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Non Circular Gears

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  • #31
    Eliptical Gears.

    Originally posted by Paul Alciatore
    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.
    Here is an extract from page 421 of machinists & draughtsmens handbook, by Peder Lobben, 1900.

    He states depending on the degree of elipse multiple cutter's may be used. I have another reference somewhere that stated the form changes for each flank, and multiple cutters were used. My plottings were to understand the principles, have not cut one, my example is even teeth which as extract shows should be odd.

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


    • #32
      Originally posted by LES A W HARRIS
      Various Fellows shapers were modified for cam operation, elliptical, square, logrithmic spiral, etc.
      Thanks Les -- that's what I had guessed earlier. Oil Mac describes how one setup worked, which sounds simply brilliant:

      Originally posted by Oil Mac
      the ram was driven by a adjustable crank pin, set for the length of stroke by adjusting its position from the centre axis,

      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
      I also found this great scan of an ancient Popular Mechanic's article, showing how to draw eliptical gears. He uses the same method you describe in your second post:

      Drawing Gear Wheels. Part 4

      But these circular arcs may be rectified and subdivided with great facility and accuracy by a very simple process, which we take from Prof. Rankine's "Machinery and Mill Work," and is illustrated in Figure 252. Let O B be tangent at O to the arc O D, of which C is the centre. Draw the chord D O, bisect it in E, and produce it to A, making O A=O E; with centre A and radius A D describe an arc cutting the tangent in B; then O B will be very nearly equal in length to the arc O D, which, however, should not exceed about 60 degrees; if it be 60 degrees, the error is theoretically about 1/900 of the length of the arc, O B being so much too short; but this error varies with the fourth power of the angle subtended by the arc, so that for 30 degrees it is reduced to 1/16 of that amount, that is, to 1/14400. Conversely, let O B be a tangent of given length; make O F=1/4 O B; then with centre F and radius F B describe an arc cutting the circle O D G (tangent to O B at O) in the point D; then O D will be approximately equal to O B, the error being the same as in the other construction and following the same law.
      "Twenty years from now you will be more disappointed by the things that you didn't do than by the ones you did."


      • #33
        Thanks for the link.

        Thanks for the link, hadn't seen that.
        "Gear Design & Application" (Chironis), McGraw-Hill 1967 has a good section on NCG, pg 158-165 & elipticals pg 166-168, also eccentrics, pg 169-173.

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