InvolutesIntroductionSome geometric figures are not bound by straight lines and arcs. They haveno closed form but continue to spiral. This type of geometric figure is calledan involute. Gear teeth and interlocking mechanisms are often depicted usingthis type of figure.InvolutesAn 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 ofincreasing larger diameters formed by lines, triangles, squares, and circles.Involute of alineTo draw an involute of a line, use this table:StepAction1Given line AB, use line AB as a radius and B as a center to draw asemicircle AC.2Use AC as a radius and A as a center to draw another semicircleCD.3With BD as a radius and B as a center, draw semicircle DE.4Continue 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 involuteof a line.Continued on next page2-54

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