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Dividing for prime numbers

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  • #16
    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
    Dave - you need a full universal dividing head with a set of gears and a table for the correct indexing plate as well as the gears to be put on the dividing head spindle and worm.
    Scroll down to look at all the tables and how to set the gears.: https://www.georgesbasement.com/Tool...dexingCenters/
    Don't forget to push the pin holding the indexing plate steady from the plate so your gears can move your indexing plate.

    Sorry Dave. I overlooked your statement about the Rotary table and assumed you had a 40:1 Dividing head.
    My mistake.
    For everyone having a 40:1 Dividing Head, here you can find a lot of info. https://books.google.com/books?id=4Q...dexing&f=false

    Dividing starts at pg 168.
    Last edited by Juergenwt; 01-17-2020, 05:01 PM.

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    • #17
      Originally posted by Dan_the_Chemist View Post

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

      Thanks for posting that Dan_T_C.

      I have a book "Battleship Bismarck .. A Survivor's Story," written by Baron Burkard Von Mullenheim Rechberg, who, was a young Fire Control Officer and aide to the Captain. He was the senior surviving Bismarck crew member, and after the war served several posts in Germany's diplomatic service, including Toronto, Canada. (I think Canada was where he was imprisoned after the sinking.) Though his description of the fire control system did not get deep into the technicalities, it has always piqued my interest. ...along with some other WW2 naval books, also short on details.
      Last edited by lynnl; 01-17-2020, 08:58 AM. Reason: (edit) corrected were to where
      Lynn (Huntsville, AL)

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      • #18
        I've used the 'old trick' many times. I've used chain, saw blades, band saw blades, toothed belts, tape measures. The toothed belt works great since you can cut the belt at an angle and line up the 'teeth' so there is the right number of divisions, then use another piece of the belt to lay across the gap to give a perfect alignment. This operation is done on the flat of course. Once the angled ends are aligned you can use fiberglass tape to fasten them together. Make one complete revolution with the tape with no overlap. Then you have a belt with exactly the right number of divisions, then you turn a disc with a bored center hole and an OD for a snug fit of the belt. While the disc is in the chuck you also turn a mating recess for the gear blank.

        I've had good luck using MDF for the disc. If you need a more solid center hole you can make a plug from steel or whatever, then bore the disc to insert the plug into. I've never needed to take that extra step.
        I seldom do anything within the scope of logical reason and calculated cost/benefit, etc- I'm following my passion-

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        • #19
          Use this printable divider wheel generator: https://www.cgtk.co.uk/metalwork/calculators/divider

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          • #20
            A quick look at adverts for the Victoria Universal head I have shows that what I thought were a random selection of change wheels looks like most of a set for that head. The change wheels came with my Harrison L5, not as a set for it, but as wheels which fitted it.
            The head was bought from a different person, and was just the bare head. I am missing the change wheel arm, but that looks simple to make .
            Now anyone got a set of differential dividing tables?

            Dave
            Just south of Sudspumpwater UK

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            • #21
              Originally posted by small.planes View Post
              Now anyone got a set of differential dividing tables?
              Dave
              You may want to take a look at the differential dividing head archive (DDH.ZIP) on my page. I used it to generate an example solution for 71 divisions and this is shown below. Be forewarned, it's a DOS program so needs a DOS emulator like DosBox to run.

              ================================================== =========

              DIFFERENTIAL DIVIDING SOLUTION(S)

              DH Worm Gear Ratio = 40:1
              Number of divisions = 71
              Allowable gear ratio matching accuracy = 0.010000 %

              ------------

              Hole plate = 18
              Indexing increment = 10
              Hole plate and crank rotate in same direction
              Gear ratio = 40.000000 / 72.000000 = 0.555556

              Acceptable gear trains include:

              40:72 0.555556 0.000E+000 %

              ------------

              Hole plate = 21
              Indexing increment = 12
              Hole plate and crank rotate in opposite directions
              Gear ratio = 40.000000 / 70.000000 = 0.571429

              Acceptable gear trains include:

              32:56 0.571429 0.000E+000 %

              ------------

              Hole plate = 27
              Indexing increment = 15
              Hole plate and crank rotate in same direction
              Gear ratio = 40.000000 / 72.000000 = 0.555556

              Acceptable gear trains include:

              40:72 0.555556 0.000E+000 %

              ------------

              Hole plate = 33
              Indexing increment = 18
              Hole plate and crank rotate in same direction
              Gear ratio = 93.333333 / 73.333333 = 1.272727

              Acceptable gear trains include:

              56:44 1.272727 1.919E-013 %

              ------------

              Hole plate = 43
              Indexing increment = 24
              Hole plate and crank rotate in same direction
              Gear ratio = 26.666667 / 71.666667 = 0.372093

              Acceptable gear trains include:

              32:86 0.372093 -7.012E-013 %

              ------------

              Hole plate = 49
              Indexing increment = 28
              Hole plate and crank rotate in opposite directions
              Gear ratio = 40.000000 / 70.000000 = 0.571429

              Acceptable gear trains include:

              32:56 0.571429 0.000E+000 %



              Regards, Marv

              Home Shop Freeware - Tools for People Who Build Things
              http://www.myvirtualnetwork.com/mklotz

              Location: LA, CA, USA

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              • #22
                Thanks Marv.
                I have 40 and 72 so will give that a go assuming that the plate has an 18 hole track.
                I also have an actual DOS box hanging around for sentimental reasons (was my first PC).

                Having never done differential dividing I assume you just count holes from where you are to where you go, but the holes move very slightly as you do so? So is it hard to keep track of where you are aiming at, or is the movement so small that it isn’t really noticeable?

                Dave
                Just south of Sudspumpwater UK

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                • #23
                  Originally posted by martik View Post
                  Use this printable divider wheel generator: https://www.cgtk.co.uk/metalwork/calculators/divider
                  Double check the printout for matching diameters across the height and width. Some printers stretch or squish the print slightly. My old one I don't use any more did this by about 1.5%. Have not checked the new one yet.

                  I'd "fix" this issue when the drawing needed to be perfect by using my CAD program to alter the drawing in the direction needed by that amount and save it as a special version just for that printer. Depending on the file format from that online source you might be able to do the same with CAD or some image handler like GIMP.
                  Chilliwack BC, Canada

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                  • #24
                    Originally posted by small.planes View Post
                    Thanks Marv.
                    I have 40 and 72 so will give that a go assuming that the plate has an 18 hole track.
                    I also have an actual DOS box hanging around for sentimental reasons (was my first PC).

                    Having never done differential dividing I assume you just count holes from where you are to where you go, but the holes move very slightly as you do so? So is it hard to keep track of where you are aiming at, or is the movement so small that it isn’t really noticeable?

                    Dave
                    Once you've downloaded the program you'll have a copy of its data file (DDH.DAT, example below). Modify that file to suit your equipment and what you have available. Then the program will only report configurations based on that data. (Despite the .DAT extension, the file is pure ASCII and can be modified with any text processing program).

                    ================================================== =====

                    Data for DDH

                    data need not be in numerical order - program sorts before use

                    anything above the line below is ignored

                    STARTOFDATA

                    ;note: ratio must be first entry in data area
                    40 ; DH worm gear ratio : 1 (e.g. 40:1)

                    ; holes in rapid indexing plate on main spindle must be second entry
                    ; if dh has no rapid indexing plate, enter -1
                    24 ; rapid indexing plate on main spindle

                    15 ; holes on plate A
                    16
                    17
                    18
                    19
                    20

                    21 ; holes on plate B
                    23
                    27
                    29
                    31
                    33

                    37 ; holes on plate C
                    39
                    41
                    43
                    47
                    49

                    -1 ; data separator between holes and gears - do not remove

                    ;available gears

                    24
                    24
                    28
                    32
                    40
                    44
                    48
                    56
                    64
                    72
                    86
                    100

                    ;above the line below requires a semicolon
                    ENDOFDATA
                    this is below the line and has no semicolon



                    Regards, Marv

                    Home Shop Freeware - Tools for People Who Build Things
                    http://www.myvirtualnetwork.com/mklotz

                    Location: LA, CA, USA

                    Comment


                    • #25
                      Originally posted by BCRider View Post

                      Double check the printout for matching diameters across the height and width. Some printers stretch or squish the print slightly. My old one I don't use any more did this by about 1.5%. Have not checked the new one yet.

                      I'd "fix" this issue when the drawing needed to be perfect by using my CAD program to alter the drawing in the direction needed by that amount and save it as a special version just for that printer. Depending on the file format from that online source you might be able to do the same with CAD or some image handler like GIMP.
                      They all do in the US, or used to. Makes it harder to copy money well enough that it will work in optical bill readers..
                      1601

                      Keep eye on ball.
                      Hashim Khan

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                      • #26
                        I would buy any 71T gear or sprocket from ebay and use that for indexing or even to drill the plate.



                        "...do you not think you have enough machines?"

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                        • #27
                          It may not be practical, but one way to divide a circle into 71 equal spaces would be to use a 72 hole and a 70 hole plate, and mark the midpoints for 71 holes. Like this:

                          Click image for larger version

Name:	Dividing_71.jpg
Views:	36
Size:	76.1 KB
ID:	1849551
                          http://pauleschoen.com/pix/PM08_P76_P54.png
                          Paul , P S Technology, Inc. and MrTibbs
                          USA Maryland 21030

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