You probably asked all of your math teachers “when and I’m going to use this stuff?”. Well that day is today. NESIT has a hand router that is missing the base plate. The base plate allows the router to smoothly slide across a piece of wood without getting hung up while also providing a sturdy base for the user to hold the router. NESIT has the technology available to make a replacement. Here’s how it’s done… and guess what, it includes some fun math!

We’ll need a few dimensions to make the router base plate. The diameter of the base is easily measured, the screw hole size is easy to determine and for the inner diameter, 2 inches was picked just because it seemed right. The only think left was to determine the spacing of the mounting holes for the screws. There are 3, making it difficult to directly measure the bolt hole circle diameter. The bolt hole pattern is the size of the circle the screw holes are spaced on.

Although we can’t measure the bolt hole pattern directly, we can do it in-directly using our friend Math. We start by measuring the distance between two of 3 screw holes that are in the base of the router. You could use a ruler to eye-ball the spacing but that is quite inaccurate. Using a caliper to eye-ball the distance between the holes is also kinda sketchy. There’s a trick you can do with a digital caliper to measure the center-to-center distance between two holes. Screw in screws to each hole. Then, instead of setting the digital caliper to zero with the jaws closed, set the caliper to zero with the jaws tightened on the screw diameter. Then use the calipers to measure the outside of one screw to the outside of the other. The value displayed on the digital caliper will be the center-to-center distance which is the value we need for our math equation later.

To help illustrate our situation, let’s draw a representation of the screw holes and their locations. It doesn’t necessarily have to be to scale or dimensionally accurate. Drawing some lines between the center of the bolt hole circle and each screw and another line between the two screws we measured creates a few triangles. These triangles will simplify our calculations, even if the high-level task seems a bit daunting. Such a drawing would look like this:

Our goal is to determine the bolt hole circle radius. We need that value in order to draw the hole position accurately in Corel Draw because the plate will be cut out using the Epilog laser. Looking at the triangles that we just drew, we notice that the radius of the bolt hole circle is one of the sides of one of the triangles (highlighted orange). We know one of the angles is 60 degrees and also know the length of one of the sides (because we just measured the screw center-to-center distance using digital calipers). The center-to-center distance turned out to be 4.642 inches, and our triangle side is half of that: 2.321 inches.

If you think back hard to good ole Geometry class from high school, you’ll remember the trigonometric mnemonic device: SOH CAH TOA. That saying reminds us how to use the trigonometric functions Sine, Cosine and Tangent. We’ll use one of these to calculate the bolt hole circle radius of the Router’s base.

Using the **SOH** from SOH CAH TOA, we recall that **S**ine of an angle equals the length of the **O**pposite side divided by the length of the **H**ypotenuse. So…

Sinθ = O/H

Sin60 = 2.321 / H

Sin60 * H = 2.321

H = 2.321 / Sin60

H = 2.680 inches

See, easy! We now know that the radius of the bolt hole circle is 2.680 inches. We use that dimension to position the center of the screw hole 2.680 inches above the center of the Outside Diameter of the plate. Copy that top hole 2 times and rotate those 120 degrees left and right and we have our plate mounting pattern. Before using up some valuable acrylic, a cardboard template was made to test the fit. It was dead on! After the plate was cut out on the laser cutter, the screw holes were countersunk on the drill press. The following photos are of the final product.