Impossible Dovetail Cube

I decided to lay one out in SolidWorks. I chose a face angle of 60º. which requires a cut angle of 67.7923º. A 60º cut angle would yield a face angle of 50.77º. A cut angle of 76º (common woodworking dovetail angle) would yield a face angle of 70.58º.

For those interested in making one, the relationship between the cut angle A and the face angle B is tan(A) = sqrt(2)*tan(B).
.Dovetail Cube.JPG
 
I decided to lay one out in SolidWorks. I chose a face angle of 60º. which requires a cut angle of 67.7923º. A 60º cut angle would yield a face angle of 50.77º. A cut angle of 76º (common woodworking dovetail angle) would yield a face angle of 70.58º.

For those interested in making one, the relationship between the cut angle A and the face angle B is tan(A) = sqrt(2)*tan(B).

I realize I'm not the brightest colored crayon in the 64 box of Crayolas, but you lost me... what is this cut angle? In my simple terms, a 60 degree dovetail has a 60 degree angle. Please elaborate.

Thanks,
Ted
 
I realize I'm not the brightest colored crayon in the 64 box of Crayolas, but you lost me... what is this cut angle? In my simple terms, a 60 degree dovetail has a 60 degree angle. Please elaborate.

Thanks,
Ted

The cut angle is the angle of the actual cutter. Since the path of the dovetail cutter is at a 45º to the faces of the cube, the apparent angle on the faces is less than the cut angle. BTW, cut angle is a descriptive term that I coined, not necessarily the correct term.
Here are two views of the base. The first is from a plane perpendicular to the cut path and the second is from a plane parallel to a face. The difference between the actual and apparent angles is clear.
Dovetail Base, view 1.JPGDovetail Base, view 2.JPG
 
BTW, cut angle is a descriptive term that I coined, not necessarily the correct term.

OK, that clears things up. When I drew it up in Fusion 360, I made a custom view of the cube at a 45 degree angle so the actual cuts I needed to make on the mill (roughing) and shaper (finishing) were straight on since this is the way I had them oriented on my machines. I set and used 75 degrees for everything.

Didn't mean to hijack the thread, but this is all good info for anyone wanting to make one of these.

See my recent post here: https://www.hobby-machinist.com/threads/impossible-dovetail-puzzle-my-version.79744/

Thanks for the clarification,
Ted
 
Just to add to the content, the way I drew it up was the same as I had the pieces lined up in my machines... at a 45 degree angle. You can either turn your vise (or however you are holding them) to 45 degrees or use V blocks like I did. There are probably other ways of holding them and, of course, if you are using a CNC you can hold them any way you want with the proper programming.

Dovetail View.jpg

Using Fusion 360 I created a construction plane at 45 degrees and drew everything up in that view. In the view above, the center is looking head on to one of the corners. Everything is inline and no need for additional calculations for machining.

Also, I kept the two partial dovetails on the outside edges of this view at 1/2 the dovetail width. That makes everything come out right and look proportional.

Ted
 
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