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A different kind of indexing wheel for the lathe

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  • A different kind of indexing wheel for the lathe

    I recently received my new issue of The Home Shop Machinist (March/April 2013) and noted an article written by James Schroeder on Building a Modified Brooks Cutter Grinder. While reading through the article, Mr. Schroeder references an indexing wheel on the spindle of his lathe and includes a picture (p.18). The indexing arrangement utilizes the approach used on a spin indexer, 36 holes in a concentric circle with an overlay plate using 10 spaced holes to generate 360 degree points; no problem here, fully understood. I also understand that I can use this section for direct indexing of the number 36 or any number that will evenly divide into 36 and converting the decimal increments to degree increments.

    The index plate also has another set of holes, 20 this time, again in a concentric circle and also used with the overlay plate section having five spaced holes. Regarding the 20 hole section of the index plate and associated 5 hole overlay, the author states, "The inner row of holes provides increments of 1.8 degrees for marking decimal values......."

    So it seems the 20 hole section is at least used for making fixed numbered (decimal based) divisions, obvious for 20 divisions and any number that will evenly divide into 20, but there must be more. The 20 hole section also apparently operates in some fashion as the 36 hole section, but I'm at a total loss to fully understand the use (math) of this section and it's total ability. It's probably as plain as the nose on my face, but right now it's escaping me.

    Anyone know?

    P.S. The URL listed for NEMES on p. 17 appears to be incorrect, it should be www.neme-s.org..........

  • #2
    Without having seen the article it doesn't make sense to me either.

    36 with a 10 vernier will generate 36 *10 = 360
    However 20 * 5 = 100 and 360 / 100 is 3.8 degrees which is double 1.8

    So should it have had a 10 vernier giving 20 * 10 = 200 and 360/200 = 1.8

    Or is it a typo ? 1.8 stated when 3.6 was meant.

    The plot thickens.
    .

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



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    • #3
      It makes 5, 10, 15, 20, etc.

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      • #4
        Actually, it makes 0, 1, 2, 3, 4, 10, 11, 12, 13, 14, 15, 20, 21, 22, 23, 24, 25, 30, etc

        The way the math works is if you want 5 subdivisions between each of the 20 index holes, the overlay's holes have to be (5+1)/5 * (360/20) degrees apart.

        6/5 * 18 = 21.6 degrees.

        The overlay plate would need 5 holes spaced 21.6 degrees apart. It would span a 90 degree arc.

        If the index plate and the overlay plate line up at 0, then the 2nd hole in the overlay would be (18+3.6)* past the first, the 3rd would be (18+3.6)* past the 2nd, and so forth. After five 3.6* increments, the index plate has moved 3.6 * 5 = 18*, lining the first overlay hole up with another index hole and the process can repeat.

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        • #5
          Clear as mud to me too. If the "overlay plate" with the 5 holes were completed to a full circle, how many holes would it have? I think 16, but I'm dense as a stone when it comes to math.
          Jim

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          • #6
            I believe this is the setup your talking about?
            Go to "Number 7" http://www.projectsinmetal.com/forum...r-g0602-lathe/
            Thats the same as my lathe only mine is a King Canada, I was pleasantly surprised to see it in the last HSM... It gives me hope
            Cheers,
            Jon

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            • #7
              Originally posted by Jon Heron View Post
              I believe this is the setup your talking about?
              Go to "Number 7" http://www.projectsinmetal.com/forum...r-g0602-lathe/
              Thats the same as my lathe only mine is a King Canada, I was pleasantly surprised to see it in the last HSM... It gives me hope
              Cheers,
              Jon
              Yes, Jon, that is exactly what I am posting about.

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              • #8
                1.8 degrees per step is 1/200 of a circle. Two such divisions is 1/100- good for marking out degree wheels, etc.
                I seldom do anything within the scope of logical reason and calculated cost/benefit, etc- I'm following my passion-

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                • #9
                  Originally posted by Tony Ennis View Post
                  Actually, it makes 0, 1, 2, 3, 4, 10, 11, 12, 13, 14, 15, 20, 21, 22, 23, 24, 25, 30, etc

                  The way the math works is if you want 5 subdivisions between each of the 20 index holes, the overlay's holes have to be (5+1)/5 * (360/20) degrees apart.

                  6/5 * 18 = 21.6 degrees.


                  The overlay plate would need 5 holes spaced 21.6 degrees apart. It would span a 90 degree arc.

                  If the index plate and the overlay plate line up at 0, then the 2nd hole in the overlay would be (18+3.6)* past the first, the 3rd would be (18+3.6)* past the 2nd, and so forth. After five 3.6* increments, the index plate has moved 3.6 * 5 = 18*, lining the first overlay hole up with another index hole and the process can repeat.
                  Thanks for your response, Tony. If you would run through the math and process for a divide by 13, it might help me better to understand.

                  Thanks.

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                  • #10
                    The theory of these divisions is the same as the theory behind a Vernier scale. Generally speaking if you have X divisions on the main scale and Y divisions on the Vernier scale, then you have X x Y (X times Y) divisions all together.

                    So the 36 division scale with a 10 division Vernier gives 36 x 10 or 360 divisions. This allows indexing into 1 (trivial), 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 72, 60, 90, 120, 180, and 360 divisions.

                    And the 20 division scale with a 5 division Vernier gives 20 x 5 or 100 divisions. This allows indexing into 1, 2, 4, 5, 10, 20, 25, 50, and 100 divisions.

                    The above numbers of EVEN divisions are ALL the ones that are possible with these two rings of holes. I do not know where Tony came up with 11, 13, 14, 21, 22, and 23. Absolutely none of these are possible with either the 36/10 or 20/5 arrangements. They all involve prime numbers that are not present in any of these numbers (5, 10, 20, and 36). In order to get any prime number of divisions, that prime MUST be present in one of the elements that do the actual division. Example: 21 = 3 x 7, both of which are prime. In order to do 21 divisions with a scale plus a Vernier, each of these primes must be present as a factor in either the basic scale or in the Vernier. So the 36 division scale has the factor of 3 in it (2 x 2 x 3 x 3 = 36) but it does not have the 7. A 7 division (hole) Vernier would allow 21 divisions to be made with the 36 hole scale. You could also do several higher multiples of 21 (42, 63, 84, 126, 189, 252, 378, and 756). And of course, it will do 36 and the even divisions of 36 (1, 2, 3, 4, 6, 9, 12, 18 and 36).

                    An interesting combination might be a 36 hole circle with a 25 hole Vernier. The maximum number of divisions with this is 900. It combines some of the best of the 36 and 20 hole circles with the following divisions being possible: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 456, and 900. This combines most of the small numbers plus the all important 100 divisions that is needed for so many dials. It omits the 1 degree divisions but I submit that that is only rarely used.

                    Another interesting combination would be a 90 hole circle with a 20 hole Vernier. It would provide most of the small numbers as well as 100 and 360 divisions. And many others that I leave it to you to work out.

                    Some of the Verniers that I have suggested may seem a bit difficult to do in the real world, but there is nothing that says that the Vernier holes or divisions must only be spaced approximately the same as the main divisions (10 Vernier divisions spread over 9 or 11 main divisions). For instance, it would be possible to have a Vernier scale with 10 divisions that are spaced approximately half as far apart as the main divisions. They would be numbered like this 0, 5, 1, 6, 2, 7, 3, 8, 4, 9, 0. This could be done with any number of Vernier divisions so that the 25 hole Vernier that I suggested above could only take up about 13 divisions on the main scale. I have seen Vernier scales that are spaced approximately two times as far apart as the main divisions for easier readability. But if you are using holes, you do not need to read the match-ups so closer spacings are more practical. With these odd-ball Vernier arrangements a table of the various possible divisions would totally necessary.

                    Sorry if this is too much of a rant. I promise to be good, for a while at least.
                    Paul A.

                    Make it fit.
                    You can't win and there is a penalty for trying!

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                    • #11
                      Sorry for the delay in responding to the original question by Pherdie on how the math works for the index wheel that I use for making calibrated dials. Paul A has it right. The twenty positions on the wheel times the five positions on the vernier provide one hundred divisions for a circle. I typically use that for a dial calibrated 0-25 or 0-50 as an example but many other combinations are possible.

                      I discovered that making these wheels was more of a challenge than I had originally thought. The smallest difference results in scribed lines that are uneven and readily visible. It took me three attempts before I was satisfied with the results.

                      Jim
                      Jim Schroeder

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                      • #12
                        I want to make a device similar to that for my lathe. I don't have a dividing head or rotary table, so I'll have to use the saw blade method to do the divisions. Math is my downfall, and I can't tell from the picture how many degrees the 5 positions on the vernier plate take up. If that semicircle of five positions is extended to a full circle, how many holes will it contain? I can use the bandsaw blade method if I know that. Thank you.
                        Jim

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                        • #13
                          Thanks for posting, as I have to make index plates, and even with all the reading im doing on it, your description cleared up a few fuzzy questions I had

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                          • #14
                            Hi Jim, let me try and break down the math related to index plates and vernier plates. To start the objective is to divide a circle into 100 uniform parts.

                            1. The inner ring of holes contains 20 holes and the vernier plate has 5 giving 20 x 5 = 100 possible positions. Each position is 3.6 degrees from an adjacent position. Each unit of division is equal to 3.6 degrees.
                            2. The index wheel has twenty holes, 360 / 20 = 18 degrees apart.
                            3. The vernier plate has 5 holes, each hole is 5 units (18.0 degrees) plus 1 unit (3.6 degrees) for a total of 6 units (21.6 degrees).
                            4. The 5 vernier plate holes are then "0" units, "6" units, "12" units, "18" units, and "24" units apart.
                            5. With the locating pin inserted into any combination of index plate holes and vernier plate holes there another pair of holes that will come into alignment by rotating the index wheel 3.6 degrees.

                            I do not have a good answer on how to accurately divide a circle into 3,600 units without a rotary table. I have seen arrangements that use gear trains to provide indexing, perhaps with some thought and creativity that would be a solution. I would point out that when making calibrated dials or knobs that have scribed marks one degree apart any irregularity in the spacing is very visible. I always use a spotting drill to locate the position and then use a screw machine drill to drill the hole.

                            Jim
                            Jim Schroeder

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                            • #15
                              4. The 5 vernier plate holes are then "0" units, "6" units, "12" units, "18" units, and "24" units apart.

                              Thanks Jim;

                              I had found most of the figures, but hadn't thought of breaking the vernier into units. Sometimes when I look at math problem I just draw a blank.

                              I recently made a disk of MDF with 72 teeth of a bandsaw blade wrapped around it to graduate a protractor to 5 deg. It worked well, the protractor is too small to graduate to 1 deg. without precise equipment. I tried to make a 1 deg vernier for it, but that didn't work because I couldn't keep the alignments correct with the equipment I had to work with.
                              Jim

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