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Author Topic: How to calculate tenon angle for kneebrace that is not equilateral triangle?  (Read 534 times)

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Offline Mad Professor

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The "Star of David"

1) Scribe a line, chalkline or centerline.   From a point of reference on this line, using the compass scribe a circle of desired radius.  This could be timber within a timber.

2) Where this 1st circle radius/arc intersects centerline, use these points as a center, to scribe two more circles of same radius.

3) Note that each of these circles intersect original circle, twice.  Where the arcs intersect, on each pair of circles, connect the points.  These lines will be perfectly square to the centerline, and the intersect the arc of the first circle and centerline.

4) From the intersection of the circle arcs in 3, Draw lines to the center of the 2nd or 3rd circle/intersection of first circle radius/arc at centerline, giving two 1 1 1 equilateral triangles.  You should now have two "Stars of David".

5) Connecting the intersection of the points of the star/original circle, on either side of the centerline, gives a perfectly parallel lines to the centerline.    

This method of making 90o and 180o to centerline is more accurate than using modern tools.

If you just need a 90o to centerline this can be done much quicker.   From the first point, only intersecting arcs need be drawn. Set your compass, draw two points both sides of reference centerline point.  Open compass for bigger circle. From outer points scribe two arcs from each side of center point.  The arcs will cross from each side, a when connected form a 90o line to centerline

I spent a whole summer just drawing and re-learning geometry/analytic geometry.  This is the most basic where you never need trig/tables/calcs/rulers/squares


Offline Yokosukadweller

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Thank you for adding a big task for me here. I have to admit I need it. It has been too long since I learnt trigonometry. And as excuse I might say, back then it was all just on paper and never applied. I will carefully try to visualise and practice it when the winter comes.

For now, and because I need those two braces cut, I basically had to find another way out. Assemble and trace a jig to get the right angles. I had already cut one brace with wrong angles, I dont know if it was because the wood was not entirely straight, or my speed square is off, or a combination. But luckily there was enough wood left over to adjust the angle and cut again. Such heavy, beautiful and fragrant timber hinoki is. I did not want to waste it.



Dane living in Japan

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