{"id":2967,"date":"2012-10-12T20:00:49","date_gmt":"2012-10-13T00:00:49","guid":{"rendered":"http:\/\/www.paleotechnologist.net\/?p=2967"},"modified":"2012-10-12T13:38:22","modified_gmt":"2012-10-12T17:38:22","slug":"euclidean-construction","status":"publish","type":"post","link":"https:\/\/www.paleotechnologist.net\/?p=2967","title":{"rendered":"Euclidean Construction"},"content":{"rendered":"

The other day, I had an unusual request at work. (Actually, unusual requests aren’t<\/a> really <\/a>that<\/a> unusual<\/a> around here, which is one reason why my job is generally pretty cool.) Part holders were needed for ultrasonic calibration blocks — and these blocks had a strange, nonlinear shape.<\/p>\n

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The calibration block in question. (Click for larger.)<\/p><\/div>\n

Using calipers, I determined that the block was about 25.4mm (one inch) thick — and therefore, was probably calibrated in inches. The length of the top (hypotenuse?) measured right about three inches across, so this seemed to confirm the idea.<\/p>\n

How to measure the diameter of the semicircles, though, since only a small arc of each was available? High-school geometry, and a few assumptions, provided the answer. Both arcs looked to intersect the top at a 90-degree angle, meaning that the center of each arc had to be somewhere along that line. For the larger arc, a chord can be constructed between the two endpoints. Taking the perpendicular bisector of this arc (with a compass and straightedge) provides a bisector of the arc. The intersection of this line with the top of the piece locates the center of the circle. It turned out to have a radius of two inches, and its center turned out to also be the center of the smaller arc (with a radius of one inch).<\/p>\n

The final question was where to begin and end the arcs. Measuring the distance across the larger arc resulted in a length of very nearly two inches. Since this made sense (calibration blocks normally use nice round number measurements like this), I decided to treat this as exact. Using a virtual compass, I drew a third circle with radius two inches to locate the end point of the larger arc. Finally, I reasoned that the line segment from this point was tangent to the smaller circle, and added it accordingly.<\/p>\n

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The construction for the calibration block shape in Google SketchUp. (Click for larger.)<\/p><\/div>\n

Now that the measurements were known, it was fairly straightforward to design a holder jig in Google Sketchup and send it to our 3D printer. Score one for high-school geometry!<\/p>\n

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A Google SketchUp rendering of the holder. (Click for larger.)<\/p><\/div>\n","protected":false},"excerpt":{"rendered":"

It turns out that tenth-grade Geometry class has practical applications… Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_exactmetrics_skip_tracking":false,"footnotes":""},"categories":[306,220,222,380],"tags":[],"class_list":["post-2967","post","type-post","status-publish","format-standard","hentry","category-design","category-drexel","category-math","category-reverse-engineering"],"_links":{"self":[{"href":"https:\/\/www.paleotechnologist.net\/index.php?rest_route=\/wp\/v2\/posts\/2967","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.paleotechnologist.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.paleotechnologist.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.paleotechnologist.net\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.paleotechnologist.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2967"}],"version-history":[{"count":5,"href":"https:\/\/www.paleotechnologist.net\/index.php?rest_route=\/wp\/v2\/posts\/2967\/revisions"}],"predecessor-version":[{"id":2978,"href":"https:\/\/www.paleotechnologist.net\/index.php?rest_route=\/wp\/v2\/posts\/2967\/revisions\/2978"}],"wp:attachment":[{"href":"https:\/\/www.paleotechnologist.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2967"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.paleotechnologist.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2967"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.paleotechnologist.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2967"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}