THE WHEEL AND AXLE.

A ship's capstan is another form of the wheel and axle.

EXAMPLE FOR PRACTICE.

In weighing anchor 6 capstan bars are used; from center of capstan to point of pressure is 6 feet; diameter of axle of capstan 24 inches. Now then, if each man exerts 80 lbs. with his bar.

=

Fig. 8.

The leverage for force (radius of 12 ft. diam.-6.

Number of men 6

36

Lbs. for each man 80

Divide by radius of axle 1)2880

2880 lbs. Ans.

If an allowance of ten per cent. is made for friction and the rigidity of the cord, the answer will be 2592 lbs. Ans.

EXAMPLE FOR PRACTICE.

The diameter of a steering wheel on a ship is 5 feet and the barrel is 15 inches in diameter. If a man applies a force equal to 200 lbs. what resistance would he overcome? Ans. 800 lbs.

THE CHINESE WHEEL AND AXLE.

To combine the requisite strength with moderate dimensions and great mechanical power has been accomplished by giving different thicknesses to different parts of the axle and carrying

THE WHEEL AND AXLE.

Fig. 9.

a rope which is coiled on the inner part through a pulley at. tached to the weight and coiling it in the opposite direction on the thicker part as in fig. 9.

We see here exemplified the principle, that the weight sustained by a given power, may be increased as its velocity is diminished. By inspecting fig. 9 it will be seen that the rope connected with the thinner part of the axle unwinds, while that connected with the thicker part winds up, by which means the ascent of the weight may be rendered slow in any degree, and a proportionally greater quantity of matter may be added.

To find power in this arrangement follow the

RULE.

The power multiplied by the radius of the wheel, in feet, is equal to half the weight multiplied by the difference in the half diameters (radii) of the thicker and thinner parts of the axle. This will be made clear by the following

EXAMPLE.

The diameters in fig. 9 are 1 foot and of a foot; the length of the handle 2 feet 3 inches; if the exertion put forth is equal to 80 lbs. what weight will be lifted.

Now then to follow the rule.

the difference in the radii .0625) 18000 (2880 lbs. Ans.

1250

5500

5000

5000

5000

In all these examples the diameter of the rope has been supposed to be so small in comparison to that of the drum or barrel that it has been neglected; if it is a thick rope, then the leverage must be measured from the center of the barrel to the center of the rope.

EXAMPLE.

Wheel and axle, the barrel is 10" in diameter, the rope is 1 inches in diameter, the crank handle is 15" radius, and the weight to be lifted is 500. What force must be applied to the handle if 10 per cent. is to be added for friction. Now, then Leverage of weight 5"+" 575. Being radius of barrel

and rope.

=

THE WHEEL AND AXLE.

These examples are worked in decimal fractions, the rules and examples of which will be given later.

=

To find the difference in the half diameter of the axlc, (Fig. 9.) proceed thus: 1 foot foot; this for the radius= one-eighth foot, and half this is one-sixteenth, or in decimals .0625. (See example.)

THE PULLEY.

The pulley is a wheel over which a cord, or chain or band is passed, in order to transmit the force applied to the cord in another direction. The practical effect of the machine depends upon the rope, the wheel being introduced to diminish friction and the effect of imperfect flexibility, but the whole effect of imperfect flexibility and friction are not destroyed, although in calculations, we proceed as though they

were.

Fig. 10.

There is no mechanical advantage gained by a single rope over one or more fixed pullies; but this combination is of the greatest use by enabling us to change the direction of the force.

Pulleys are divided into fixed and movable. In the fixed pulley no mechanical advantage is gained, as already explained, but its use is of the greatest importance in accomplishing the work appropriate to the pulley, such as raising water from a well. Thus, it is far more convenient to raise a bucket from a well by drawing downward, as is the case where the rope passes over a fixed pulley above the head, than by drawing upward leaning over the curbing.

From its portable form, its cheapness and the facility with which it can be applied, especially in changing or modifying the direction of motion, the pulley is one of the most convenient and useful of the mechanical powers.

THE PULLEY.

It must be observed that in using any system of covable pullies, the whole weight of the pulleys themselves, together with the resistance occasioned by the friction and rigidity of the ropes all act against the power and so far lessen the weight which it is capable of raising.

The moveable pulley by distributing the weights into separate parts, is attended by mechanical advantages proportioned to the number of points of support. Movable pulleys may be arranged according to different systems which increase the efficacy of a given power in different degrees.

By means of the pulley great facilities are afforded in raising heavy weights, as boxes of merchandise or heavy blocks of stone. Fig. 11 represents a convenient method in building brick chimneys for steam plants which has been observed by the author, as used by Glasgow, Scotland, masons and builders.

The crane at B enables the workmen when the brick and mortar are raised, to swing it around to the point where it is to be laid or to a platform near it.

The lower cord of the rope C D is connected with a wheel and axle; in the illustration, it may be seen, that instead of the wheel and axle we might fasten a horse to the rope, or attach a sweep to the top of the axis and join a team of horses to the end of it to expedite the work.

The employment of this device, in sufficiently large chimneys, enables the builder to dispense with the use of scaffolding, the workmen building into the corners of the chimney, as the work progresses, a ladder of or inch round iron every fifteen inches, to enable them to go up and down in the interior of the flue. Thus a large expense is saved in cost of scaffold, aud the risk is less for the mason.