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When using a CNC machine to cut out designs, it's very important to understand how to draft good inside corners to be cut by the round bit.  I see a lot of very poor methods in designs and posts on the internet, so I thought I would help explain how best to do it.

First, lets look at a simple inside corner in a drawing.

We want to take the upper right corner, and cut it from the inside as the bit approaches from the lower left.  We'll use this red circle to describe the round spinning bit.  As you can see, it won't fit cleanly into the corner.

If we cut it like this, we would result in a picture like this.  You can now follow the white line around the corner.  This is often called a fillet when done intentionally, but we didn't want this.  The yellow dashed area is what we wanted, and was not cut.

When cut, it would look like this.

So now lets look at how most people solve this, without putting too much thought into it.  This isn't a very good way.  They simply draw a circle at the corner, that is the same size as the bit.

When we look at the cut result, you can see that it does do the job.  In this picture, red is again the bit, the white line is the resulting cut, yellow is where we wanted the corner, and green is the toolpath that the center of the bit would trace out.

And here is what it would look like, without any of the extra information.

Why would this not be a good method, since it obviously clears the entire corner and gets the job done?  It's lazy, and overkill in a bad way.  We've removed WAY more material, and weakened the corner far more, than we need to.

A good corner will take the bit so that the edge of the cut just touches the actual corner shape we want to cut.  Notice that the bit, in red, completely contains the corner.

How do we get this positioning?  It's simple, and works because our bit is round and has a radius.  When we look at this round bit, we know that the radius is touching the corner, and also the bit's center.  Here you can see that the radius has been added as a magenta (purple/pink) line.

To work backwards, if we have a corner that we want to cut this shape into, we draw a line that is the same length as the bit's radius.  (The line always bisects, or divides in half, the angle of the corner.  In our case here, it's a 90-degree angle so the line is drawn at 45-degrees.  If the interior angle was a different angle, you could just divide it in half.)

You then draw a circle with a center at the internal end of the line, and a radius to the corner.  You can see here in yellow where we've cut through the "walls" of the corner.  The bit, in red, will slip into the corner and get it clear with minimal material removed.

Cleaned out, by trimming out all the extra lines, we get this clean optimal corner.

Here is what the toolpath, in green looks like.  You can see it comes into the corner, along the edge, then dips briefly in towards the corner, then goes back out and continues down the other wall.  (The green line toolpath never crosses into the magenta radius line.  It only goes right up to the tip of the radius line, then turns back.)

So how efficient is this?  Very.  In these drawings, which are enlarged, it looks like the bit is removing quite a bit of material, but it's not really.  Look at this picture, where we have added the height of the chord at the top, in cyan (light blue).  The cyan line is the "height" of the mound created by the arc, in our case, how far into the corner's ideal wall that our bit had to go in order to clear the corner.  Compare the length of the cyan line to the magenta line (the bit's radius).  The ratio of this chord height to the bit's radius is always about 1:3.41.  In other words, it's less than 1/3 of the bit's radius!  With a 1/4" bit, it's a little over 1/16".

Above, we talked about the most efficient corner.  It was balanced, since it didn't favor either side of the corner.  What if we needed to make sure one side of the corner was flat, so that it could support forces better for instance?  We essentially have two options - the T-Corner and the H-Corner.

Here is the basic double inside corner.

And using our efficient corner we learned above, it would look like this.

To build a T-Corner, in order to leave a nice flat landing in the pocket of the corner to support the force of whatever fits inside, we add two radii like we did for the efficient corner.  We draw line segments that are perpendicular (90-degrees) to the flat bottom of the pocket.  In this case, those magenta lines go right down the sides of the pocket, but would not if the corners were not 90-degrees too.  Just like before, we then draw circles from the open end of this line, with the radius to the corner.

This will result in a cut that obviously deserves the name "T-Corner".

The toolpath, in green, for a T-Corner follows an obvious 'T' shape.

An H-Corner is similar, but is used when we want to favor the sides of the notch.  We draw our magenta radius perpendicular to the sides, which puts them along the top in this case.

The H-Corner looks like this when finished.

Here's the toolpath, in green, for an H-Corner.

The most efficient corner design is created by drawing a circle that touches the corner, using a line the same length as the bit's radius as a construction line.

We also have a couple options, if we need to favor strength in a particular direction, or hide the extra cutout.  We can use the same efficent corner, a T-Corner, or an H-Corner.

Some CAM software can do this cornering for you, so that you don't have to draft the drawing hard-coded to the bit's diameter.  If your CAM software does not, it may be possible to write a plugin for it to make it do this cornering.  If you're not sure, check the options in your software.