Announcement

Collapse
No announcement yet.

Dividing for prime numbers

Collapse
X
 
  • Filter
  • Time
  • Show
Clear All
new posts

  • Dividing for prime numbers

    Morning,
    Anyone got any good tips for making prime number divisions?
    I would like to make 71 and 113 tooth gears.
    I have a 90:1 rotary table with the usual plates (15,16,17, 18,19,20,21,23,27,29,31,33, 37,39,41,43,47,49 holes) a 40:1 universal dividing head and a few random change wheels.

    Dave
    Just south of Sudspumpwater UK

  • #2
    Originally posted by small.planes View Post
    Morning,
    Anyone got any good tips for making prime number divisions?
    I would like to make 71 and 113 tooth gears.
    I have a 90:1 rotary table with the usual plates (15,16,17, 18,19,20,21,23,27,29,31,33, 37,39,41,43,47,49 holes) a 40:1 universal dividing head and a few random change wheels.

    Dave
    I have suggested before to do the divivin you need and you will find a pattern out there to print out. JR

    Umm, 40 and 90. It took years for me. JR
    My old yahoo group. Bridgeport Mill Group

    https://groups.yahoo.com/neo/groups/...port_mill/info

    Comment


    • #3
      Attach a stepper motor to the rotary table and you'll be able to do any division

      Comment


      • #4
        113 and 71 are “not directly possible” with the plates and heads I have.

        Hence asking for good tips.

        I don’t really want another project to add a stepper and controller.

        Dave
        Just south of Sudspumpwater UK

        Comment


        • #5
          Using the 71 tooth for example, each tooth is 5deg, 4min, 13.5sec + just a tiny bit more:-) so if you go half way around each way using those numbers the error at the midpoint will only be about a sec or so on the last tooth

          Comment


          • #6
            Two stage process. Second stage is to put a paper/cardboard 71 point "plate" on your dividing head handle. The inaccuracies are averaged out in the final process.
            First stage is to make that "plate". As JR mentioned to find a website that prints out such circles, or do a spreadsheet of 360/71 rounded numbers to use on the rotab, or mark out 7.1 inches on a strip of paper and wrap around a wooden disc which you turn to just the right diameter, or use a bit of old 35mm film strip that has the square punch marks along the edge, or ditto 16mm, or 71 links of a chain, or print a line of 71 of the same character on your printer, or line up 71 one cent coins on a strip of sticky tape etc.

            But it is much more fun to get a universal dividing head and use compound indexing.
            For 71 it is 15 holes on the 27 plate using a gear ratio of 9:5 with 1 idler to reverse direction
            113 is 13 holes on 39 plate with gear ratio of 3:7 with 1 idler again.
            Last edited by Baz; 01-16-2020, 09:58 AM.

            Comment


            • #7
              I once needed an indexing wheel of 111.111 teeth, but of course, couldn't find it. I ended up just using a paper facsimile attached to a piece of plywood and a pointer. It wasn't as perfect as I wanted, but it was close enough. I'm still looking for that 111.111 tooth gear so I can get things perfect!

              Comment


              • #8
                Or for stage 1 you can use 9 holes on your 16 plate, doing half the holes in each direction which will put the 35th index point out by 1/4 of a hole. That translates into 15 minutes of arc in the stage 1 plate so will add maximum errors of 22 seconds on the final item. On a 4 in wheel that is about 2 tenths error.

                Comment


                • #9
                  You don't need to use plates or compound gearing to divide prime numbers. Go to this link follow instructions to download the spreadsheet that will calculate the deg/min. settings on your rotary table for any number. Simple to use and less aggravation.

                  https://sites.google.com/site/bluewa...xing-converter
                  The shortest distance between two points is a circle of infinite diameter.

                  Bluewater Model Engineering Society at https://sites.google.com/site/bluewatermes/

                  Southwestern Ontario. Canada

                  Comment


                  • #10
                    An old trick for HSM magazine.
                    Use a piece of bandsaw blade, use the number of teeth required or a multiple thereof.
                    now turn a plywood disc, close to size, then start sanding to fit the bandsaw blade to the disc. Use another piece of sawblade to match pitch at the joint.
                    Then fasten blade to disc, glue, hoseclamp or screws. Then make a shot pin to engage into tooth on blade.
                    May I ask what uses those numbers as divisions.

                    Comment


                    • #11
                      Make the value a composite number rather then prime, 5.002 for example is no longer a prime number.
                      2 X .251

                      Comment


                      • #12
                        71/113 x5 is a very good approximation to PI - 0.000000266764189 out according to my iPhone calc.
                        Those gears are typical change gear tooth counts.

                        As I don’t have a PI set for my CVA I have to make / acquire some to cut DP pitches.

                        Dave
                        Just south of Sudspumpwater UK

                        Comment


                        • #13
                          I had to produce 118, which was not achievable with the dividing plates available, and Dick kindly printed out a spreadsheet with all the figures rounded to the nearest minute of angle and the engraving for the lathe cross slide was done the slow way successfully. The computer had done each calculation separately, so the tiny error was the same in each place and did not add up as it went.

                          Comment


                          • #14
                            I'm wondering if you're thinking that you need a solution where you cut each tooth in turn. I'm wondering if there is a solution using the plates you have which will actually generate the spacing needed to cut something like every fourth or seventh gap in steps around the blank and you just need to go around the blank a few times doing these multiple tooth skip steps to achieve the final result.

                            For those of you that have done this sort of thing before is that how some of these oddball numbers are cut? I ask in all honestly as I've never used my own dividing plates. But the question in this thread got me considering how such things might be possible.

                            I did a search for dividing plate calculators and got a few links to options that may help. One that is promising is THIS LINK . Of course you'd need to be at least a little comfy with spreadsheets to put in the information.
                            Chilliwack BC, Canada

                            Comment


                            • #15
                              Originally posted by 754 View Post
                              Use a piece of bandsaw blade, use the number of teeth required or a multiple thereof.
                              now turn a plywood disc, close to size, then start sanding to fit the bandsaw blade to the disc. Use another piece of sawblade to match pitch at the joint.
                              Then fasten blade to disc, glue, hoseclamp or screws. Then make a shot pin to engage into tooth on blade.
                              Great use of this technology. The use of straight and curved racks in analog computing is an old technology that is largely forgotten today. But it flourished in the analog fire control computers of warships in WW2 and for a couple of decades after that.

                              By curving the rack around the circle you get

                              rotation(degrees) = ( count(rack_teeth)/total(rack_teeth) ) * 360

                              But imagine the the rack is only attached at one point and is tangent to the circle. Not surprisingly

                              rotation(degrees) = tangent(count(rack_teeth)) * constant


                              Where the constant depends on the number of TPI, the radius of the root circle, etc...

                              Bend the rack around a parabolic "disk" and you get a parabolic function, useful for basic trajectories.

                              Here is a nice video that explains some of the basics. I love these old analog computers.

                              Last edited by Dan_the_Chemist; 01-16-2020, 03:26 PM.

                              Comment

                              Working...
                              X