Involutes
Introduction
Some geometric figures are not bound by straight lines and arcs. They have
no closed form but continue to spiral. This type of geometric figure is called
an involute. Gear teeth and interlocking mechanisms are often depicted using
this type of figure.
Involutes
An involute is the path of a point on a string as it unwinds from a line,
polygon, or circle. Involutes are compound tangential arcs and semicircles of
increasing larger diameters formed by lines, triangles, squares, and circles.
Involute of a
line
To draw an involute of a line, use this table:
Step
Action
1
Given line AB, use line AB as a radius and B as a center to draw a
semicircle AC.
2
Use AC as a radius and A as a center to draw another semicircle
CD.
3
With BD as a radius and B as a center, draw semicircle DE.
4
Continue to repeat this pattern until the drawing is complete.
Darken all outlines.
Figure 2-52 is an example of an involute of a line.
Figure 2-52.—The involute
of a line.
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