On 2010-04-30, wrote:
On Apr 30, 8:54*am, Chris Wilson wrote:
My maths is appalling, I am sorry to say. Yesterday I wanted to work out
the X and Y axis movement on a milling machine to drill two holes opposite
one another skewed 45 degrees from the vertical at a known PCD . I had the
machine zeroed on the centre of the hole around which these drillings were
needed. Took me ages as I have forgotten most of my Trig and I couldn't
find a suitable calculator Is there any easy to use engineering software
for this sort of thing? It's at times like this a CNC machine seems
wonderful Ta!

A cheap CAD package would probably do it, or a little work with
memorizing what the trig functions REALLY mean along with a dollar
store "scientific" calculator would do as well. I've picked those up
for as little as $6 from Big Lots. I find the calculator is faster
for most things. Holes in a circle might be the break-point. It also
helps to know that the length of the hypotenuse of a 45 degree right
triangle is the square root of 2 times either side in length, a
special case along with a 30-60-90 triangle. See Pythagorean
theorem. From that it should be dead easy to work out X-Y, even with
a pocket four-banger calculator. Banging away at problems 5 days a
week at 7:30 in the morning for a couple of years will embed this
stuff permanently.

If you have a scientific calculator like the HP-15C which has
polar to rectangular and rectangular to polar conversions it is dead
easy. Assume that the first hole is on the X axis in line with the
center hole, and you will be putting an integer number of holes evenly
spaced around the center hole. Divide the number of holes into 360 to
get the angular increment (6 holes is 60 degrees per hole, the most
common arrangement). Key in the angle (60 degrees) and the radius (say
a 4" circle of holes would have a radius of 2", and then hit the P-R
button and this puts the second hole at 1.0000" X and 1.7321" Y. Add
another 60 to make 120 degrees, and repeat with the same radius and you
get -1.0000" X and 1.7321" Y. Another increment is 180 degrees, and
gives -2.0000" X and 0.0000" Y exactly opposite the first hole which was
our starting point, not calculated. Continue for another 60 degrees and
you get 240 degrees, -1.0000 X, -1.7321" Y, and another 60 degrees makes
it 300 degrees, 1.0000" X and -1.7321" Y. Note that with six holes, the
numbers start to look very familiar fairly quickly.

Now if you were to go for something like 7 holes 51.4286 degrees
per increment, things will look pretty ugly after the starting point of
2.000 X, 0.000 Y. Let's put them in table form for this one.

hole# Angle X Y
0 0 2.0000 0.0000
1 51.4286 1.2470 1.5637
2 102.8571 -0.4450 1.9499
3 154.2857 -1.8019 0.8678
4 208.7143 -1.8019 -0.8678
5 257.1429 -0.4450 -1.9499
6 308.5714 1.2470 -1.5637
7 360.0000 2.0000 0.0000

Note that hole #7 is back to the beginning.

You'll still see some repeating numbers with different signs,
but not as many as with six.

If you don't want to start with your first hole on the X axis,
you can do something like divide the increment by two and calculate
every hole. For a 6-hole circle this will give equal spacings of first
and last hole above and below the X axis, and put the 2nd and 5th holes
on the Y axis. Or, you could divide the starting angle by four and miss
all of the axes. All depending on what you want.

While I can't set my machine to 0.0001" increments, I calculate
to four significant figures (especially when generating it all
mathematically) to get a feel for which way to round. :-)

If you want to write a program in BASIC or C or most other
languages, beware that the default angular measurement is radians (2 pi
of them per full circle) so you will have to convert your degrees to
radians before calculating.

In a spreadsheet, you might have degrees available. Check what
you have. Take the arc sine of 0.707 (which should come out close to 45
in degrees.) If you get 0.7852 or close, you are in radians. If you
get almost 50, you are in gradians (100 per quarter circle, or 400 per
full circle).

Enjoy,
DoN.

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