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A Math and Mechanism problem

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  • mklotz
    replied
    " My learning style is closely coupled to having to have a use for the knowledge before really learning it."

    While I fully understand this attitude, I'm of the opinion that a good student should, as part of his learning process, determine why his teachers think it's important to teach him the subject at hand. One has to presume that, given a decent school, the curriculum has been chosen with the eventual benefit to the student as primary consideration.

    "My math teachers all thought you should be thrilled with the answer and usually did not know how to apply the knowledge to an actual problem."

    It depends on the problem. If one is studying multiplication, then the answer is everything. If one is learning to prove geometric theorems then the process is everything.

    Put yourself in the position of the teacher. The students have only very limited experience and seldom do much of anything involving math beyond simple arithmetic in their everyday life. If you teach the Pythagorean theorem to twelve year-olds, what sort of application is going to resonate with them?

    What they really need to teach is an expansion of what I said in my first paragraph - a course that shows them HOW to learn and explains, as much as possible, WHY they need to learn even if no immediate application of the subject occurs to their immature minds.

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  • A.K. Boomer
    replied
    I cannot remember the number of holes in the cam or the cam sprockets but this is how your set up your valve timing on the older porsche 911's and in fact is just a great system esp. on DOHC engines as you can separate the cams and retard the intakes and advance the exhausts for higher end (RPM) power...

    of course now with VVT this system is becoming obsolete - still - for back in the day it was all they had to personally tune an engine to your particular needs...

    Leave a comment:


  • Stepside
    replied
    Barrington

    That is a great chart and will give me information for future projects. The quadrant should give me more than enough adjustment. If my workmanship is of any quality whatsoever, I should need only a degree or two of adjustment. The rest of the adjustment would be there to cover "foggy thinking" as well as some "outside the box" ideas.

    Thank you for taking your time to work up the chart.

    Pete

    Leave a comment:


  • Lew Hartswick
    replied
    Originally posted by Stepside View Post
    Paul

    Thank you for the input. The vernier scale information will be of use for future projects or to answer a question on Jeopardy. My learning style is closely coupled to having to have a use for the knowledge before really learning it. My math teachers all thought you should be thrilled with the answer and usually did not know how to apply the knowledge to an actual problem.

    Thanks again
    Pete
    Re - Teachers: That is what made for the best math teacher I ever had. Math 55 in college, the teacher was a lady who had worked at MIT during WWII on some military projects
    and she REALLY could make the point of the relation between the stuff in the book and real life work.
    ...lew...

    Leave a comment:


  • Barrington
    replied
    Originally posted by Stepside View Post
    As I do not need the entire 360 degrees I will just drill the holes lie in one quadrant.
    Pete, I don't know how much adjustment your application will require, but if you just drill holes in one quadrant, that will only provide a 'continuous' range of 36°.

    If that's o.k. then please ignore the following...

    If you do need more, then the table below might be useful to work out how many holes are needed. The box covers the available settings using only one quadrant - the green area shows the 342°->18° available without gaps; 341° and 19° cannot be set.

    (Columns are 10° steps, rows 9°, table is simply the difference of the two.)



    Cheers

    .
    Last edited by Barrington; 04-11-2015, 09:52 AM. Reason: typo

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  • oldtiffie
    replied
    I do appreciate the maths as provided by our two resident Physicists and others here.

    But.

    From the application of the indexing/vernier application the degrees accuracy of the manufacturing will determine the usefulness of the discs.

    This will include the accuracy of the location of the discs and (guessing here) the location pin on the pitch circle as well as the diameter of every hole and the diameter of the locating pin (to be inserted into both discs).

    Perhaps the "pinned" disc and pin as a set will need to be allocated by the same pin in a fixed block (as on a "Spindex").

    The OP will need to determine his allowable tolerances - including the circular pitches.

    Various tolerances (and their limits) at various points will be either/and accumulative (+ve or -ve) - ie additive or subtractive.

    It all depends on the output accuracy that the OP requires - as well as the machines and measuring tools that the OP has available.

    This may well be heading toward some serious metrology applications - including ambient temperature/s.

    Having the design in say a good CAD system is one ting but the quality of the output (finished job) may not live up to the design parameters.

    I hope it does.

    Leave a comment:


  • Stepside
    replied
    Paul

    Thank you for the input. The vernier scale information will be of use for future projects or to answer a question on Jeopardy. My learning style is closely coupled to having to have a use for the knowledge before really learning it. My math teachers all thought you should be thrilled with the answer and usually did not know how to apply the knowledge to an actual problem.

    What I am making is a rotary valve with adjustable timing for a compressed air engine.

    Thanks again
    Pete

    Leave a comment:


  • Paul Alciatore
    replied
    Yea, the other favorite my math professors used was, "It is obvious that ...". That usually meant you had two or three hours of effort in store that night. And an embarrassing question at the next session of that class. Marv, I guess your professors were higher class than mine and had further refined that statement.

    I know my statement above is true. I also know it is going to take a bunch of math to prove it. And I really do not have time for that now. Take my word for it or do the math and post it, your choice.

    Leave a comment:


  • mklotz
    replied
    Originally posted by Ripthorn View Post
    Paul, I loved your "exercise for the reader" comment. I am a physicist and my favorite thing to read in text books in school was something along the lines of "the astute reader will see" or something because it just assumed so much about the reader. My absolute favorite incarnation of that line was "even the most casual of observers will note...", which was science speak for "you're a total idiot if you don't see...", which of course the conclusion was not obvious.

    Anyway, back to your regularly scheduled programming.
    When I went to college, the line was,

    It is intuitively obvious to the most casual observer that...

    Leave a comment:


  • Ripthorn
    replied
    Paul, I loved your "exercise for the reader" comment. I am a physicist and my favorite thing to read in text books in school was something along the lines of "the astute reader will see" or something because it just assumed so much about the reader. My absolute favorite incarnation of that line was "even the most casual of observers will note...", which was science speak for "you're a total idiot if you don't see...", which of course the conclusion was not obvious.

    Anyway, back to your regularly scheduled programming.

    Leave a comment:


  • adatesman
    replied
    Originally posted by becksmachine View Post
    If you have the time, read the thread, Mother of invention, written by RJ Newbould over on PM.

    But only if you have time. ...... ....... It caused some late nights for me.

    Dave
    Quite possibly the most interesting thread on PM, and I too lost a lot of time to it. Absolutely fascinating.

    Leave a comment:


  • Paul Alciatore
    replied
    You are correct with your first example using 15 and 16 holes. This is because these two numbers do not have any common factors so when you align each line of the 16 hole circle with a hole of the 15 hole circle, no other lines will align. 15 = 3 X 5 and 16 = 2 X 2 X 2 X 2.

    Unfortunately, in your second example the two numbers you choose DO have a common factor. 20 = 2 X 2 X 5 and 18 = 2 X 3 X 3. The common factor of 2 is the problem and it will pop up below.

    Now, if you line up the first hole on the 20 hole circle with the first hole on the 18 hole circle and look down the line, you will see that the 11th and 10th holes also are in alignment. And as you rotate the 20 hole circle, every succeeding hole from 2 to 10 will have a hole on the 18 hole circle which it is in alignment with.

    So instead of a 20 part Vernier, what you have is TWO 10 part Verniers in a row. (There is that 2 again, as I predicted.) And you will have only 18 X 10 or 180 distinct positions. That gives a 2 degree spacing.

    Most Verniers are constructed with only ONE extra hole over the SAME distance on the primary scale. This ensures that there are no common factors. (That can be proven mathematically and I leave it as an exercise for the reader.) There are variations on this general method, but they also ensure that there are no common factors.

    If you want 1 degree spacing you are going to have to use different numbers or a different scheme. Now, notice that I said "... over the SAME distance on the primary scale." So, we can make the the 18 and 20 hole idea work if you use the 20 hole circle as the primary scale and space the 18 holes over the space covered by 17 or 19 of those 20 holes. This is not convenient for a couple of reasons. First, using 20 holes for your primary gives 360/20 = 18 degrees and that is not a round number like 10 or 15 or 20 so counting around the complete circle is not so nice. Second, there will be a small space at the end of the Vernier scale which may also be confusing. And using the 18 hole circle will not allow the 20 holes to be spaced over 19 or 21 of those holes as you will run out of holes on the 18 hole primary.

    So, you will need more holes on the primary circle. I would suggest 30 holes which would have a 12 degree spacing. Then a 12 part Vernier would provide one degree spacing. That would be the smallest number with convenient numbers in use. The 12 holes would be spaced over 13 holes on the primary circle or at 13 holes X 12 degrees /12 holes = 13 degree spacing.

    The next good set of numbers would be 36 holes on the primary circle (10 degree spacing) and 10 on the Vernier. The Vernier holes would be at 11 holes X 10 degrees / 10 holes = 11 degree spacing.

    Of course if a different final spacing, like 1.5 degrees, is allowed, then different, possibly smaller numbers can be used.



    Originally posted by Stepside View Post
    For a project I am working on I need some "Timing " between components. If I have a disc with 15 evenly spaced holes arrayed around a circle and a second disc with 16 holes arrayed around the same diameter circle "How many combinations are possible?" If I am correct, there are 240 possibilities (15 x 16) or 1 degree 30 minutes (360/240). If that is correct, then 20 and 18 would yield 1 degree spacing.

    Is there a flaw in my reasoning?

    Thanks in advance
    Pete
    Last edited by Paul Alciatore; 04-10-2015, 01:37 PM.

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  • Stepside
    replied
    Barrrington

    The 36 and 40 works perfect. As I do not need the entire 360 degrees I will just drill the holes lie in one quadrant.

    Thanks to all who helped.

    Pete

    Leave a comment:


  • becksmachine
    replied
    If you have the time, read the thread, Mother of invention, written by RJ Newbould over on PM.

    But only if you have time. ...... ....... It caused some late nights for me.

    Dave

    Leave a comment:


  • Barrington
    replied
    I think that for a 1 degree resolution I think you would need a 36 hole (10°) and a 40 hole (9°) (i.e. a 1 degree difference.)

    Each degree position would however have four possible hole combinations giving the same result.

    Cheers

    .

    Leave a comment:

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