gear wheels, remembering that the effort and load are applied to the shafts of the gears, the reader should not find it difficult to show that,

Wheel and axle principle. Gears
Wheel and axle principle. Gears

 

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