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How do you determine a gear's pressure angle?

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  • How do you determine a gear's pressure angle?

    I'm fixing a friend's lathe and it needs a couple new gears in the apron. Apparently the size is odd enough that I can't get an off-the-shelf Boston (or anywhere else) and make to fit, so I have to make them complete.

    The pitch is simple enough to figure (12DP in this case), but how does one go about determining the pressure angle? The lathe is pre-1920 vintage so I'm not sure I can assume it's 20 degrees, not that I'd feel comfortable assuming anyway. There's enough 14-1/2 out there even today to mess up the mix a bit, and I understand that the percentage was higher back in the day.

    I have an optical comparator to make some measurements of the tooth profile if that helps. I can cut a gear, but I'm still a gear rookie I guess. Is there an easy way to determine pressure angle of an existing gear?


  • #2
    I use a set of gear tooth gages that look like thread pitch gages, made by Starrett.
    Today we carve our own omens Leonidas at Thermopylae


    • #3
      I've got sort of the same problem. My pre 1920 south bend came with only a couple of change gears, and I don't know the pressure angle. Since I don't have a nice shiny Starret tool (which for me would be just about a one-time-use tool,) I tried to measure the angle. I think I used a 6" rule eyeballed from the center of the gear (to form the hypotenuse of a right triangle,) and then with a square followed the surface of the gear tooth. Looks like it was less wrong than I expected:
      cos 14.5 * 6" = 5.80884
      cos 20 * 6" = 5.63814
      I measured a 5.6875, so I think it's 20.

      Pretty close considering how rough the eyeballed measurement was. Although knowing my luck, if I measured it with the right tool, it'd probably wind up being some really odd angle that's not used anymore and impossible to find.


      • #4
        Vinito, Ryobiguy.

        John Lawson has it bang on when he says get some gear tooth gauges.
        I believe that MSC carries these, [ not sure we don't have a MSC here ]

        Most early gears were 14.5 degree PA, it was only later than 20 degrees became more common to get a better tooth form.
        Chances are your apron gear of that age is 14.5.

        South Bend lathe change wheels are 18DP and 14.5 PA throughout the life of these machines.
        Many machine tool maker kept to 14.5 because of legacy and spares issues.

        One shortcut to buying these gear tooth gauges is to compare the gear in question to a same gear of both PA's
        Yes I know if you had one to hand you wouldn't need to make one

        Don't worry all isn't lost, go here:-
        and download a small shareware DOS program called Geargen, unzip this and run the program.
        You get a choice to select 14.5 or 20 degree PA gears so select any one first.
        Then feed in the DP and number of teeth.
        Click generate gear, you may have to do this a couple of times to get rid of the three tooth message, ignore that.
        Then go Plot and you have a choice to plot to screen with one tooth, one space or the whole gear.
        You can also plot to a file and save the tooth, space or gear as a DXF file which you can print out.
        If you study the two tooth spaces in both PA's you can clearly see the difference and match it to your gear.

        As a footnote I have studied gears quite a lot and this program, Geargen, draws the most accurate geometrically correct gear I have found at any price.
        Unfortunatly although it's shareware and not crippled other than the splash screens it's no longer supported.
        I have tried to get a registered version if only to support the author but emails and letters to the address shown do nothing.
        Fortunately the program does still run.

        Loser John - still looking for his floor

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


        • #5
          Thanks guys.
          John, I downloaded geargen and it runs OK. Thanks for the link.
          I'll dig a little bit and see what I can find out. Amazing what can be learned from books when I'm not so lazy.
          I might be able to print out a transparency from geargen and see if it matches the gear I'm trying to mesh with on the comparator. That would be "cheap like John S." if transparency sheets weren't so darned expensive.


          • #6
            A good place to check the pitch and the PA is on the rack (fastened to the front of the lathe bed) some times the pitch may be different but the chance of the PA is 99.9%
            same throughout the machine, unless some previous owner cobbled it up.



            • #7
              There is another way to check what the pressure angle is. If you look in the Machinery's Handbook in the Gearing section there is a means to check the backlash diminsion over a certain number of teeth (the number varies with the number of teeth the gear has) with a caliper. The diminsions for 20D and 14.5D gears are different
              Forty plus years and I still have ten toes, ten fingers and both eyes. I must be doing something right.


              • #8
                14 1/2 degree P.A. is somewhat more forgiving of errors in gear center distances, which makes it attractive for change gears where the center distance is pretty much set by guess.

                Try to make a living, not a killing. -- Utah Phillips
                Don't believe everything you know. -- Bumper sticker
                Everybody is ignorant, only on different subjects. -- Will Rogers
                There are lots of people who mistake their imagination for their memory. - Josh Billings
                Law of Logical Argument - Anything is possible if you don't know what you are talking about.
                Don't own anything you have to feed or paint. - Hood River Blackie


                • #9
                  Take one of the gears to a gear retailer (Motion Industries is one I know). They have gear gages and can tell you the pressure angle in a minute or two.