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Non Circular Gears

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  • #16
    Originally posted by lazlo
    Sure, but the point is that they are involute teeth. So how did they cut involute teeth on gears with complex curves, pre-cnc?
    I'm trying to get my head around indexing, but the individual tooth can be cut by touching off on the blank and infeeding the required depth.

    As I mentioned, the ellipse can probably be treated as two circles, the large arc being one and the small radius on the ends another. Use the cutter corresponding to gears of those dimensions, say a #1 on the arc and a #8 on the ends. You will have to fake the transition. It won't be exact, but then, gear cutting seldom is.
    Jim H.

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    • #17
      Originally posted by JCHannum
      The most common non-circular gear shape is the rack.
      Nope, a rack is a circular gear of an infinite radius.

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      • #18
        Originally posted by dfw5914
        Nope, a rack is a circular gear of an infinite radius.
        Technically maybe, but let's be realistic here.
        Jim H.

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        • #19
          Were you thinking of a Reuleaux Triangle? This is a closed curve of constant width
          Yes, that is what I was thinking of. The two are closely related.


          As mentioned, the rack is the limit case of the circle and the teeth are the involute of an infinite diameter circle.

          Sure, but the point is that they are involute teeth. So how did they cut involute teeth on gears with complex curves, pre-cnc?
          Use a copy attachment on a shaper. The variety of attachments available for shapers was large. The could copy complex curves as well as anything that was an object of revolution.
          Free software for calculating bolt circles and similar: Click Here

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          • #20
            Originally posted by Evan

            Even if involute teeth are used laying it out isn't difficult, just tedious. Back when everything was done by draughtsmen on paper a it was normal practise to actually draw the teeth accurately to scale. A method called Unwin's Construction was commonly used and is still used internally by CAD programs to calculate involute tooth shape.

            .
            Nearly, the calculations were done by Grant, Unwin, who is still alive, brought the idea up to date.
            Grants Ondontograph is published in all the early copies of machinery handbook.
            .

            Sir John , Earl of Bligeport & Sudspumpwater. MBE [ Motor Bike Engineer ] Nottingham England.



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            • #21
              Originally posted by JCHannum
              Technically maybe, but let's be realistic here.
              Ahh, but that would be infinetly less fun.

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              • #22
                i think i saw this on this forum before, but check this out of you like crazy gearing..

                http://blog.makezine.com/archive/200...ear_heart.html

                and its all made from paper

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                • #23
                  Originally posted by John Stevenson
                  Nearly, the calculations were done by Grant, Unwin, who is still alive, brought the idea up to date.
                  It's way older than Grant. The excersize of drawing the involute curves is described in the Brown & Sharpe and Fellows gear handbooks from the late 1800's, early 1900's.

                  Here's a great tutorial on drawing the involute curve from the 1910 American Machinist:

                  http://books.google.com/books?id=bGY...esult&resnum=1

                  As TexasTurnado pointed out, if you scan back a couple of pages to "The Origin of the Involute Gear", it talks about a French book published in 1694, "An Essay on the Teeth of Wheels", which describes the involute gear in great detail, including the math necessary to generate the tooth form:


                  "Twenty years from now you will be more disappointed by the things that you didn't do than by the ones you did."

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                  • #24
                    A little earlier publication -
                    Machine design, construction and drawing: a textbook for the use of young engineer

                    By Henry John Spooner pub. in 1908 is available for download as a pdf file
                    at http://books.google.com/books?id=GVd...gbs_navlinks_s

                    Starting on page 293 is a description of Willis' Ondontograph from Principles of mechanism. A treatise on the modification of motion by means of the elementary combinations of mechanism, or of the parts of machines (1896)'.

                    This pdf is available from http://www.archive.org/details/princ...mech00robirich

                    This thread about Non Circular Gears leads to some very interesting and old texts.

                    Thanks so very much for starting it.

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                    • #25
                      The theory behind the involute shape is if you take a string and pull it off the perimeter of a wheel the pattern generated would be an involute. If you put Prussian Blue on the gears and rotate them you will see constant contact if the gears are cut right. There are also indicator contraptions sold that will check gear contact and record it on paper.
                      Many years ago I worked in a large gear shop with customers all over US and Canada. One job was to duplicate oval gears for some sort of antique machinery. After much profanity coming from the office we finally wound up beating them out on a shaper with a rotary table on it. This was 1968, before CNC. Each X-Y location had to be calculated separately. No $5 calculators either, in those days "pocket calculator" was yellow and had an eraser on the end.

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                      • #26
                        I'm still trying to figure out where the assumption that the teeth are involute came from. There is another shape that looks almost the same but is much better suited as it will easily make gears that will mesh universally with any other size of gear as long as the same radius is used to generate the curve of the teeth and the pitch is similar. It is the predecessor of the involute form and is called the cycloidal gear. They are much less sensitive to variations in separation and even tooth pitch at the expense of greater sliding friction. They are also a lot easier to make because the shape of the sides of the teeth is a simple curve. They would be well suited to this sort of application.
                        Free software for calculating bolt circles and similar: Click Here

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                        • #27
                          Originally posted by Evan
                          It is the predecessor of the involute form and is called the cycloidal gear. .... They would be well suited to this sort of application.
                          Evan,

                          Your comment caused me to dig up my old 1959 edition of Kinematic Analysis of Mechanisms, by Shigley. This has a section describing cycloidal gears. Here are two paragraphs from that section:



                          Last edited by aostling; 08-24-2009, 03:45 PM.
                          Allan Ostling

                          Phoenix, Arizona

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                          • #28
                            The main thing I recall about cycloidal gearing is that they can tolerate variations in the tooth pitch that involute cannot. That would be very uncommon except in non-circular gearing.
                            Free software for calculating bolt circles and similar: Click Here

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                            • #29
                              NCG cutting.

                              Just got in last night from 16 day vacation.


                              Paul,
                              Cam on hobber, very possible, tough getting a budget to try it these days?


                              Laslo,
                              Various Fellows shapers were modified for cam operation, elliptical, square, logrithmic spiral, etc. CNC coversions were also done.

                              Early on, 1800's multiple cutters were used, different form on each flank, calculate at each pitch radius for the same DP but varying N.O.T. like this.

                              Note angle varies from each space!




                              Cheers,
                              Les H.
                              The Impossible Takes Just A Little Bit Longer!

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                              • #30
                                Thanks Les. Finally a real clue as to how it was done before CNC.

                                Several have said CNC, but is that for real or just a quick way to dismiss the question? Would anyone use a small diameter cutter to do the profile of the CAD drawn teeth? I guess it could be done, but is it done?

                                I know gear teeth can be drawn to any degree of accuracy you want with CAD. I have done so. But would this ensure proper mesh with involute or any other tooth form or would modifications need to be made to each individual tooth? Les' drawing suggests that this is the case.

                                This may be the true apex of gear design and construction.
                                Paul A.
                                SE Texas

                                Make it fit.
                                You can't win and there IS a penalty for trying!

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