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Non Circular Gears

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  • Non Circular Gears

    Years ago I observed an exhibit in a showcase that was placed in the main lobby of the New Orleans International Airport by a local shop that made gears. It contained almost every type of gear from simple spurs on up. They were all meshed together and a motor drove the exhibit to demonstrate the actions of the various types. The pair that I was most fascinated by was two that were cut on blanks that were probably elipses instead of circles. They were the same tooth count and were meshed with the high spots on one matched to the low spots on the other. The driver was turning at a constant speed and the driven gear would cycle from faster to slower twice each revolution. But they had the same average RPM.

    I saw an ad in the latest HSM with a drawing of such a pair of gears and it brought back the fascination.

    What I wonder is; how are such gears cut? I would think that each tooth is a different shape from the ones next to it. Probably even the two flanks of a single tooth (or space) are different. I am not even sure that the shape of the pitch line is even an ellipse. Would two ellipses rotate together in contact with fixed centers? If not, what curves would do so? Ovals? The question is complicated by the fact that the poing of contact between two such curves may not necessairly be on the line between their centers at all points in the rotation.

    I doubt that a form cutter would work. The best idea I can think of is to use a hob and while the blank rotates, it also moves back and forth toward and away from the hob. This would tend to generate teeth that would mesh with a rack that also moved in relation to the gear in the same manner. At least I think it would.

    Anybody know how such gears are actually cut?
    Paul A.
    SE Texas

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

  • #2
    You can buy them at the non-circular gear store;

    http://www.gearshub.com/non-circular-gears.html

    Clarence Myers has a trailer with a collection of full sized sream engines, one of which has square gears, it is hypnotic to watch it run.

    One set of elliptical gears has non involute teeth, but I would guess you could use standard involute cutters, changing them to correspond the diameter of the arc of the particular section of the ellipse. Since there is a range of tooth count for a given cutter, probably only two or at most, three different cutters would be needed depending on the shape of the ellipse. Each space would need to be cut individually to get the proper depth.
    Jim H.

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    • #3
      One word: CNC
      Play Brutal Nature, Black Moons free to play highly realistic voxel sandbox game.

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      • #4
        Paul,would that have been Prager?

        http://www.pragerservice.com/Services.htm
        I just need one more tool,just one!

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        • #5
          Many years ago I saw a file cutting machine that had that same type of gears. This machine was well over 100 years old, so no CNC. The gears were cast ( I saw the patterns) and most likely hand finished

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          • #6
            I am presently at the Portland engine show, which runs next week, Wednesday through Saturday. There is usually a party set up across from my exhibit who has a pump jack that has this sort of gearing. The idea is that the engine be able to provide lots of lifting power on the pump's upstroke, yet cycle the pump piston back down quickly, thus increasing the average pumping speed (strokes/minute) over what it would otherwise be. Gives the same effect as upshifting your car and speeding downhill, and downshifting for the uphill run. Much faster overall speed than having to keep it in the lower gear.

            This pump jack was made well before CNC. :-)

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            • #7
              Originally posted by wierdscience
              Paul,would that have been Prager?

              http://www.pragerservice.com/Services.htm
              As I said, I really can't remember. The name Prager does sound somewhat familiar, but I just don't know. Since New Orleans is a major port city and also close to the oil business, it has many shops capable of the kind of work you would need to repair or even build large ships and that would include some serious gears. Probably more than one gear shop capable of making them. Likely more than a dozen.
              Paul A.
              SE Texas

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

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              • #8
                When you mentioned oval and stuff it makes me cringe on the math involved,
                In the books ingenious mechanisms they have about every strange gear design you could imagine.
                Last edited by A.K. Boomer; 08-23-2009, 10:14 AM.

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                • #9
                  Originally posted by Black_Moons
                  One word: CNC

                  Isn't that three?

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                  • #10
                    Originally posted by Paul Alciatore
                    Anybody know how such gears are actually cut?
                    "Attention Walmart Shoppers: Sir John or Les to the gear desk"

                    Seriously, I'm intrigued by this question. It doesn't seem possible to manually index these gears on a dividing head. For a square gear, you could do the flats, but the corners would be another operation, and that approach wouldn't work for oval shapes.

                    Just a guess, but were these non-circular gears done on a Fellows shaper, with a matching cam that offset the shaper head?
                    "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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                    • #11
                      There is no particular reason they must be made with involute teeth. Prior to the use of involute gearing there were pretty good compromises that were a lot easier to lay out.

                      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.

                      To lay out the teeth on a non-circular gear one would simply determine the pitch circle for each tooth on the gear and proceed normally using Unwin's Construction as if that tooth were on a circular gear.

                      The same can be done with some difficulty using a CAD program to lay out the teeth for a series of gears all stacked on top of each other with a common centre. Then the teeth that are required for each portion of the shape are used from each of the developed gears and the rest discarded.

                      The two most common non-circular gear shapes are the ellipse and the trochoid. The trochoid is particularly interesting because it will roll between two plane surfaces just as well as a circle will and yet is not round.
                      Free software for calculating bolt circles and similar: Click Here

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                      • #12
                        Originally posted by Evan
                        The trochoid is particularly interesting because it will roll between two plane surfaces just as well as a circle will and yet is not round.
                        A trochoid is not a closed curve like an ellipse. A bicycle pedal follows the path of a trochoid.

                        Were you thinking of a Reuleaux Triangle? This is a closed curve of constant width. http://en.wikipedia.org/wiki/Reuleaux_Triangle.
                        Allan Ostling

                        Phoenix, Arizona

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                        • #13
                          The most common non-circular gear shape is the rack.
                          Jim H.

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                          • #14
                            Originally posted by Evan
                            There is no particular reason they must be made with involute teeth. Prior to the use of involute gearing there were pretty good compromises that were a lot easier to lay out.
                            Sure, but the point is that they are involute teeth. So how did they cut involute teeth on gears with complex curves, pre-cnc?
                            Last edited by lazlo; 08-23-2009, 02:36 PM.
                            "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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                            • #15
                              Many years ago, in Scotland, the old machine tool firms of Thomas shanks & co & also Loudon brothers, used to make large slotting machines, (for our American readers, vertical shapers) In these machines the ram was driven by a adjustable crank pin, set for the length of stroke by adjusting its position from the centre axis, still the same systems are used yet in more modern shapers of the 20th century,
                              This crank system was driven, by a large epicycloidal gear which was cast on the back of it, This gear had two tracks at different radii, driven by a smaller matching gear which was similar When the two gears tracked on the large ratio, (slow cutting speed) before it reached the end of its track, the larger of the elliptical track on the small primary gear, picked up on the matching smaller gear on the matching ram crank, thus throwing the ram upwards on its return, or non cutting part of the cycle at a ratio of double the cutting speed.
                              This was a most fascinating and smooth system to see in operation, The last of these big machines, i observed in production work, was 15 years ago, The teeth on the gears were cast,

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