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PROBLEMS IN GEOMETRICAL DRAWING. I 9 I
To draw an epicycloid (see Fig. 26), the generating circle a
and the fundamental circle B being given.
Solution :
Fig. 26
Concentric with the circle B, describe
an arc through the center of the generating
circle. Divide the circumference of the
generating circle into any number of equal
parts and set this off on the circumference
of the circle B. Through those points draw
radial lines extending until they intersect
the arc passing through the center of the
generating circle. These points of inter-
section give the centers for the different positions of the gener-
ating circle, and for the rest, the construction is essentially the
same as the cycloids. In Fig. 26, the generating circle is shown
in seven different positions’, and the point n, in the circumfer-
ence of the generating circle, may be followed from the position
at the extreme left for one full rotation, to the position where it
again touches the circle B.
To draw a hypocycloid. (See Fig. 27).
The hypocycloid is the line generated
by a point in a circle rolling within another
larger circle, and is constructed thus: (See
Fig. 27).
Fig. 27.
Divide the circumference of the gener-
ating circle into any number of equal parts.
Set off these on the circumference of the
fundamental circle. From each point of
division draw radial lines, 1, 2, 3, 4, 5, 6.
From 11 as center describe an arc through
the center of the generating circle, as the
arc c d. The point of intersection between this arc and the
radial lines are centers for the different positions of the gener-
ating circle. The distance from 1 to a on the fundamental
circle is set off from 1 on the generating circle in its first new
position ; the distance 2 to a on the fundamental circle is set off
from 2 on the generating circle in its second position, etc. For
the rest, the construction is substantially the same as Figs. 25
and 26.
Note.—If the diameter of the generating circle is equal to
the radius of the fundamental circle, the hypocycloid will be a
straight line, which is the diameter of the fundamental circle.
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