Use one side of AB as a radius and A as the center. Draw
an arc from B to the extension of side AC, as shown in
view B. Next, measure a radius the length of AC plus
its extension. With C as the center, draw an arc to the
extension of side BC. With BC plus its extension as the
radius and B as the center, draw an arc to the extension
of side AB, as shown in view C. Continue in this
manner until the figure is the desired size.
Drawing the Involute of a Circle
Consider the circle as a polygon with many sides.
Divide the circumference of the circle into several equal
segments (fig. 14-32, view A). Then, draw tangents
from each segment (view B). With the cord of a
segment as a radius, draw an arc from one segment to
intersect the tangent of the next segment, as shown in
view B. With the intersection point on this tangent to
the point of tangency as a radius, draw an arc to intersect
the next tangent (view C). Continue until the figure is
the required size.
Figure 14-33.--Drawing the spiral of Archimedes.
Drawing a Spiral of Archimedes
as a center, draw an arc from each of the numbered
segments that intersect the corresponding numbered
The spiral is generated by a point moving around a
divisions on the radius (view B). These intersections
fixed point, its distance increasing uniformly with the
are the points of the curve (view C).
angle. To draw a spiral that makes one turn in a given
circle, divide the circle into several equal segments (fig.
Drawing the Helix
14-33, view A). Then, divide the radius of a circle into
the same number of parts, and number them from the
Consider the helix (fig. 14-34), a curve that is
center outward (view A). Using the center of the circle
generated by a point moving uniformly along a straight
line that revolves around an axis. If the line moves
parallel to the axis, it will generate a cylindrical helix.
If it moves at an angle to the. axis, it will generate a
conical helix. The lead of a helix is the distance along
the axis to which the point advances in one revolution.
To draw a helix, draw two views of the cylinder, as
shown in view A. Divide the lead into an equal number
of parts. Divide the circle into the same number of parts
(view B). The intersection of the lines from these points
(view C) are the points of a cylindrical helix.
AREAS AND VOLUMES
You must be able to calculate the amount of
material needed to manufacture or repair many different
items used throughout the Navy. You must also be able
to determine the weight of the finished product to
calculate the approximate weight of an object. To do
this, you must have a knowledge of geometry and be
able to determine areas and volumes of geometric
shapes and figures.
Figure 14-32.--Drawing the involute of a circle.