Cogwheels are modifications of the wheel and axle.  Teeth cut in A fit into similar teeth cut in B, and hence rotation of A causes rotation of B.  Several revolutions of the smaller wheel, however, are necessary in order to turn the larger wheel through one complete revolution; if the radius of A is one half that of B, two revolutions of A will correspond to one of B; if the radius of A is one third that of B, three revolutions of A will correspond to one of B.

[Illustration:  FIG. 113.—­Cogwheels.]

Experiment demonstrates that a weight W attached to a cogwheel of radius 3 can be raised by a force P, equal to one third of W applied to a cogwheel of radius 1.  There is thus a great increase in force.  But the speed with which W is raised is only one third the speed with which the small wheel rotates, or increase in power has been at the decrease of speed.

This is a very common method for raising heavy weights by small force.

Cogwheels can be made to give speed at the decrease of force.  A heavy weight W attached to B will in its slow fall cause rapid rotation of A, and hence rapid rise of P.  It is true that P, the load raised, will be less than W, the force exerted, but if speed is our aim, this machine serves our purpose admirably.

An extremely important form of wheel and axle is that in which the two wheels are connected by belts as in Figure 114.  Rotation of W induces rotation of w, and a small force at W is able to overcome a large force at w.  An advantage of the belt connection is that power at one place can be transmitted over a considerable distance and utilized in another place.

[Illustration:  FIG. 114.—­By means of a belt, motion can be transferred from place to place.]

166.  Compound Machines.  Out of the few simple machines mentioned in the preceding Sections has developed the complex machinery of to-day.  By a combination of screw and lever, for example, we obtain the advantage due to each device, and some compound machines have been made which combine all the various kinds of simple machines, and in this way multiply their mechanical advantage many fold.

A relatively simple complex machine called the crane (Fig. 116) maybe seen almost any day on the street, or wherever heavy weights are being lifted.  It is clear that a force applied to turn wheel 1 causes a slower rotation of wheel 3, and a still slower rotation of wheel 4, but as 4 rotates it winds up a chain and slowly raises Q.  A very complex machine is that seen in Figure 117.

[Illustration:  FIG. 115.—­A simple derrick for raising weights.]

[Illustration:  FIG. 116.—­A traveling crane.]