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Thread: Ancient Tools - Divider & Compass

  1. #1
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    Ancient Tools - Divider & Compass

    Judging from the responses to a previous post about Crucible-brand dividers, I believe a post about how to use dividers and compass would be beneficial.

    let's begin the discussion with a basic technique. I encourage others to add their techniques to this thread. I will try to add more later.

    I learned how to use dividers/compass for carpentry and woodworking as a boy from my father, and from carpenters and other craftsman on jobsites over the years. But I learned the most from drafting classes in college. This was before drafting heads, digital protractors, dot-matrix printers, and CAD. Even lettering was done by hand or using plastic/metal templates. The professors were justifiably proud of their hard-earned skills and the beautiful and precise documents they could deftly produce.

    The first lesson we were taught was this: Never lay the tape or rule or scale on the drawing/workpiece and mark directly using pencil or pen, but instead use dividers to first measure the required distance on the scale/ruler, indexing the divider's points in the engraved lines, and then use those same dividers to transfer and mark the distance onto the workpiece or paper.

    The intuitive, but inefficient, way most careful people do the job is lay the ruler or yardstick or tape measure on the workpiece, index one end (a careful man will always "burn" 1" or 12" and not index directly on the tool's end), locate the target distance on the measuring tool, and make a mark. But if he is trying to layout an irregular distance like 2-3/64" (= 52 (51.99) mm), for instance, a pencil's lead or pen's tip is too wide for precision, so he will use a scribe or marking knife. To be more precise, a careful man will tip the scale or ruler on its edge, kneel down so he can see the scale's/ruler's marks clearly, fit the scribe point or knife tip into the engraved line on scale/ruler, and then transfer that to the workpiece, paper, or story stick with a quick "tick." The problem is that the far end of the ruler/scale at the point he is measuring from may wiggle out of alignment messing up his precision. Or the scribe/knife point may shift while making the "tick." With practice, these tendencies can be overcome, but clearly this method is time consuming and the results may be questionable.

    But if he uses dividers, he can fit/index their points quickly and precisely into the engraved lines in scale/ruler at each end of the measurement, first time everytime, and without kneeling or squinting or pressing down, or worrying about wiggling and shifting. Once he has set the dividers to the required distance, he can fit one of the sharp points precisely into the index hole, or onto the line he is measuring from, and then use the other point to make a precise scratch or hole in the workpiece, which can be used again for future layout reference.

    This works with dividers or trammel heads.

    Standard dividers are quickest, but a locking divider with screw adjustment is easier to adjust precisely and is more likely to retain the measured distance with repeated usage. You will find when drafting or doing layout that you repeat some distances frequently. Having 2 or 3 locking dividers set to these distances close at hand will allow you to layout those distances quickly and accurately without the need to refer to scale/ruler.

    The quality of your scale/ruler becomes important when attempting precision layout. A high-quality, professional-grade scale or ruler must of course be of proper length and uniform width and thickness, be free of twist, and have accurate lines. Be careful to procure one that will pass these 3 simple quality tests, not an easy task nowadays. Pay attention that the ruler/scale you use has engraved lines of uniform depth and width to properly index divider and scribe points, and marking knife tips.

    These principles apply to story sticks as well.

    Give it a try.

    Stan

    PS: We should also create similar threads that deal with other ancient and venerable tools such as the square, plumb bob, and various versions thereof.
    Last edited by Stanley Covington; 09-12-2017 at 7:26 AM.

  2. #2
    Good stuff - thank you Stan!

    (I, for one, would like to read more about using a plumb bob.)

    Fred

  3. #3
    Thanks Stan,

    ken

  4. #4
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    Good start Stan. As a divider and story stick user and a believer that many errors are made by transferring measurements with a rule or a tape I'm in for a discussion.
    Jim

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    Here is one good thing. Dividers don't have cumulative errors as rules or tapes. Since its point to point it does not matter which set of dividers you use to pick up a measurement.
    Jim

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    I think that what Stanley outlined above is a far more useful purpose for dividers than the trial and error approximation technique discussed in the other thread. It is far more often, for me anyway, that I know the dimension desired and need to transfer it to my workpiece (or tablesaw sled for example). Using the divider in the outlined fashion would certainly improve the accuracy of my work. Thanks Stan

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    Quote Originally Posted by James Pallas View Post
    Here is one good thing. Dividers don't have cumulative errors as rules or tapes. Since its point to point it does not matter which set of dividers you use to pick up a measurement.
    Jim
    I might need to take my 'trusty' Stanley tape measure (with the painted on markings) and check it for incremental accuracy using a dividers. It would be interesting to know just how bad (or good it is) because I have always assumed its correct enough for whatever I'm doing. I have never seen it fail me and any errors I have experienced have been of the sort Stanley outlined above

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    One of the most basic drafting exercises - find the midpoint of a line:
    1. From your subject line (red), strike an arc from the end of the line at any length greater than 1/2 of the subject line.
    2. Repeat from the other end of the subject line using exactly the same radius.
    3. Strike a line from the 2 intersections formed by the arcs.
    4. The resulting line bisects the subject line (and is perpendicular).


    Midpoint.jpg
    Yes, you can 'walk' this with dividers and trial-and-error, but the above method may be more useful and intuitive to some.

    Stan - Thanks for this trip down old-time drafting lane.

    PS - I recall reading somewhere that US tape measures are required to be accurate to +/- 3/16" in 6ft. So, two tapes could be off by as much as 3/8" in 6ft relative to each other. (always use 1 tape per project!)
    Last edited by Malcolm McLeod; 09-12-2017 at 8:41 AM. Reason: tolerances
    Molann an obair an saor.

  9. #9
    Quote Originally Posted by Pat Barry View Post
    I think that what Stanley outlined above is a far more useful purpose for dividers than the trial and error approximation technique discussed in the other thread. It is far more often, for me anyway, that I know the dimension desired and need to transfer it to my workpiece (or tablesaw sled for example). Using the divider in the outlined fashion would certainly improve the accuracy of my work. Thanks Stan
    Here is an example where a trial and error technique is helpful. Suppose you want to lay out a turned finial to carve seven flutes on the finial. In 78 seconds I was able to divide the finial into sevenths to within a thousandth of an inch. No ruler required.

    Alternatively I could measure the diameter (1.326), calculate the circumference (4.166), divide by seven (0.595), and try and wrap the tape measure around the finial. very sloppy.

    Or I could try and calculate the side of a heptagon that can be inscribed in the 1.326 diameter circle and then set the dividers to this length and then mark it off with the dividers. But the dividers sink into the wood a little, so even here you might have to make an adjustment after a trial. This is a lot of work just to avoid having skills.

  10. #10
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    Quote Originally Posted by Pat Barry View Post
    I might need to take my 'trusty' Stanley tape measure (with the painted on markings) and check it for incremental accuracy using a dividers. It would be interesting to know just how bad (or good it is) because I have always assumed its correct enough for whatever I'm doing. I have never seen it fail me and any errors I have experienced have been of the sort Stanley outlined above
    Pat, I'm certain your tape is just fine. As long as you use that tape for all of your measurements. It's when you change from your tape to a rule or your tape to mine that problems arise. I have at least 4 Stanley tapes and they all very some. I don't worry about it because I only use them for rough measurements. I'll take that back a little, I'll use a tape as the finest device when doing rough carpentry work. If this thread continues I'm sure you will come to see that dividers are not trial and error tools.
    Jim

  11. #11
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    Here is another practical layout technique using dividers.

    Let's say you need to layout a tenon or mortise centered on a line. BTW, if there is ever any question about the thickness/width of the material involved, as in timber framing, always make a centerline on each member, and layout from this line. It may seem like more work, but in the end, precision will be increased.

    First, select the width of the chisel you plan to use to cut the mortise, and which should match the corresponding tenon. This assumes that your chisel is reasonably precisely ground/honed to a consistent width, the cutting edge is sharpened square to the blade's centerline, and you have the skill to cut a clean mortise.

    Second push this chisel into some straight-grained softwood scrap cutting a mark the width of the chisel's cut. BTW, this is also the width you need to set your marking gauge to.

    Third, make a straight, very shallow line elsewhere on the scrap with a marking knife.

    Fourth, use dividers to measure the width of the chisel's cut, and transfer this distance onto the straight line made in step 3 above.

    Fifth, use your dividers to divide this distance exactly in half. One or two minor trial-and-error adjustments may be required, but this is an easily-learned skill you need to develop in any case.

    Sixth, place one point in the mortise's centerline, swing the divider to each side, and make a tiny mark each side of the centerline (not an arc). If you were to draw a line between these two points, that line should be perpendicular to the centerline. Set your marking gauge or mortise gauge using these two points. The dual-blade "kama kebiki" is the most precise for this job, IMO, but most any style can do the job.

    If you are making a story stick, or layout stick, use this divider setting to mark it. I always mark the mortise width using a mortise gauge on my layout sticks at this stage, but it is not critical.

    Give it a try.

    Stan
    Last edited by Stanley Covington; 09-12-2017 at 10:22 AM.

  12. #12
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    Quote Originally Posted by Malcolm McLeod View Post
    One of the most basic drafting exercises - find the midpoint of a line:
    1. From your subject line (red), strike an arc from the end of the line at any length greater than 1/2 of the subject line.
    2. Repeat from the other end of the subject line using exactly the same radius.
    3. Strike a line from the 2 intersections formed by the arcs.
    4. The resulting line bisects the subject line (and is perpendicular).


    Midpoint.jpg
    Yes, you can 'walk' this with dividers and trial-and-error, but the above method may be more useful and intuitive to some.

    Stan - Thanks for this trip down old-time drafting lane.

    PS - I recall reading somewhere that US tape measures are required to be accurate to +/- 3/16" in 6ft. So, two tapes could be off by as much as 3/8" in 6ft relative to each other. (always use 1 tape per project!)
    Malcolm:

    Thanks for showing us this essential technique. Great graphics!

    An interesting thing about this technique is that it is often a more accurate way of creating a perpendicular line away from an edge than using a square, especially if there is enough room to use a big divider, or better yet, trammel heads.

    There are a lot of these techniques.

    Stan

  13. #13
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    Quote Originally Posted by Warren Mickley View Post
    Here is an example where a trial and error technique is helpful. Suppose you want to lay out a turned finial to carve seven flutes on the finial. In 78 seconds I was able to divide the finial into sevenths to within a thousandth of an inch. No ruler required.

    Alternatively I could measure the diameter (1.326), calculate the circumference (4.166), divide by seven (0.595), and try and wrap the tape measure around the finial. very sloppy.

    Or I could try and calculate the side of a heptagon that can be inscribed in the 1.326 diameter circle and then set the dividers to this length and then mark it off with the dividers. But the dividers sink into the wood a little, so even here you might have to make an adjustment after a trial. This is a lot of work just to avoid having skills.
    Thanks, Warren. A perfect example of real-world speed, precision, and simplicity.

    This is another technique every serious woodworker and stone mason needs to know, and one that is applicable in many situations, not just round work.

    Stan

  14. #14
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    Quote Originally Posted by James Pallas View Post
    Pat, I'm certain your tape is just fine. As long as you use that tape for all of your measurements. It's when you change from your tape to a rule or your tape to mine that problems arise. I have at least 4 Stanley tapes and they all very some. I don't worry about it because I only use them for rough measurements. I'll take that back a little, I'll use a tape as the finest device when doing rough carpentry work. If this thread continues I'm sure you will come to see that dividers are not trial and error tools.
    Jim
    Does anyone know how to procure a very precise measuring tape? I understand the Starrett brand is quite accurate, but I am not certain.

    Here in Japan you can pay a little extra for tapes with the JIS Class One mark which are quite precise. What about the States and elsewhere?

    Of course, the clip on the end of all tape measures must always be suspect.

  15. #15
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    I bought a 16' tape measure for $3.00. Curiously,it was in a large bin of them in the front of a grocery store. The tape measured quite accurately its whole length,though the standard acceptable accuracy of tape measures is about 3/16" off in a 6' length. That is the established acceptable accuracy,i believe.

    Now,I don't mean that the tape is accurate to .001". Its divisions just line up perfectly with my vintage Lufkin and Starrett steel rules,which are fine for woodworking.

    I built my 30' x 40' shop using this tape,and still use it to this day. Made in China,of course. I could be proved wrong as I looked up acceptable tape accuracy many years ago.

    Of course,if you are building something using ONLY the same measuring device,accuracy is not so important. After the 2 x 4's inside the walls were all installed,I took a page of my plans,and measured and recorded n the plan, the center line distances between all the 2x4's starting from a corner for each wall. This was because I was going to make shelving all around inside the finished,painted plaster boarded walls. Using my measurements to locate the screws that held the shelves up,I think I only missed the unseen 2x4's twice in 450' of shelving ultimately installed. And that could have been caused by slightly curved ,or slightly out of vertical 2x4's.2x4's. The measurements were taken at the bottoms of the walls. They might have been a bit different higher up on the walls.

    I think the contractors did rather well,as it was known in a school I went to had a gymnasium that was 4' out of square! And,that was in the 1950's. Nor did I find in my 1949 house,any wall,closet,or whatever that was out of square using a rafter square. I had had to replace all the missing quarter round moldings on the base boards. They had all been removed,probably back in the 70's to install shag carpeting. To save on the dust,I used only my Jorgensen miter box and Lion miter trimmer to cut and fit the moldings.
    Last edited by george wilson; 09-12-2017 at 9:56 AM.

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