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MECHANICS.
safe, although, under certain circumstances, for instance, in a
mechanism working continuously, such a load may be too much
for the best results with regard to wear.
For anything working like a jack-screw, when the diameter
of the screw is over one inch, the load given in the last column
is perfectly safe. It is impossible to give rules which will suit
all cases ; the experience and judgment of the designer are the
best guide with regard to the selection of the proper load. It
may seem too much to use 0.16 as the coefficient of friction in
the thread of the screw, but the author believes, from careful
experiments made on common square-thread screws, as used in
commercial machinery,—not made for experimental purposes,
but for every-day use,—that this coefficient of friction is a safe
average. It is well to remember that the surfaces of the thread
on screws with cast-iron nuts do not always have the best of
finish, and the nut especially is liable to be a little rough when
new ; therefore, this coefficient of friction may be a little greater
than that found in screws in machinery when well lubricated
and with surfaces smoothed down and glazed over from wear.
The Parallelogram of Forces.
A line may be drawn to such fig. 20.
scale that its length represents a ^""T\
given force acting in the direction c^’ \ \
of the line. Another line is drawn
to the same scale, from the same
point of application, and its length
represents another force acting in
the same direction as this line. If
these two lines are connected by
two auxiliary lines, a parallelogram
is formed and the diagonal of the parallelogram will represent
both the magnitude and the direction of the resulting force.
Example.
Let the lines a and b in Fig. 20 represent two forces acting
in the direction of the arrows. Draw the lines to any scale, for
instance, T\ inch to a pound ; if the force represented by a is 64
pounds, the line a will be 64 X TV = 4" long. If the force rep-
resented by b is 50 pounds, this line will be 50 X T
X
,
T = 3>6"
long. Completing the parallelogram by drawing lines c and </,
the diagonal, x, will indicate the magnitude and direction of the
resulting force. Suppose these two forces act in such direc-
tions that when the parallelogram is completed and the diagonal
drawn, it is, by measurement, found to be 4U" long = |f;
then the result of the two forces, a and b, is a force of 76
pounds. In many cases, the result of force and stress in ma-
chinery and structures may very conveniently be obtained in this
way with much less labor than by calculation, and with accuracy
consistent with good, legitimate practice.
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