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  • nickel-city-fab
    replied
    Yah its a good question -- you can bisect an angle but cannot trisect it. Pentagon has been done before, but I never practiced that one. Just for the fun of it I'm thinking "What if I wanted to lay out every degree from zero to 10 degrees" I think you would have to divide the chord to do it.

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  • mklotz
    replied
    Originally posted by Baz View Post
    Actually I don't think you can make any shape. like that. I believe the first one you can't do is quite low, like under 20 and there is a mathematical proof for which ones cannot be achieved. There was a programme on the BBC radio within the last two weeks about the mathematician who proved it.
    Everyone knows that a regular hexagon can be easily constructed in a circle using only a compass and a straightedge. With the compass set to the radius of the circle, simply walk it around the circle striking off points on the circumference. There will be exactly six points. Connect these points with straight lines and the result will be a regular hexagon.

    This raises the question of what other regular polygons can be constructed using only compass and straightedge? Obviously, three and four sides are easy and we know from above that six is possible. What about five or seven?

    Karl Friederich Gauss, the German mathematical prodigy and genius, solved the generalized problem. He proved that a regular n-gon can be constructed with compass and straightedge if n is the product of a power of 2 and any number of *distinct* Fermat primes (including none).

    A Fermat prime is a Fermat number of the form

    Fk = 2^(2^k)+1

    that is also a prime. The known Fermat primes are:

    k Fk

    0 3
    1 5
    2 17
    3 257
    4 65537

    Not all Fermat numbers are prime. The list above includes all the currently known Fermat primes. For example, for n = 5, we have the Fermat number 4,294,967,297 which has the factors 641 and 6,700,417 and so is not prime.

    Also, the restriction to *distinct* primes is important. A 9-sided polygon cannot be constructed. 9 has prime factors 3*3 and, while 3 is a Fermat prime, ALL the factors of 9 must be DISTINCT Fermat primes for it to be constructible.

    So, based on the above, a regular septagon cannot be constructed, but a pentagon can. A procedure for the latter is shown here...

    https://www.mathopenref.com/constinpentagon.html

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  • Mcgyver
    replied
    Originally posted by nickel-city-fab View Post
    . Lately I've been interested in how many ways one can divide the circle,
    And hobby machinists are a strange bunch? lol sorry couldn't resist

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  • MattiJ
    replied
    Use large-ish lathe and offset the round stock by 6 feet.
    if the final part has 1/4” hex sides nobody is going to notice that the sides are not flat and actually have 6 feet radius

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  • 754
    replied
    If I was using the compound as a shaper I would likely use a 3 jaw chuck, could hep with the indexing.
    if lathe was big enough I would probably hold it in a 4 tool post on the side, and flycutter in the chuck.

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  • darryl
    replied
    You'd be laying something across the chuck, between the jaws, to back up the piece you're machining I'd assume- you need the alignment in both directions, rotation plus parallel to the chuck face. Something straight, and the right height to place the workpiece where you want it as you tighten the jaws. If you use a piece of wood, you can put two screws on one edge of it to keep that piece centered in the chuck hole. That way you can leave the piece in there for continued support as you do the machining.

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  • nickel-city-fab
    replied
    Originally posted by 754 View Post
    I need to know diameter and length of part..
    Say for example 6" long and 3/4" dia. But it could be anything. I'm looking for creative ways to do the work holding and setup, the actual sizes and numbers don't matter.

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  • 754
    replied
    I need to know diameter and length of part..

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  • nickel-city-fab
    replied
    Originally posted by JoeLee View Post
    that would be my first thought, unless you mount your work between centers, lock the spindle and mount a shaper bit in the tool post, then run the carriage back and forth feeding the cross slide in .001 increments and shave your flat sides.
    What what I do this?? Absolutely not but this is just a thought.

    Some people use their mills quill for broaching, sort of the same idea.

    JL....

    My back already hurts... yes you are right, I totally wouldn't have thought of that. I bet it gives a nice finish too, and it pretty accurate over short distances. (modulo tool/part deflection)

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  • JoeLee
    replied
    Originally posted by danlb View Post
    Assuming the piece would fit in the 4 jaw sideways, you'd face the first side and then rotate 60 degrees. Assuming that it would not fit in the chuck, fasten it to an angle plate fastened to the cross slide and use an endmill or flycutter in the chuck to cut off one side at a time. In either case I'd leave a collar on the end to preserve the original spacing so that as long as I'm cutting to the same depth each time I don't have to calculate the offset.

    With or without measuring devices? With protractors, dividers, calipers and things it becomes much easier.

    Dan
    that would be my first thought, unless you mount your work between centers, lock the spindle and mount a shaper bit in the tool post, then run the carriage back and forth feeding the cross slide in .001 increments and shave your flat sides.
    What what I do this?? Absolutely not but this is just a thought.

    Some people use their mills quill for broaching, sort of the same idea.

    JL....


    Leave a comment:


  • nickel-city-fab
    replied
    Originally posted by Baz View Post
    Actually I don't think you can make any shape. like that. I believe the first one you can't do is quite low, like under 20 and there is a mathematical proof for which ones cannot be achieved. There was a programme on the BBC radio within the last two weeks about the mathematician who proved it.
    I recall hearing similar, but I can't recall the details. Lately I've been interested in how many ways one can divide the circle, using technologies that have been available since the beginning of time. Its not hard to do squares or triangles, or anything based on them. But what would I do to get all 360 degrees with just a can of layout blue, a scriber, a ruler, and dividers?

    Leave a comment:


  • nickel-city-fab
    replied
    Originally posted by Bented View Post
    Polygon turning
    Fast yet unlikely to meet the expectations of the .0005 accuracy sought by many hobbyists.
    yeah, hobbyists are a strange bunch. I'd be OK with .020 or so on this, like a chunk of hot roll rusting away in a corner. It doesn't have any critical fits for what I'm thinking of.

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  • Bented
    replied
    Polygon turning
    Fast yet unlikely to meet the expectations of the .0005 accuracy sought by many hobbyists.

    Leave a comment:


  • Baz
    replied
    Actually I don't think you can make any shape. like that. I believe the first one you can't do is quite low, like under 20 and there is a mathematical proof for which ones cannot be achieved. There was a programme on the BBC radio within the last two weeks about the mathematician who proved it.

    Leave a comment:


  • nickel-city-fab
    replied
    Originally posted by danlb View Post
    Assuming the piece would fit in the 4 jaw sideways, you'd face the first side and then rotate 60 degrees. Assuming that it would not fit in the chuck, fasten it to an angle plate fastened to the cross slide and use an endmill or flycutter in the chuck to cut off one side at a time. In either case I'd leave a collar on the end to preserve the original spacing so that as long as I'm cutting to the same depth each time I don't have to calculate the offset.

    With or without measuring devices? With protractors, dividers, calipers and things it becomes much easier.

    Dan
    That's pretty much what I was thinking -- yes, with dividers and a ruler. I would chuck it sideways in the 4-jaw, face one side. Flip 180 and face the opposite side. Then use a large nut against the face of the chuck to establish the hex. Face that side, flip 180 and face the other side. Repeat...

    Actually you can make most any shape or angle with just the dividers and ruler. Once as a student, I made my own fishtail gage that way, perfect 60 deg every time. A lot cheaper than Brown and Sharpe, too.

    Leave a comment:

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