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190 PROBLEMS IN GEOMETRICAL DRAWING.
way marked out, draw the ellipse by using a scroll. It is a
property with ellipses that the sum of any two lines drawn from
the foci to any point in the circumference is equal to the largest
diameter. For instance
:
/1 e +fe, = ab, or/61
-f-/
1
6\ = a b.
Cycloids.
Suppose that a round disc, c, rolls on a straight line, a b, and
that a lead pencil is fastened at the point r; it will then describe
a curved line, a, /, r, n, b. This
line is called a cvcloid. (See
Fig. 24).
This supposed disk is usual-
ly called the generating circle.
The line a b is the base line of
the cycloid and is equal in length
to 7T times m r, or practically 3.1416 times the diameter of the
generating circle. The length of the curved line a, I, r, «, b, is
four times r ?n, (four times as long as the diameter of the
generating circle).
A circle rolling on a straight line generates a cycloid.
(See Figs. 24 and 25).
A circle rolling upon another circle is generating an
epicycloid. (See Fig. 26).
A circle rolling within another circle generates a hyfio-
cycloid. (See Fig. 27).
To draw a cycloid, the generating circle being given.
Solution
:
Divide the diameter of the
rolling circle in 7 equal parts.
Set off 11 of these parts on each
side of a on the line d e. This
will give a base line practically
equal to the circumference.
Divide the base line from the
point a into any number of equal parts; erect the perpendicu-
lars, with center-line as centers and a radius equal to the radius
of the generating circle describe the arcs. On the first arc from
d or e set off one part of the base line. On the second arc set
off two parts of the baseline; on the third arc three parts, etc.
This will give the points through which to draw the cycloid.
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