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  • darryl
    replied
    I'm sure this is redundant now, but laying out a perfect 90 is pretty easy. Draw one line, mark a point in the middle of it, roughly. Use a compass from that mark to draw two other marks along that line. Then from those marks, increase the spacing of the compass and draw two marks above the line. Where those marks intersect, draw a line through the first mark you put on the line. That's a perfect perpendicular.

    In our woodwork shop, I had to repair the saw a few days ago. In order to do that I had to crank an angle to the blade so I could access what I needed to. Then I had to return it to 90 degrees. The standard way is to use the pointer and adjust to the mark. That is very close to 90, but maybe not 100%- so I make a cut across a piece of scrap. Then turn one piece over and butt the edges together. If the pieces are laying flat, but the edges don't touch all the way across, you don't have a 90. On our saw, the pointer has to align with one edge of the marking, not down the center of the mark, to give a perfect 90. I know this is only a fraction of a degree, but I like my corners to fit perfectly, and this is a way to check it.

    There are many way of 'mcgyvering' in metalworking. Some are quite simple, and it's mainly some rational thinking that will lead you to ways of achieving an accuracy. I've read some of that book on foundations of accuracy- or at least the same kind of thing in another book. It is interesting how accuracy was brought about over time.

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  • Stargazer
    replied
    Originally posted by nickel-city-fab View Post
    "Foundations" is one of the most excellent books, I have re-read it several times. Dividing the circle has had applications since ancient times. The Babylonian astronomers had a protractor with a 40-meter radius, dividing the circle into minute parts.

    Being able to divide the circle is very useful for navigation among other things -- since ancient times, traders and sailors have used this.
    In more modern times, it is used for gear teeth, and all kinds of locating and positioning. The hard disks in a computer, or a DVD, depend on positioning very accurately, for example -- all of that accuracy began somewhere. (Probably at IBM Research in the 60's -- they pioneered the hard drive and had fantastic machine shops)

    It masterful book. Thanks again for recommending it. I spent the entire weekend on the circle division section. When I googled the subject, I came across a post from last October on some Internet message board topic on the Whitworth Three Plate method where one poster wrote:

    "A similar process can also get you a master square, although there are other ways to do it (such as via circle division)." https://news.ycombinator.com/item?id=24684365

    That I can't see to understand how you go from a layout trick (circle division) and obtain a master square. What could he be referring to?

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  • Stargazer
    replied
    Originally posted by JRouche View Post

    You got that right, it is both.

    Problem being, you are trying to mix circles with angles. Wont work.

    The circle is perfect, the angle is not.

    Simple math here right? Divide (Subtract if you need) a circle into its self, Zero. Try to do that mathematically with an angle. No can do, too many angles LOL JR
    If you were "starting from scratch" (conceptually, not necessarly in real life) how would you relate circle division to making more precise linear measurements?

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  • JRouche
    replied
    Originally posted by Stargazer View Post
    Is circle division used as a basis for establishing consistent linear measurements, or is it only used to create angle standards, (or both)?
    You got that right, it is both.

    Problem being, you are trying to mix circles with angles. Wont work.

    The circle is perfect, the angle is not.

    Simple math here right? Divide (Subtract if you need) a circle into its self, Zero. Try to do that mathematically with an angle. No can do, too many angles LOL JR

    Leave a comment:


  • darryl
    replied
    Circle division is interesting. Divide by 2 is easy- draw a line across the diameter, crossing the center. Divide by 6- first divide by 2. Then set a compass to the radius. Pivot at a point where the diameter line crosses the circle. Swing around and mark two points on the circle. Pivot where the diameter crosses the other side of the circle, and mark out two points on the circle. That gives 6 equidistant points. Divide by 7 is interesting- start with divide by 6. Then draw a line through two of those points perpendicular to the diameter line. Where that line crosses the diameter, set your compass from that point to where that line crosses the circle. That's your compass spacing to divide the circle into 7 parts. I'm sure this can go on and on. There is a way to divide by 5, but I don't remember it.

    The compass is a pretty simple device, but you can obviously use it to mark out some interesting geometry. If you're marking out bolt hole locations for instance, the accuracy you get is determined by how well you can center your center punch, and not anything ambiguous about the method of layout.
    Last edited by darryl; 02-13-2021, 12:35 AM.

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  • Mcgyver
    replied
    Originally posted by Stargazer View Post
    What is the main purpose of circle division if not for measurement?
    anything you need to divide a circle for....e.g. dividing plate, a gear, graduated collar, etc

    Leave a comment:


  • nickel-city-fab
    replied
    "Foundations" is one of the most excellent books, I have re-read it several times. Dividing the circle has had applications since ancient times. The Babylonian astronomers had a protractor with a 40-meter radius, dividing the circle into minute parts.

    Being able to divide the circle is very useful for navigation among other things -- since ancient times, traders and sailors have used this.
    In more modern times, it is used for gear teeth, and all kinds of locating and positioning. The hard disks in a computer, or a DVD, depend on positioning very accurately, for example -- all of that accuracy began somewhere. (Probably at IBM Research in the 60's -- they pioneered the hard drive and had fantastic machine shops)

    Leave a comment:


  • Stargazer
    replied
    Originally posted by Paul Alciatore View Post
    Another old trick for producing circular divisions is to wrap a linear scale around a cylinder. When the linear scale fits the circumference of the cylinder exactly, it then divides that circle. Again, this is one of usage, not any fundamental principle.
    It might not be fundamental, but it's still pretty cool and practical.

    What is the main purpose of circle division if not for measurement?

    Leave a comment:


  • Paul Alciatore
    replied
    I have not seen any fundamental connection between circle division and linear measure. But in practice there are some obvious ones. For instance, a micrometer relies on a well made, accurate screw thread and a thimble that is accurately divided into a number of equal, circular divisions. This is more of a practical matter and not fundamental to the idea of measurement. There are other ways to accurately measure things that do not use either a screw or divisions of a circle. A vernier caliper is one.

    Another old trick for producing circular divisions is to wrap a linear scale around a cylinder. When the linear scale fits the circumference of the cylinder exactly, it then divides that circle. Again, this is one of usage, not any fundamental principle.

    Leave a comment:


  • Stargazer
    started a topic Circle Division

    Circle Division

    I downloaded a copy of "Foundations of Mechanical Accuracy" that you guys recommended in my other threat. Wow! What a fascinating book and a wealth of information.

    In Part 3, Moore describes dividing the circle as one of the four pillars of mechanical accuracy. Is circle division used as a basis for establishing consistent linear measurements, or is it only used to create angle standards, (or both)?
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