geometric solution for circular bolt hole

[New chips]

I just came across this geometric solution to laying out bolt hole patterns on a circle. For any diameter circle AD divide the diameter into as many equal part as bolt holes needed. Then draw an arc intersection that has a radius of the diameter of the circle from A and D and labial this E. A,D,E form an equal lateral triangle with A,D as diameter of circle. Now draw a line from E throw the second equal point from A on the diameter to intersect with the far side of arc of the circle and labial this F. Now take dividers and set to length A,F. Use this length to work around circle to divide the circle evenly.

[Paul Alciatore]

Before looking for a mathmatical proof of this, I tried a few examples with my CAD program. It works for 3, 4, and 6 divisions but not for 5, or 12. It appears to be an approximation that is limited to some low count divisions.

[luthor]

Why not just use TRIG, it's spot on for any number of holes, or refer to Machinery's Handbook.

[Carld]

Yep, Machinery handbook, Everede bolt circle slide rule or DRO. Works perfect everytime.

BUT, if you have to lay out the bolt circle by hand, then using cordinates don't work. I use the guess work method and keep trying untill all the holes fit evenly on the circumference.

[Dawai]

Marvin Klotz posted a program to do this in dos,

I posted one that does polar holes locations in visual basic.. runs in windows.. It is archived on the www.metalillness.com site in documents section.

[New chips]

Paul
It does work for 5 divisions. I jest ran it on my CAD program. It is not approximate I expect you set your cad program to round to only 3 digits set to 6 or more it is dead nut on.
Luthor
Can you measure 100 thousands I cant you can use jest parallels and scribe and careful layout to do it.
Carld, David
Yes DRO and dividing head will do it. I have seen posts of Newbes asking how to make dividing plates this will work with jest careful layout.

[luthor]

[QUOTE=New chips]Paul
Luthor
Can you measure 100 thousands I cant you can use jest parallels and scribe and careful layout to do it.

Huh????????

[Dawai]

I've done it with graph paper, caliper and a punch too.

You can lay it out on cad, print it 1:1 and punch right through the paper.. I used to do printed circuits like this too.. drill right through the paper.

Stubborn as heck.. You have to be when you are poor.

[boslab]

buy youself a chord rule and a dividers, it works, flanges that fit arent that difficult with a little practice and a lot of faith

[Paul Alciatore]

Paul
It does work for 5 divisions. I jest ran it on my CAD program. It is not approximate I expect you set your cad program to round to only 3 digits set to 6 or more it is dead nut on.
Luthor
Can you measure 100 thousands I cant you can use jest parallels and scribe and careful layout to do it.
Carld, David
Yes DRO and dividing head will do it. I have seen posts of Newbes asking how to make dividing plates this will work with jest careful layout.

My CAD is "set" to more than 6 digits. Five inch circle divided into five and it was off by about 0.002" per hole: total error at the end was about 0.010". Eight inch circle divided into eight and each hole is off by 0.013": total error about 0.104". Six inch circle divided into 12 and each hole was off by almost 0.025": total error about 0.300". I don't know.

Have you seen any proper mathematical proof of this method? Are you sure you did it properly in the CAD program? There are so many other ways that I wouldn't risk using this.

[Paul Alciatore]

I've done it with graph paper, caliper and a punch too.

You can lay it out on cad, print it 1:1 and punch right through the paper.. I used to do printed circuits like this too.. drill right through the paper.

Stubborn as heck.. You have to be when you are poor.

Yea, I print a lot of non critical stuff with my CAD program on label stock and punch, drill, and cut to the printed lines. I have label stock up to 17" X 22" size. Real handy. Great for sheet metal work and WD-40 will easily remove the label paper when done.

[Evan]

For any diameter circle AD divide the diameter into as many equal part as bolt holes needed.

How is this done? If a marked ruler is used to measure then it isn't a geometric construction. Even if it is possible to then find the spacing on the circumference requires multiplying the diameter by pi which is impossible geometrically. It is equivalent to the problem of squaring the circle. It is also equivalent to the general case of trisecting an angle, also impossible except for certain special cases only. In particular, one cannot by euclidian construction create an equilateral triangle on a circle. See Morely's Trisector Theorem for the proof.

[Paul Alciatore]

Evan,

I don't think anyone was saying that this was a classic geometric construction. I certainly wasn't. For those who don't know what a classic geometric construction is, it means a construction or layout that could be accomplished by the use of a straight edge and compass ONLY. No markings on the straight edge and in the purest form, the compass would NOT even retain it's setting when lifted from the paper (this is often ignored). So it means straight lines and arcs only. And you must get the length of any new arc from previous lines and points on the paper. It does assume that you can locate the straight edge on existing points and lines and the points of the compass on existing points.

A geometric proof does not require that the construction be a classic geometric one. I was only asking if a proof was known. I am curious and would attempt to find a proof if the construction passed some CAD tests, but it does not seem to do so. I still strongly suspect that it only works in some special cases.

[Evan]

From the description, which is incomplete, it seems to indicate that this is a classic construction technique. Omitted is how the original division of the diameter is accomplished although that doesn't change the impossibility of trisecting an angle in the general case. The part that isn't obvious is that a valid classic construction using straight edge and divider is absolutely mathematically precise, for example bisecting an angle. The accuracy is limited only by the physical technique. Any other method is only an approximation if it doesn't meet the criteria for a classic construction OR is not in itself mathematically exact.

I mentioned this also because the history of mathematics is littered with both mistaken "proofs" as well as outright scams purporting to have solved the problem of trisecting an angle in general. This is despite the fact that the proof that it cannot be done is mathematically absolute in it's correctness.

[Paul Alciatore]

I thought the procedure was clear, but perhaps there is some confusion. Here is the drawing of the way I have been doing it.



This is an attempt to divide the circle by five. The angle should be 72.00000 degrees. All CAD constructions here were done with the complete precision of the program. It is accurate to well over six places. Points were selected with end point or intersection modifiers to prevent false selections. The circle was drawn as 10 inches in diameter and the five divisions were taken from the grid. As you can see, the procedure failed.

It is obvious that it will work for two and four divisions. It seems to work for three. All others I have tried have failed.

If I have not follwed the directions correctly, please let me know.