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ELLIPSE BY PIN-AND-STRING
METHOD The dimensions
of an ellipse are given in terms of the lengths of the major (longer)
and minor (shorter) axes. Figure 4-44 shows a method of con- structing
an ellipse that is called the pin-and-string method. The problem is to
construct an ellipse with a major axis, AB, and a minor axis, CD. Set a
compass to one-half the length of AB, and, with
C as a center, strike arcs intersecting AB at
F and F. The points F and F are called the
foci of the ellipse. Set a pin at point C,
another at F, and a third at F. Tie the
end of a piece of string to the pin at F, pass the
string around the pin at C, draw it taut, and fasten
it to the pin at F. Remove the pin at C, place the
pencil point in the bight of the string, and draw
the ellipse as shown in view C, keeping the string
taut all the way around.
Figure 4-45.-Ellipse by four-center method. ELLIPSE BY FOUR-CENTER METHOD The four-center method is used for small ellipses. Given major axis, AB, and minor axis, CD, mutually perpendicular at their midpoint, O, as shown in figure 4-45, draw AD, connecting the end points of the two axes. With the dividers set to DO, measure DO along AO and reset the dividers on the remaining distance to O. With the difference of semiaxes thus set on the dividers, mark off DE equal to AO minus DO. Draw perpendicular bisector AE, and extend it to intersect the major axis at K and the minor axis extended at H. With the dividers, mark off OM equal to OK, and OL equal to OH. With H as a center and radius R1 equal to HD, draw the bottom arc. With L as a center and the same radius as R1, draw the top arc. With M as a center and the radius R2 equal to MB draw the end arc. With K as a center and the same radius, R2, draw the end arc. The four circular arcs thus drawn meet, in common points of tangency, P, at the ends of their radii in their lines of centers.ELLIPSE BY CONCENTRIC-CIRCLE METHODFigure 4-46 shows the concentric-circle method of drawing an ellipse. With the point of inter-section between the axes as a center, draw two concentric circles (circles with a common center), one with a diameter equal to the major axis and the other with a diameter equal to the minor axis, as shown in figure 4-46, view A. Draw a number of diameters as shown in figure 4-46, view B. From the point of intersection of each diameter with the larger circle, draw a vertical line; and from the point of intersection of each diameter with the smaller circle, draw an intersecting horizontal line, as shown in figure 4-46, view C. Draw the ellipse through the points of inter-section, as shown in figure 4-46, view D, with a french curve.
Figure 4-46.-Ellipse by concentric-circle method. |
 
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