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Non Circular Gears

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  • LES A W HARRIS
    replied
    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.

    Cheers,

    Leave a comment:


  • lazlo
    replied
    Originally posted by LES A W HARRIS
    Laslo,
    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.

    Leave a comment:


  • LES A W HARRIS
    replied
    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.




    Cheers,

    Leave a comment:


  • Paul Alciatore
    replied
    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.

    Leave a comment:


  • LES A W HARRIS
    replied
    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,

    Leave a comment:


  • Evan
    replied
    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.

    Leave a comment:


  • aostling
    replied
    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.

    Leave a comment:


  • Evan
    replied
    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.

    Leave a comment:


  • OldToolmaker
    replied
    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.

    Leave a comment:


  • Guest's Avatar
    Guest replied
    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.

    Leave a comment:


  • lazlo
    replied
    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:


    Leave a comment:


  • Dragons_fire
    replied
    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

    Leave a comment:


  • dfw5914
    replied
    Originally posted by JCHannum
    Technically maybe, but let's be realistic here.
    Ahh, but that would be infinetly less fun.

    Leave a comment:


  • John Stevenson
    replied
    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.

    Leave a comment:


  • Evan
    replied
    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.

    Leave a comment:

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