If you pull the lever handle around one turn, its outer
end has described a circle. The circumference of this
circle is equal to 2x. (Remember that n equals 3.14, or
22/7). That is the distance you must apply the effort of the
At the same time, the screw has made one
revolution, raising its height to equal its pitch (y). You
might say that one full thread has come up out of the
base. At any rate, the load has risen a distance p.
Remember that the theoretical mechanical advan-
tage (T.M.A.) is equal to the distance through which you
apply the effort or pull, divided by the distance and
resistance the load is moved. Assuming a 2-foot, or
24-inch, length for the lever arm and a 1/4-inch pitch for
the thread, you can find the theoretical mechanical
advantage by the formula
r = length of handle = 24 inches
p = pitch, or distance between corresponding
points on successive threads = 1/4 inch.
A 50-pound pull on the handle would result in a
theoretical lift of 50 x 602 or about 30,000 pounds15
tons for 50 pounds.
However, jacks have considerable friction loss. The
threads are cut so that the force used to overcome
friction is greater than the force used to do useful work.
If the threads were not cut this way and no friction were
present, the weight of the load would cause the jack to
spin right back down to the bottom as soon as you
released the handle.
In using the jack you exerted your effort through a
distance of 2nr, or 150 inches, to raise the screw 1/4
inch. It takes a lot of circular motion to get a small
amount of straight line motion from the head of the jack.
You will use this point to your advantage in the
micrometer; its a useful device for making accurate
small measurementsmeasurements of a few
thousandths of an inch.
In figure 5-3, you see a cutaway view of a
micrometer. The thimble turns freely on the sleeve,
Figure 5-3.-A micrometer.
Figure 5-4.Taking turns.
rigidly attached to the micrometer frame. The spindle
attaches to the thimble and is fitted with screw threads
that move the spindle and thimble to the right or left in
the sleeve when you rotate the thimble. These screw
threads are cut 40 threads to the inch. Hence, one turn
of the thimble moves the spindle and thimble 1/40 of
inch. This represents one of the smallest divisions on the
micrometer. Four of these small divisions make 4/40 of
an inch, or 1/10 inch. Thus, the distance from 0 to 1 or
1 to 2 on the sleeve represents 1/10, or 0.1, inch.
To allow even finer measurements, the thimble is
divided into 25 equal parts. It is laid out by graduation
marks around its rim, as shown in figure 5-4. If you turn
the thimble through 25 of these equal parts, you have
made one complete revolution of the screw. This
represents a lengthwise movement of 1/40 of an inch. If
you turn the thimble one of these units on its scale, you
have moved the spindle a distance of 1/25 of 1/40 inch,
or 1/1000 of an inch0.001 inch.
The micrometer in figure 5-4 reads 0.503 inch, that
is the true diameter of the half-inch drill-bit shank
measured. This tells you that the diameter of this bit is
0.003 inch greater than its nominal diameter of 1/2