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Sine bar question

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  • Sine bar question

    with all the talk about sine bars and the math that goes with it i have one question left looking at oldtiffie sine bar using one inch balls does the size of your balls matter?,, i couldnt help myself,, but does the size of the rolls matter? reason i ask I was cleaning my work bench and i had torn down a small block chevy and had pressed the pistons off the rods and i had a thought of using the wrist pins for the rolls on my sine bar that i may make one day the wrist pins are very hard and they both miked at .9275 isnt thats what matter the most is having 2 rolls the exzact same size also the 5 inch on center? thanks for the replies.

  • #2
    They only need be on the same plane and perfectly parallel to each other and to the working surface. It doesn't even matter how far apart they are but if they're exactly 5" on center for example you can use a lot of existing tables rather than a calculator to wring up the correct spacers.


    • #3
      Its easy!!

      Size does matter. The balls or rollers need to be the same and the "top" of the sine bar needs to be pretty close to parallel with the face the sine bar is sitting on (the dimension over each ball or roller and the "top/back" of the sine bar needs to be pretty close too. The distance between the rollers is irrelevant as the settings will probably be worked out with a calculator or a computer as I'd guess that more people would not have printed sets of sine table than those that would have them. Sine table are only easy if the sine bar is 10" as using the sine tables then only requires the decimal point top be moves "one place right". Using 5" leaves it open for a simple arithmetical slip.

      Don't get too anxious or "hung up" about sine bars as the degree of accuracy required in a HSM is easily obtained without the use of slip guages or a precision sine bar - or a surface plate either.

      If higher accuracy is needed for what-ever - fine.

      But I will re-address this later and show how it can be done quire accurately and easily at little or no cost without any need for other than simple math skills.

      I will come back to this later.


      • #4
        ok oldtiffie I will be waiting.


        • #5
          Originally posted by oldtiffie
          Size does matter.
          Size doesn't matter but they both need to be the same size, what ever that is. Good point, Tiffie.


          • #6
            One thing for sure is how are you going to drill and tap the wrist pin. They are VERY hard and you may drill it but I bet you won't tap it without annealing it. Heating it may warp it.

            Unless you are doing tool and die work or a lot of very precise angles you'll never use a sine bar. I have had one for 15 years and only used it once and really didn't need it then. I just wanted to say I had used it.
            Senior Member
            Last edited by Carld; 10-28-2008, 01:02 AM.
            It's only ink and paper


            • #7
              Three things are critical in the geometry of a sine bar, well four actually. First the two cylinders must be the same diameter. This is easy as you can purchase a piece of drill rod and cut two adjacent pieces.

              Second, the axies of the two cylinders must be parallel. This is generally assured by using a single setup to machine the two recesses they fit in.

              Third, the top surface of the sine bar, the surface that the work rests on, must be parallel to the plane through the axies of the two cylinders. Any angular error here will be an error in the angle generated.

              Finally, the distance between the two cylinders must be known with high accuracy. This is generally done by choosing a number that is easy to work with, but this is not absolutely necessary as long as the distance is accurately known.

              A 10 inch sine bar greatly simplifies the math. As it's name implies, a sine bar generates an angle by use of the sine function. With a 10 inch separation between the cylinders, the distance that one must be raised to generate a given angle is: 10 X sine(angle). So with a 10 inch sine bar, you just find the sine of the desired angle and multiply it by 10 (move the decimal point one place to the right). You almost can't miss and this is why many sine bars are 10 inch.

              A five inch bar is going to be cheaper and the same equation is used: distance between the cylinders X sine(angle). This is: 5 X sine(angle). Since 10/2 = 5, the equation can be written as: 10 X sine(angle) / 2. So you just look up the sine as above and move the decimal point one place to the right (X 10) as above and finally divide by two. Most people can divide by two easily and accurately so the 5 inch bar is almost as easy to use as the 10 inch.

              If you have a sine bar with an odd dimension, the formula is still the same, but solving it is a bit more difficult as two long numbers will have to be multiplied: distance between cylinders / sine(angle). So if the cylinders are 4.873 inches apart and the sine of the desired angle is 0.1234 then you must multiply these two numbers to find the dimension to elevate one end: 4.873" X 0.1234 = 0.6013282". So any length bar will work, but the math is harder. I cheated and used a calculator. Or is that a cheat?
              Paul A.
              SE Texas

              And if you look REAL close at an analog signal,
              You will find that it has discrete steps.


              • #8
                Yes the rolls need to be exactly the same size, 2) they have to be absolutely parallel to each other and, 3) The plane of the top surface has to absolutely parallel to the plane of the rols axis. Not close, not with in a thou or two bur dead freakin nuts. Now just the average HSM shop is going to achieve that is a very hard nut to crack. To make a sine bar a surface grinder is a prerequisite IMO. In my old job I made a matched set (not much more work to finish than a single. the extra work is in the roughing out). Not one did I ever use them in the mill. Almost never in the lathe for setting tapers. But doing grinder work for grinding profile bars for grinders and tracers lathes they were very handy. Also for making solid angles. In a way they are like the chicken and the egg. If you really need one for the work you are doing then we already have the type of machine that you use them in for set-ups.
                Forty plus years and I still have ten toes, ten fingers and both eyes. I must be doing something right.


                • #9
                  IT depends on your own perspective, but generally, size of balls does not matter as much as overall length and width of the bar.


                  • #10
                    basic sine-bars

                    Let's not get too worried about the sine bar.

                    The general principles are here:


                    Just to prove a point:
                    If the length of the sine bar in Figure 30 was 100.025 instead of 100.00 the actual angle (with correct slip guages) would be:
                    20.790/100.025 = 0.2078 = asine 11.9963 arc degree = 11 deg 59 min 47 sec.

                    If the height of the "packing/spacer" was 20.765 and the sine bar length was 100.00, the angle would be:
                    20.765/100.00 = 0.20765 = asin 11.9847 = 11 deg 59 min 4.8 sec

                    Now if I shorten the sine bar and increase the height by 0.025:
                    20.815/99.975 = 0.2082 = asin 12.0170 deg = 12 deg 1 min 1.23 sec

                    So the accuracy was pretty good since there were "errors" of 0.025mm (~0.001" - yes, one thou) introduced.

                    So if you can make a sine bar with same size "rollers" and any distance between centres (measured to 0.001") and providing that the distance over the rollers and the "top/back" of the sine-bar is also within 0.001" you will be doing OK.

                    As the "spacers/packers" need only be within 0.001" as well, slip guages and surface plates are not required. You can make your own spacers and use your mill table as a base - or even a flat piece of "float" glass (thicker the better as it is "stiffer" and won't bend as easily - or at all for all practical purposes).

                    For my purposes in my shop, I rarely if ever use a sine-bar. Setting up an angle with one is OK I guess but measuring an angle with one is a PITA as the "guages" are really being used as "feeler" guages toward the end and all the high-flying accuracy is gone. I prefer to use a good vernier or digital protractor as they have an accuracy of 6 arc minutes = 0.1 arc degree the sine of which is 0.0017 which is 0.0017" per inch which is pretty good most times and you can take the protractor to and from a job with the angle set. (Try THAT with a sine-bar!!!).

                    If I really want to set or read an angle accurately I use a bevel guage or a bevel protractor and my rotary table.

                    The bevel guage goes on my rotary table and with a good dial indicator. Setting or reading the angle to 20 arc seconds is very quick and easy.

                    Sin 20 arc seconds = sin 20/3600 deg = sin 0.0056 = 0.0001 which is 0.0001" per inch (yes - correct to 1 "tenth" per inch!!!).

                    Similarly, you can make a very accurate angle guage on your rotary table out of any old bit of scrap as well if you like.

                    So, all in all, what I have suggested is the same principles as used in sine-bar and with slip guages but with typical HSM accuracy (most times) with little or no cost and the satisfaction of making a good tool at almost no cost.

                    I have no problem with people having and/or using a sine bar and slip guages at all. Its just that they are not really needed all that often - well, here anyway - and I "get by" well enough.

                    Here are a couple of sketches that I did for a post on this forum some time ago. They might help. They are not the "be all and end all" of making a sine bar - at all. Modify them as you wish but do stick to the principles.

                    Another thought on calculated and setting/reading angles that can be a problem.

                    Angles as calculated are usually in "decimal degree" (no minutes and seconds) where-as measurement (for getting or setting) is usually in degree/minute/second as on vernier (but not digital) protractors and rotary tables etc. So do the required conversions else you will have a problem.

                    28.50 degree is NOT 20 degree 50 minutes it IS 28 degree 30 minutes (0.5 x 60 = 30 minutes).

                    31 degree 48 minutes is NOT 31.48 degree (but 31 degree 28.80 minutes IS 31.48 degree!!).

                    An angle in a triangle is only a ratio between any two sides. The length of the side/s does not matter.


                    • #11
                      Thanks to all that replied and to you oldtiffie that was a great lesson in the sine bar teaching,,many thanks Bill.


                      • #12
                        Angles etc.

                        Glad to help Bill.

                        Just a couple of items though.

                        The reason I used the "three balls" was that it is self-leveling (like a tripod) and so there is no problem with getting bars/rods parallel in all planes. Once the balls are "on" just sit the "sine-bar" on the mill table and with the head correctly trammed, take a light skim cut. That will solve the "parallel to ball/axis" problem. Take smaller diameter fly-cuts as it looks better and will pretty well cancel out any tramming errors.

                        Getting the "distances" with/for the ball centres is fairly easy too - particularly if you have a CAD system. Other than that a micrometer and a calculator will solve it using the "Law of Sines". I will cover that later - next day or so.

                        Note also that I used strong magnets - but adhesive will do. There is no need to drill and tap the balls or rod (wrist-pins etc.) as the only requirement is that the balls or rods stay in place.

                        The angle-blocks I mentioned in an earlier post can be found by searching for "angle blocks" at

                        They are very handy and as said in the page, accuracy is 0.0001" which is very good indeed. They will cover many requirements without a sine-bar or a protractor. My set which are a Chinese "Vertex " set have an extra 1/4 deg and 1/2 deg guages. They are good enough to "wring" together as a slip guage should do. But you don't need to buy than as you can make them as required with a rotary table and an end milling cutter. They are marvelous when used in conjunction with a good dial indicator as well.

                        I use them a lot with a bevel guageas I can set them veryt accurately (just like using a Machinists square) as the light does it all. They are light and portatable and can be set and taken to or from the bench and the job on the machine without getting "up-set" etc.


                        • #13
                          Just one more easy thing to remember is.
                          The height of the stack = The sine of the angle times the length between the rolls of the sine bar.
                          Every Mans Work Is A Portrait of Him Self


                          • #14
                            oldtiffie and company --

                            Sometimes the best way to use a sine bar to measure an angle is to put one edge of the angle on a surface plate, put the upside-down sine bar on the other edge of the angle, and use a height gage to measure the relative height of the rolls. Once you've done that, it's a simple matter to calculate the angle as the ArcSine of the Roll Height Difference divided by the Roll Center-to-Center Distance.

                            A worked example? Sure.

                            Let's say that the top of the higher roll is 7.653 inch above the surface table, the top of the lower roll is 5.231 inch above the surface table, and the roll centers are 10 inches apart. The angle is ArcSin [(7.653 inch - 5.231 inch) / 10.000 inch] = ArcSine (2.422 inch / 10.000 inch) = ArcSine 0.2422 = 14.016 degree.



                            • #15
                              Extension of the principle.

                              Excellent example of thinking outside the box John.

                              Too many people get limited or fixated by restricting themselves to "going by the book". It is the principles that matter - the applications follow on from that.

                              The example you give is similar to the "Tool-makers buttons" application.

                              The heights in your example don't need slip guages or a surface plate either as a mill table or sheet of flat "float glass" used with a digital or vernier height guage will do very well too.

                              One point to be made here is that in my previous example I used the 100mm (~4") sine bar in my calculations (as in the book I scanned). Now if the machinist sticks to a limit of 0.001" as I suggested, that by the principal of similar triangles (different sizes, same ratios between sides) the 10" sine-bar will be 2 1/2" times as accurate as the 4" one.

                              I will cover using discs on an angle plate the measurement or setting of angles based on the "Tool-makers Buttons" principle later. It is very simple and very accurate and providing you have a good micrometer - or even a digital or vernier caliper - and some hot rolled bar or some drill rod (silver-steel in the UK, OZ and NZ) you will be set to go.

                              I had forgotten or neglected that - many thanks for the prompt.

                              Marv Klotz showed an excellent bevel guage just using vernier or digital calipers some while ago. It was very accurate and could easily be made in the home shop. Unfortunately it got "rubbished" by too many in ways that were not justified or appreciated. I will see if I can find it.

                              I got pretty pi$$ed off when that happened to him (Marv) as he is (was?) one of the best creative and lateral thinkers that I've seen anywhere. He explained what he wanted to achieve and what he had to do it with and how he did it. In my mind he is better than Mr.Ishimura (Japanese machinist) and that is no small complement to anyone from anyone (me especially) as I am a big fan of both of them. I hold Lane in the same high regard for the same reasons.