Wednesday, September 26, 2007

Machining the Regular Hexagon

Thanks to all my readers who found the problem with my previous geometry problem. Here's today's opportunity to exercise your brain.

I need to be able to machine a regular hexagon. I've already decided that even using a template doesn't produce a sufficiently perfect hexagon. I have a tilting table for my mill that lets me put a rectangle (length = 1.156 width) at a 60 degree angle. But when the table tilts the rectangle, where do I position the cutting edge?

The first diagram shows the rectangle as it is positioned in a mill vise on the tilt table in the 0 degree position. (The thickness of the tilt table turns out not to be relevant--only the distance from the pivot point to the edge of the rectangle.) It also shows the equations that I have persuaded myself identify the position of the first cut (C) relative to the pivot point.

The second diagram shows it in the 60 degree position.

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