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Hey Tiff, after some manipulation of the size of the page of formulas I was able to get it on one page in Word and will store it and make some printed copies to use in the shop. I don't think I have ever seen a simpler set of formula to find the bolt circle dia. or sides of the circle.
If you have a mill with a dro, you can indicate center of each hole and record the xy positions. Then you can trig things out. Sort of a poor mans cmm.
I have a DRO but there are times when you can't get the part off to lay it on the table and then you need the formulas. The formulas I have are not as easy to use as these.
For any even number of hole BC take two screws and measure across them with calipers or micrometer. Subtract the size of screw. For odd number of holes. Measure between two holes and trig it out using half the distance hole to hole for the radius. Off at work we have to do drawings out on the floor of machines that come in for service. Sometimes they will have one hole offset so it has to go together the right way. Then we have to trig it out to come up with the angle. Not surprisingly the offset is usually 5D
Forty plus years and I still have ten toes, ten fingers and both eyes. I must be doing something right.
In a right angle triangle the tangent ratio (TAN) of an angle (A) is the ratio of the side opposite (OPP) the angle concerned (A) to the side adjacent (ADJ) to the angle.
TAN A = OPP:ADJ = OPP/ADJ
TAN A/1 = OPP/ADJ
The cotangent ratio is TAN/1 inverted ie it is 1/TAN
For the equation to be valid, both sides of it must be inverted ie TAN A/1 inverted becomes 1/TAN A = COT A
So.
TAN A/1 = OPP/ADJ = 1/COT A
Invert all three expressions or values and we get:
as promised, I have completed the sketches for hole spacings, centre distances and lay/set-outs for equi-sized and equi-spaced holes - Sketch/sheet 1 - as well as the general case - Sketch/sheet 2 - where the holes may or may not be the same size or equally-spaced and may be on or off the centres or pitch circles.
I really enjoy your hand drawings, Tiffie. Sometimes it's just nice to see something not drawn by CAD.
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