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| Trigonometry Homework for the Maths Gurus: Please help :) |
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| awemawson:
In the attached drawing I need to calculate the length 'L' (line A-D) that runs from the centre of circle radius R to intercept chord B-C, where the chord subtends angle B-A-C and the unknown line is at angle B-A-D. Note I need this for any angle B-A-D, not just for the line intercepting at right angles :( Why do I need this? Think Traub CNC Lathe : The circle represents a part in the chuck in the main spindle. The line L is in the direction of the X axis of the lathe - ie tool in or out, and the tool will be a milling cutter rotating with its axis parallel to the main spindle. The main spindle will progress round the circle using it's precision 'C' axis for positioning, and the X axis will move in and out producing a flat on the work represented by the chord B-C. I want to produce a general purpose algorithm for work of varying diameter and varying chord lengths. Any help from the less mathematically challenged than I would be much appreciated :thumbup: |
| mklotz:
angle ABC = (180 - BAC)/2 angle ADB = 180 - ABC - BAD Then: L/sin(ABD) = R/sin(ADB) so: L = R*sin(ABD)/sin(ADB) A remark on notation: Labeling angles as you have done can lead easily to confusion. Mathematicians generally label angles with a single (often Greek) letter to simplify identification. |
| awemawson:
Thanks Marv. It's a quick autocad sketch and I couldn't find alpha beta gamma etc :) I actually need L as a function of angles BAC and BAD. BAD will be the control variable, ie the rotation of the main spindle as the cut progresses, BAC being part of the set up defining the part. |
| mklotz:
BAC should have appeared in the first equation. Damn notation caught me. I've fixed it in my post. |
| awemawson:
Thanks Marv, but I'm obviously missing something here :) Your equation is in terms of angles ABD and ADB, neither of which are known values My known values are: R = radius of circle Angle BAC = angle subtended by the chord Angle BAD = angle of line L intersecting the chord whose length I want. (I suspect that as angle BAD sweeps from zero to ultimately being equal to angle BAC, the point of intersection of the line L and the chord describes a segment of a circle but I've not been able to prove it. It is this point of intersection that is the tangential point of cutting of the milling cutter.) |
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