Sunday, April 14, 2019

To Quote Mr. Bean: "I Concentrated on the Trigonometry"

I even received a B.  (Math classes were the only classes in high school where I did not easily get an A.)  So why is this so hard?  I am trying to cut a channel that is a right angle in a flat workpiece, with a 30 degree angle on one side and 60 degrees on the other.  This diagram:

where ACD is 30 degrees and ABD is 60.  So I wrote a program to compute a movement of my ball end mill from B to A on line b and then back up line c to B.  The first part worked pretty well, computing the depth of cut by using the distance along CD to calculate depth of cut as z=y sin 30.  (The cut is in the x direction.)

By using the right x, y, and z increments (very small), I got a pretty decent finish in redwood without any obvious steps:

(Ignore the gouge just left of center, there were several early tries.)  But the cut on the right is actually more like 30 degrees.  It is not a right angle.

So computing z for the 60 degree angle is apparently not z=y sin 60.  What am I calculating wrong?

Another solution, (clumsy).  I am not using my Sherline tilting table because the parts that show the angle prevent any mill vise larger than their 2" from going in there, and this is a 3" workpiece.  Clumsy solution to try: Make a block that is 2" wide to fit in the Sherline vise and extends out 2" above the vise to which I screw the workpiece.  This requires very precise alignment of workpiece to block in the Sherline vise, but I am running out of alternatives.

Cut a 3" x 3" block, square all sides, trim bottom to 2" x 2" x2" to fit in vise and extend beyond angle "ears."  Drill and tap two 1/2"-13 holes in workpiece and corresponding 1/2" through holes in the extension block.

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