HELP!! Sometime ago, there was an article, or a sidebar, on a trig based formula for converting two angles to one angle, as in for drilling. If you want to drill a hole that is 15.7 degrees off of vertical in one direction, and 7.2 degrees off of vertical at 90 degress to the first angle, that can be converted to a single angle, using trigonometry. Build a jig or sled to that single angle, line up a line drawn between the centers of a pair of opposite holes with the center of the column of a drill press, and you have it. I think the article or note was in connection with drilling the splayed leg holes on a windsor chair.
With this method, one need not build a sled for the first angle, and then tilt the DP table to the other, and then try to hold the stock without being clumsy.
I can’t locate this article in the FWW index, and wonder if someone can help with the Issue number.
Thanks for helping someone with all too many senior moments theswe days.
Alan
www.alanturnerfurnituremaker.com
Replies
Dont know about the FWW but the line linking the leg holes is called a sight line Drew Langsners book " The Chairmakers Workshop" has lots of info and charts on it.You need to build a tilting table for the drill NOT a sliding table.
Here's a site that looks like it might have what you need.
http://www.puzzlecraft.com/Projects/HTMAP/06kine.htm
You will still need two angle: one is the deviation from vertical, and the other is the direction you need to tilt. Here's a quick solution that should be checked, but is probably right. I make not comment on how to actually hold the work, but these should be the angles you want.
If you have a flat surface you want to drill, with a spot marked and a line going to the right (R) from it, and another at 90 degrees to the first going toward your (T), we can describe the tilt from vertical in the direction of the line to the right as R, and the tilt from vertical in the other direction as T. We are seeking the angle V from the vertical that we get after tilting to both those angles, and the direction angle D in the plane of the surface, measured from R toward T, that specifies where to point the tilt.
V = acos(cos(R) x cos(T))
Where V is the angle measured from vertical, R is angle to right, T is angle toward you.
D = atan(sin(T) / sin(R))
Where D is the direction to point the tilt, measured from R toward T.
Actually, rather than the deviation from vertical V, you may find the angle from horizontal H easier to work with. H = 90 - V. That way you can measure on the surface from R toward T, mark the direction, and then measure the angle up from there.
Make sure your calculator is set to use degrees rather than radians by checking that it gives you sin(90) = 1 and sin(0) = 0. Then plug your angles into the equations above to find the angles you want.
acos means arc cosine, and may be indicated by checking the "inverse" box on the calculator built into windows. (Under accessories in the start menu. If it doesn't show you trig functions, select "scientific" from its view menu.) Some calculators label acos as cos-1 (with the -1 as a superscript.) Similarly, atan is the inverse of tan.
Alan This was explained in FWW May/June 1980 issue 22 page 71 Chris
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