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Drilling a Triangular Hole

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rotation amount, θ
radius of small arc, r
show locus of center
show junction points and circular arcs
The construction shown allows you to turn circular motion into triangular motion and so construct a drill for triangular holes. The roller—the yellow shape that rotates inside the large triangle—consists of four circular arcs. As it rotates, the centers of the smaller circles trace out an exact equilateral triangle. You can vary the size of the roller so as to get triangular holes of different sizes without changing the ambient triangle.
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