Introduction
For those sad, sad programs such as Corel Draw and Illustrator which
still don't have CAD tools, it is useful to know how to draw fillets. CNC routers have cutting bits with a non-zero diameter, which means that sharp inside corners cannot be cut.
Fillets are cutter-diameter circles that connect two lines where they meet at a corner, and are used to tell a CNC router how to deal with an inside corner.
This HOWTO covers drawing a
dog-bone fillet, so-called because it makes rectangles look like dog bone toys. I'm using Illustrator (CS4) here because I don't have Corel Draw, and I think that the important thing is the geometric construction, which should carry over to any tool you use.
In Illustrator, make sure you have Smart Guides and Snap to Point turned on. This helps you align your shapes properly.
- dogbone1.png (79.69 KiB) Viewed 10529 times
There are three cases: one where the inside corner is exactly 90 degrees, one where it is greater than 90 degrees, and one where it is less.
Exactly 90 degrees
Let's use this sample rectangle. We will add a dog-bone fillet to the upper left corner.
- dogbone2.png (1.38 KiB) Viewed 10529 times
First, decide on what your cutter diameter is. I will use 0.25 inches. If you're in a modern country, feel free to use metric. Now, compute 1.414 (i.e., square root of 2) times the diameter, rounding up to the nearest reasonable increment (0.001 inches or 0.01 mm) which in my case is 0.354 inches. Draw a circle of that diameter, centered on the corner. In Illustrator, this is done by selecting the Ellipse tool, clock on the desired corner, press Shift and Option (Alt on Windows), and drag a circle of any size. Then, with the circle selected, type in the diameter in the W field (make sure W and H are linked first so that they keep their 1:1 proportion).
- The W and H fields are at the upper right.
- dogbone3.png (34.97 KiB) Viewed 10529 times
Next, we need to draw a circle which intersects the intersections between the circle you just drew and the rectangle. In Illustrator, this is done by selecting the Ellipse tool, clicking on one intersection, and dragging while pressing Shift and Command (Control on Windows) until the circle snaps to the other intersection. Note that Illustrator has found the circle diameter to be 0.2503, which is good enough. As long as the circle is 0.25 or greater, you're safe. You can adjust the size using the W field if the circle turns out smaller.
- dogbone4.png (35.8 KiB) Viewed 10529 times
Now delete the first circle.
- dogbone5.png (2.61 KiB) Viewed 10529 times
The next step requires getting rid of the segments inside the new shape. Pull up the Pathfinder tool (Window > Pathfinder). Select both the circle and the rectangle.
- dogbone6.png (14.27 KiB) Viewed 10529 times
Now select the Unite tool (the leftmost tool in the upper row, also called Add to Shape Area in previous versions). Hopefully, you should get a shape which is the union of the two shapes:
- dogbone7.png (13.45 KiB) Viewed 10529 times
Do the same thing for the other corners. You can draw the circles first, then use the Pathfinder to Unite all the shapes at once.
- dogbone8.png (4.87 KiB) Viewed 10529 times
- dogbone9.png (3.43 KiB) Viewed 10529 times
Woof Woof! Yes, it sucks that you can't do this in one click, but if you know the keyboard shortcuts, it's fairly quick to draw dogbone fillets. But wait! This only works if your corner is 90 degrees. What about other angles?
Greater than 90 degrees
If your inside angle is greater than 90 degrees, then the diameter of your first circle has to be D / sin (angle/2), where D is the cutter diameter. For 90 degrees, this works out to 1.414 D. For a wide angle like 135 degrees, this works out to 1.082 D.
- dogbone10.png (3.97 KiB) Viewed 10529 times
Sadly, the Shift-Command trick above will not work here. Instead, draw a line between the two intersections:
- dogbone11.png (4.39 KiB) Viewed 10529 times
Now we will get the middle of the line. With the line still selected, go to Object > Path > Average and select Both. You are left with a single point which is the center of the line.
- dogbone12.png (19.45 KiB) Viewed 10529 times
- dogbone12a.png (4 KiB) Viewed 10529 times
Now you can use that point as the center of a 0.25 inch diameter circle.
- dogbone13.png (5.34 KiB) Viewed 10529 times
Delete the big circle, select the remaining circle and the shape, and Unite them.
- dogbone14.png (2.8 KiB) Viewed 10529 times
Less than 90 degrees
For angles less than 90 degrees, use the same formula to get your initial circle. For the 45 degree inside corner in the above shape, this would be 2.613 D, or 0.654 inches.
- dogbone15.png (8 KiB) Viewed 10529 times
It's so big because the opening inside the shape needs to be 0.25 inches. The narrower the opening, the farther into the shape you need to go to get 0.25 inches between the lines. Now, if we were to continue with drawing a line, taking the average, and drawing a 0.25 diameter circle,
we run into trouble:
- dogbone16.png (8.99 KiB) Viewed 10529 times
The problem is that the circle does not include the corner. Constructing the proper shape in this case is much more complex, and I hope you don't have to do many of them. But here's how. Start with drawing the line.
- dogbone17.png (7.49 KiB) Viewed 10529 times
Now, draw a line from the corner to the middle of that line. In Illustrator, you don't have to use average, since the smart guides will guide your line to the center of the first line.
- dogbone18.png (8.25 KiB) Viewed 10529 times
Now draw a circle of diameter TWICE that of your cutter diameter, centered on the corner. So I will draw a 0.5 inch diameter circle.
- dogbone19.png (10.75 KiB) Viewed 10529 times
Now select your second line segment and use the Pen tool to add an anchor point at the intersection of the line and the circle you just drew.
- dogbone20.png (10.51 KiB) Viewed 10529 times
Delete the circle, and use the direct selection tool to delete the endpoint of the line.
- dogbone21.png (8.12 KiB) Viewed 10529 times
Average the line to get its center point.
- dogbone22.png (7.73 KiB) Viewed 10529 times
Draw a cutter-diameter circle at that center.
- dogbone23.png (9.14 KiB) Viewed 10529 times
Make a COPY of the remaining line segment and move it so its center snaps to the center of the circle. You can do this by selecting it, then pressing Option (Alt) and dragging the line. If you did it right, you'll end up with a drawing like this:
- dogbone25.png (9.47 KiB) Viewed 10529 times
If, however, you did it wrong, you will have summoned the Great Duke of Hell
Vepar, who can apparently make men die in three days from worm-infested wounds, but will heal you if you ask nicely. Banish Vepar and try again.
Now use the Pen tool to make a box whose endpoints are the endpoints of the lines:
- dogbone26.png (10.19 KiB) Viewed 10529 times
Delete the big circle, select everything, and Unite.
- dogbone30.png (4.64 KiB) Viewed 10526 times
Note that there's a tiny piece left from the corner which may or may not be there. If it is, it shouldn't be a problem, it's just Illustrator drawing the anchor point funny.
Conclusion
Done! That sucked incredibly, but you got what you needed.
