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formula for determining angle between two known dimensions

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  • OaklandGB
    replied
    Oh, my aching head....

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  • JRouche
    replied
    Originally posted by jmm03 View Post
    Math not being my strong suit, could anyone either point out where I can find the formula or tell me what it is please. I am turning down a piece of material to make a solid spacer for a suspension part and it would be certainly faster to set the angle once than to trial and error it. Thanks, Jim
    I was never good at math so I always go to tools. An adjustable angle finder has always worked for me. That and measuring three times very slowly. JR

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  • JohnMartin
    replied
    Originally posted by psomero View Post
    If you have two dims, hopefully they compose a right angle or you can turn it into a right triangle. If not, you might have to do a couple of iterations of the formulae to build the right triangle, then resolve the final angle you're seeking.

    https://mathalino.com/reviewer/plane...djacent%20side.

    Just remember soh cah toa. That'll get you the correct combination of legs on the right triangle and the corresponding angle of one of the other ends 95% of the time. I recall the cho sha cao thing, but never use it and don't remember it from sophomore year trig.

    When using a calculator, be sure to remember to put it in degrees mode, not radians, or you'll have to convert from rad to deg.
    What about the other 5% of the time? How can you be sure that your answer is correct?

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  • Bented
    replied
    Originally posted by Paul Alciatore View Post

    My apologies for not taking the time to actually draw sketches of both of these examples. If you do not understand them without a sketch, then it would be doubly informative for you to make one.

    Not a question, just a coincidence that the day after someone here posts a question about determining angles from known dimensions my employer gives me the job of boring a coupling from a sample that is damaged and therefor difficult to measure, I made the drawing as my best guess as to what the original intent was.

    The last time that I did this sort of thing for this customer I turned two external samples, one using the closest taper per foot and one using whole degree dimensions, sent them both to the plant and they picked which fit best, made the parts from this input. This of course does not preclude the shaft also being damaged.

    These parts also have keyways but that is another kettle of fish entirely.
    Last edited by Bented; 03-16-2021, 06:11 PM.

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  • Paul Alciatore
    replied
    I assume this is not the OP's part. But here goes with the mathematical solution:

    There is enough information on the drawing to calculate the angle. But remember that the angle is shown, to three decimal places on the drawing and IMHO, that number should be taken as the more accurate one here.

    We can mentally sketch a right triangle on that drawing. This triangle consists of a horizontal side starting at the point where the 2.944" dimension meets the corner, a vertical side where the 3.250" dimension meets the corner on the opposite end of the hole, and the diagonal line between those points (the hypotenuse of our triangle). Our angle of interest is the angle at that starting point of my horizontal side: this angle is half of the included angle which is shown as 6.000°.

    The horizontal side is given by the 2.922" horizontal dimension at the top of the drawing. The vertical side is one half of the differences between the two given hole diameters. This is (3.250" - 2.944")/2 which is 0.153".

    Since this triangle is a right triangle and we have the adjacent and opposite sides, we choose to work with the tangent function. Tan(half angle) = opposite side / adjacent side. Tan(half angle) = 0.153" / 2.922" = 0.0524. And according to my calculator, using the arc tan function, the half angle = 2.9973° and the full, included angle is 5.995°. That is close enough to the 6° shown on the drawing for all practical purposes.

    In this case the tangent function was the most convenient one to work with.

    And that is how you use linear dimensions, either from a drawing or from actual measurements, to find an angle.

    Incidentally, a taper specified as 1 1/4" per foot is calculated as:

    Half Angle = arc tan((1.25" / 2) / 12")
    Half Angle = arc tan(0.625" / 12")
    Half Angle = arc tan(0.0521)
    Half Angle = 2.981°
    or
    Included angle = 5.963°

    Notice that it is necessary to work with the half angle by dividing the 1.250" or the difference in the diameters by two to work with the half angles in both of these examples. this is because the drawing and the 1 1/4" per foot taper both show an angle that goes both ways from a rectangular line. And unfortunately the tangent or any other trigonometric function of twice an angle is not equal to twice that function of the original angle.

    My apologies for not taking the time to actually draw sketches of both of these examples. If you do not understand them without a sketch, then it would be doubly informative for you to make one.



    Originally posted by Bented View Post
    Curiously enough this afternoon I was given a shaft coupling sample part that is used and damaged and a new part with an unfinished bore and told to "bore it like the used part".

    The only thing that I know about the customer is that it is an old factory, it could be from a piece of equipment that is anywhere between 2 and 92 years old.
    Much old equipment was made using taper per foot and a more recent machine may be whole degrees.

    A used worn part is not exactly easy to measure accurately but have determined that it is either 1 1/4" taper per foot or 6 degrees included.



    I only get to do this once, the new one was supplied by the customer.
    Like so.

    Leave a comment:


  • Bented
    replied
    Originally posted by psomero View Post

    For this kind of stuff, I don't even bother trying to directly measure an angle. Who cares if it's 6.00 degrees, one inch per foot, or whatever? Most of the old timey stuff is not founded rational or whole numbers and I have numbers OC and my desire to make it a round number bites me in the ass with an incorrect result.

    Chuck the "good" part, set the compound or taper attachment angle using a test indicator relative to the known "good" part, bore the fresh one using angle established by indicating off known "good" part? The only numbers you have to concern yourself with in that case would be the 0 TIR on the test indicator, and some arbitrary gage diameter so the mating part seats at the correct depth.
    No compound or taper attachment, no known good part and the shaft that it fits is attached to a 40,000 lb machine in a paper mill (-:

    Leave a comment:


  • LKeithR
    replied
    Originally posted by psomero View Post

    For this kind of stuff, I don't even bother trying to directly measure an angle. Who cares if it's 6.00 degrees, one inch per foot, or whatever? Most of the old timey stuff is not founded rational or whole numbers and I have numbers OC and my desire to make it a round number bites me in the ass with an incorrect result.

    Chuck the "good" part, set the compound or taper attachment angle using a test indicator relative to the known "good" part, bore the fresh one using angle established by indicating off known "good" part? The only numbers you have to concern yourself with in that case would be the 0 TIR on the test indicator, and some arbitrary gage diameter so the mating part seats at the correct depth.
    IF you have an original part this is the easiest way to do it. You can get it perfect and never worry what
    the exact angle is. All you want is a nice finished part--that's where the money is.

    On the other hand, if you don't have a part to measure but have two diameters and a length 5 minutes
    spent with a CAD program will tell you exactly what angle you need. Easy peasy...

    Leave a comment:


  • psomero
    replied
    Originally posted by Bented View Post
    Curiously enough this afternoon I was given a shaft coupling sample part that is used and damaged and a new part with an unfinished bore and told to "bore it like the used part".

    The only thing that I know about the customer is that it is an old factory, it could be from a piece of equipment that is anywhere between 2 and 92 years old.
    Much old equipment was made using taper per foot and a more recent machine may be whole degrees.

    A used worn part is not exactly easy to measure accurately but have determined that it is either 1 1/4" taper per foot or 6 degrees included.



    I only get to do this once, the new one was supplied by the customer.
    Like so.
    For this kind of stuff, I don't even bother trying to directly measure an angle. Who cares if it's 6.00 degrees, one inch per foot, or whatever? Most of the old timey stuff is not founded rational or whole numbers and I have numbers OC and my desire to make it a round number bites me in the ass with an incorrect result.

    Chuck the "good" part, set the compound or taper attachment angle using a test indicator relative to the known "good" part, bore the fresh one using angle established by indicating off known "good" part? The only numbers you have to concern yourself with in that case would be the 0 TIR on the test indicator, and some arbitrary gage diameter so the mating part seats at the correct depth.

    Leave a comment:


  • psomero
    replied
    If you have two dims, hopefully they compose a right angle or you can turn it into a right triangle. If not, you might have to do a couple of iterations of the formulae to build the right triangle, then resolve the final angle you're seeking.

    https://mathalino.com/reviewer/plane...djacent%20side.

    Just remember soh cah toa. That'll get you the correct combination of legs on the right triangle and the corresponding angle of one of the other ends 95% of the time. I recall the cho sha cao thing, but never use it and don't remember it from sophomore year trig.

    When using a calculator, be sure to remember to put it in degrees mode, not radians, or you'll have to convert from rad to deg.

    Leave a comment:


  • Bented
    replied
    Will have to make a plug gauge as I do not have access to the shaft that the part fits onto.

    Leave a comment:


  • Bob Engelhardt
    replied
    Originally posted by Bented View Post
    Curiously enough this afternoon I was given a shaft coupling sample part that is used and damaged and a new part with an unfinished bore and told to "bore it like the used part". ... A used worn part is not exactly easy to measure accurately ...
    ...
    Would you ever make a male test piece to accurately fit (blued) the supplied part & use it to make measurements?

    Leave a comment:


  • Bented
    replied
    Curiously enough this afternoon I was given a shaft coupling sample part that is used and damaged and a new part with an unfinished bore and told to "bore it like the used part".

    The only thing that I know about the customer is that it is an old factory, it could be from a piece of equipment that is anywhere between 2 and 92 years old.
    Much old equipment was made using taper per foot and a more recent machine may be whole degrees.

    A used worn part is not exactly easy to measure accurately but have determined that it is either 1 1/4" taper per foot or 6 degrees included.



    I only get to do this once, the new one was supplied by the customer.
    Like so.

    Leave a comment:


  • Paul Alciatore
    replied
    If you really want the correct answer, you really should post a drawing or sketch with the dimensions. It sounds like you are doing something like a sine bar arrangement, but you could need either the sine or the tangent function, depending on the exact geometry. And at larger angles these two can be a lot different.

    Leave a comment:


  • JRouche
    replied
    Originally posted by tom_d View Post

    mklotz's formula is correct, and yes, you will find the angle in the trig tables. Doing the calculation electronically you would return the arctan function of the number in the formula. To find the angle in the trig tables look in the Sine column. The Machinerys Handbook I have gives an example where the large diameter is 1.5" the small diameter is 1.0" and the distance is 5"
    1.5- 1.0=.5
    .5/ (2x5) = 0.0500
    on a calculator: arctan .05 = 2.8624 degrees or 2 degrees 51 minutes 44.66 seconds
    Looking down the sine column in the handbook 0.05001 is sine for 2 degrees 52 minutes
    "Doing the calculation electronically you would return the arctan function of the number in the formula"

    Right!! Many ways to skin a ca.... JR


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  • mklotz
    replied
    Originally posted by BCRider View Post

    Not only can you easily download a full scientific calculator with trig functions for your phone but assuming you typed your post on a Windows operating system then you have a full scientific calculator included. Just bring up the calculator and up in the top left corner click on the three lines (Win 10) and all your options for calculating will appear as a list box.
    And, if you're really clever, you'll go here and download and install this excellent emulator of HP's HP35S...

    https://www.educalc.net/2336231.page

    It has some things that most of those built-in calculators don't have...

    Switchable between RPN and algebraic mode (although I can't imagine why anyone would use the latter)

    Is fully PROGRAMMABLE (just like the one HP sells)

    The onscreen window looks just like the real calculator, so, using the emulator, will get you in shape for using the real thing, should you buy one (~$60).

    Highly recommended!

    Leave a comment:

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