[Fig. 117] gives a type of winch in its simplest form. The mechanical advantage gained by its use depends upon the difference between the radius of the driving wheel and the radius of the axle; or the circumference of the wheel and the circumference of the axle.
If the radius of the axle were the same as the radius of the wheel, no mechanical advantage would be gained by its use. The advantage that is gained by the arrangement can be calculated as follows:
As the radius of the wheel is to the radius of the drum so is the weight that can be lifted to the power applied to the handle.
Example.
Let radius of wheel = R,
radius of drum = r,
power applied to handle = P,
and weight lifted = W.
(R × P)/r = W.
Then if R = 12 inches,
r = 4 inches,
P = 60 lbs.
(12 × 60)/4 = 720/4 = 180 lbs. weight that can be lifted, giving a mechanical advantage of 3.
It is obvious that, owing to the restriction of size, the mechanical advantage that can be gained by the simple machine shown on this figure is limited. To overcome this difficulty one, two, or three pairs of toothed wheels are introduced into the machine, being thus known as a single, double, or treble purchase winch or crab. The difference in the number of teeth between the pinions and wheels gives the increased mechanical advantage that is required. The method by which to find the mechanical advantage gained is as follows:
The pressure exerted on the handle is to the weight lifted as the radius of the drum multiplied by the number of teeth in the pinions is to the radius of handle multiplied by the number of teeth in the wheels.
Winches, besides lifting from the barrel, are also used in conjunction with pulley wheels to change the direction of the force and to gain additional mechanical advantage. If a double rope be used, considerable time will be saved in the progress of the work.
Fig. 117
[Fig. 118] shows the double rope. The middle of the rope is given a few turns round the drum, and the ends are continued over the pulleys, one sufficiently far to reach the ground. On raising the load the higher end of the rope descends, and is ready to carry up the next load by the time the first has been taken off. The illustration also shows the winch at work in connection with one movable pulley; but unless the material is to be raised to different heights, the same system of pulleys should be used on each rope.