Ancient Tools - Divider & Compass

[Stanley Covington]

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.

[Frederick Skelly]

Good stuff - thank you Stan!

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

Fred

[ken hatch]

Thanks Stan,

ken

[James Pallas]

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

[James Pallas]

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

[Pat Barry]

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

[Pat Barry]

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

[Malcolm McLeod]

One of the most basic drafting exercises - find the midpoint of a line:

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.
Repeat from the other end of the subject line using exactly the same radius.
Strike a line from the 2 intersections formed by the arcs.
The resulting line bisects the subject line (and is perpendicular).


367719
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!)

[Warren Mickley]

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.

[James Pallas]

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

[Stanley Covington]

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

[Stanley Covington]

One of the most basic drafting exercises - find the midpoint of a line:

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.
Repeat from the other end of the subject line using exactly the same radius.
Strike a line from the 2 intersections formed by the arcs.
The resulting line bisects the subject line (and is perpendicular).


367719
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

[Stanley Covington]

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

[Stanley Covington]

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.

[george wilson]

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.

[James Pallas]

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.
Stanley, my experience is that no tapes are accurate enough to depend on for finish work. Most are ok for most carpentry work. Many people will do what is generally referred to as "burn an inch" to avoid the clip when trying to make an "accurate" measurement. Ok if your looking for 3/16 accuracy over 6'. YMMV of course. Steel surveyors tapes are pretty good in my experience, no clip and a stretching device to pull it tight, no fine markings on most.
Jim

[bridger berdel]

...... a lot of work just to avoid having skills.



Hey, it's the American way!

[Pat Barry]

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.
Of course, there are other ways to accomplish this. One involves the use of another measuring instrument, a protractor, and measuring the degrees of rotation from one location to the next - in your case 360/7 = 51.42 degrees - a strange number of course, and even more difficult to mark onto the part. The other means being to use a 'flexible' measuring tape (not your typical tape measure tape of course), measure the circumference, and then divide by 7 to get the increments.

Using the divider as you described seems to be a great solution however, although I doubt your one thousandth of an inch accuracy, I do get the gist of the method. It would seem that this method also has significant inaccuracies - how do you know the points landed exactly (within a thousandth of an inch).

All cases involve inaccuracies - its just a question of how close do you need to get.

[Warren Mickley]

Of course, there are other ways to accomplish this. One involves the use of another measuring instrument, a protractor, and measuring the degrees of rotation from one location to the next - in your case 360/7 = 51.42 degrees - a strange number of course, and even more difficult to mark onto the part. The other means being to use a 'flexible' measuring tape (not your typical tape measure tape of course), measure the circumference, and then divide by 7 to get the increments.

Using the divider as you described seems to be a great solution however, although I doubt your one thousandth of an inch accuracy, I do get the gist of the method. It would seem that this method also has significant inaccuracies - how do you know the points landed exactly (within a thousandth of an inch).

All cases involve inaccuracies - its just a question of how close do you need to get.

Something tells me you have never tried the methods you suggest.

If my dividers were .001 off, then after seven repetitions, going around the turning, it would be .007 off, something I could easily see. Reminds me of the time I marked off 1/32 on a board with a marking gauge, then counted shavings until I got down to the gauge line. Maybe more accurate than trying to measure a very thin shaving with a micrometer. They used to teach this stuff in school.

[Mel Fulks]

Warren, good technical writing there! And a good method .....until the bearings on the dividers get worn out!!!

[James Pallas]

Working with story sticks and dividers is different than working with rulers or tapes or other marked devices. When working with dividers you don't have to talk about fractions. When dividing for drawers or spaces I just use the dividers and story stick. I don't care if it is a measurement of 4 and 13/64 it's just evenly divided very accurately. No adding or subtracting fractions or trying to read 64ths off a rule. Mark your story stick and your good to go. Again YMMV. That is just part of it. If you need better than a single point or a knife line your getting into machinist work, not woodworking.
Jim

[James Pallas]

Warren, good technical writing there! And a good method .....until the bearings on the dividers get worn out!!!
Good one Mel. If that happens to me I just break out my forked branch with the animal sinew and porcupine quills and keep going. Just like Alley Oop:D

[Pat Barry]

Something tells me you have never tried the methods you suggest.

If my dividers were .001 off, then after seven repetitions, going around the turning, it would be .007 off, something I could easily see. Reminds me of the time I marked off 1/32 on a board with a marking gauge, then counted shavings until I got down to the gauge line. Maybe more accurate than trying to measure a very thin shaving with a micrometer. They used to teach this stuff in school.
I've certainly done both the protractor and the measuring tape. Never done the divider - you got me there. How close a discrepancy can you actually see with your dividers? To my point, certainly not .001" although I bet you MIGHT be able to see .005"

[Edwin Santos]

Working with story sticks and dividers is different than working with rulers or tapes or other marked devices. When working with dividers you don't have to talk about fractions. When dividing for drawers or spaces I just use the dividers and story stick. I don't care if it is a measurement of 4 and 13/64 it's just evenly divided very accurately. No adding or subtracting fractions or trying to read 64ths off a rule. Mark your story stick and your good to go. Again YMMV. That is just part of it. If you need better than a single point or a knife line your getting into machinist work, not woodworking.
Jim

Count me in your camp. I started out using tapes and rules, but when I migrated to the use of dividers and story sticks, my rate of mistakes and errors diminished dramatically. A teacher once told me that numbers are not real, they're only one interpretation of reality. There are many times I build things with no idea what the measurements are in numerical terms. I know this is the neander forum, but after abandoning numbers as much as possible for layout, the next step for me was making quick setup blocks from the story stick (or using the story stick itself) for setting up machine cuts.

This is an interesting and informative thread. I was not aware of gauging the dividers in the engraved lines of a high quality rule. This would explain one reason why high quality dividers with sharp, even points are important.

[Roger Nair]

I have considered the problem of how much spread I get when I adjust the dividers. The thread on the screw adjuster is 32 to the inch. The screw is located I/4 the leg length. A full revolution moves the points I/8. I have considered dividing the knob by sixteenths yielding 1/128 increment. Using a thumb nail as an index I believe I could get reliably close to 1/512 by interpolation. So that will gain a fairly good method of calibrating even steps but working with the tool does get easier with extended use. So what might seem like a random process can be refined by habit or calibration. Of course all this depend on the quality of threading but with a spring loaded feed sloppiness is limited.

Incra rules are very handy for setting points.

[Jim Koepke]

I've certainly done both the protractor and the measuring tape. Never done the divider - you got me there. How close a discrepancy can you actually see with your dividers? To my point, certainly not .001" although I bet you MIGHT be able to see .005"

The discrepancy is multiplied by the number of divisions. If after 7 steps there isn't a discernible discrepancy, then it is likely close enough.

Just for the heck of it one can train oneself to gauge small sizes by eye. Here is a training exercise I wrote years ago:


The Calibrated Eye
The purpose of this exercise is to train your eye to recognize small sizes for what they are. To do this exercise one needs a lot of mixed spacing washers. The sizes found on our TTMs are .001, .005, .010, .016, .030 and .040 with occasionally some other odd sizes.
A dial or digital caliper is also needed. Small containers or pieces of paper to separate the washers into different piles are also needed.
With all the washers mixed in a pile, start measuring with the caliper. Look at the edge of each one during the measuring process. Separate the washers into piles of washers that measure the same. After a short time, look at the washer before measuring it and see if you know what it will measure before it is put in to the caliper. Keep doing this until you get good.
Congratulations you now have calibrated your eyes. Recalibration may be needed if not used on a regular basis.
The Unseen Measuring Device

We also had some .003, .020, .025 and other odd sizes in the mix. My co-workers and I became fairly adept at keeping our spacing washers sorted after this training.

This not only helps at gauging sizes, it helps to train the eye to see small features like a nick in the edge of a blade.

Another training piece was on using known screw thread and the amount of rotation of a screw as a method of measurement. After all, that is all a micrometer is doing.

jtk

[Dave Anderson NH]

Keep it coming folks. This thread is probably going to end up as one with a sticky. Great content!!

[Patrick Chase]

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.

Oh goodness I *hated* that course. The actual drafting (including techniques such as you described) was great, but getting graded on lettering, not so much.

[Patrick Chase]

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

Technically they DO have cumulative errors, but they're very small.

The point can "wander" a tiny bit for one reason or another (grain-following, uneven surface, etc) while you rotate the divider. Also if the points that you choose aren't along exactly the same line then you'll accumulate cosine error that will progressively cause you to undershoot, though again this is *small*.

[Patrick Chase]

One of the most basic drafting exercises - find the midpoint of a line:

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.
Repeat from the other end of the subject line using exactly the same radius.
Strike a line from the 2 intersections formed by the arcs.
The resulting line bisects the subject line (and is perpendicular).


367719
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!)

"required by some standard somewhere" is not the same as "are". Modern metal tapes are pretty darned accurate once you get past the sliding thingy on the end.

[Patrick Chase]

If my dividers were .001 off, then after seven repetitions, going around the turning, it would be .007 off, something I could easily see. Reminds me of the time I marked off 1/32 on a board with a marking gauge, then counted shavings until I got down to the gauge line. Maybe more accurate than trying to measure a very thin shaving with a micrometer. They used to teach this stuff in school.

I think Warren is right here. I'm about as "numbers-obsessed" as they come, and I wouldn't try to do this any way but the one Warren suggested.

[James Pallas]

Technically they DO have cumulative errors, but they're very small.

The point can "wander" a tiny bit for one reason or another (grain-following, uneven surface, etc) while you rotate the divider. Also if the points that you choose aren't along exactly the same line then you'll accumulate cosine error that will progressively cause you to undershoot, though again this is *small*.
i agree with you Patrick. Your engineer "shorts" are showing a little on this one. We can also readily see a human hair, +\- 3 thou or so. If I try to get much better than that woodworking I'm bald tires on ice, IMHO.
Jim

[David Eisenhauer]

Nowhere anyway near Warren's league in any way, shape or form, but I could see/understand what he was talking about. Once again, thanks Warren for the great advise. But Jim just blew me away with the "Eye Calibration" exercise. I got to try that as soon as I acquire a digital micrometer. Like Edward, I graduated to using story sticks when turning out a set of kitchen cabinets or other household build-ins years ago when I was doing that, but have just started scratching the surface of divider use after reading through some of the "By Hand and Eye" content. "Numbers are not real, only one interpretation of reality". Thanks for that Edward - a very, very good one.

[Pat Barry]

i agree with you Patrick. Your engineer "shorts" are showing a little on this one. We can also readily see a human hair, +\- 3 thou or so. If I try to get much better than that woodworking I'm bald tires on ice, IMHO.
Jim
Yes, you can see a hair. I don't think you could see a spread of .003" between points of a divider. Let's face it, the points aren't .001" diameter.

[Joe Tilson]

Thanks folks, This reminding of what was taught in shop class during High School years. I have started using dividers again, but hadn't thought of story sticks. Thanks Stan for bring this to mind. I use a scale to get accurate measurements, or sometimes a folding rule for consistency. Took blueprint drawing after mechanical drawing, very interesting. Still make numbers that way today.

[James Pallas]

Yes, you can see a hair. I don't think you could see a spread of .003" between points of a divider. Let's face it, the points aren't .001" diameter.
If you are stepping off you are only looking at one point and a previous pin prick. I don't know how small that would be exactly but if right next to each other good enough for me.
Jim

[Glen Johnson]

We need to remember why they are called dividers. They are useful for division. Imagine you have a board that is 5 7/32 inches in width and need to divide it in three. The mental math needed to a this slows down all but math geniuses. On the other hand, doing this division with dividers is simple and fast. You take the divider, set the width to what looks like a third and then set one point on the edge and the other on a line across the width. Then you step across the width moving the point on the edge rotating the divider 180 degrees pivoting on the other point. You then do the third pivot by rotating the divider a third time to the far edge. You look at the gap at the edge of the board. If the edge point is off the edge of board, adjust in by a third of the distance. If the point falls short of the edge, adjust the divider out by a third. Then repeat the process until three steps across the board results in the divider point stopping exactly on the edge of the board. No fancy fractional math needed. Once set, the dividers can transfer the correct measurement distance to a marking gauge, fence, story stick, or rule.

[James Pallas]

Maybe a little practical use knowledge for some of those that don't use dividers regularly. This is what I do if dividing. I step off from my start point with very light pressure, no mark needed yet just enough to set the leg. Step off until I get what I like. Now walk down applying more pressure to make a deep mark you can see easily. Now if you want to square off put the point of your knife in the mark slide your square up and knife in. I would guess others do differently. This works for me.
Jim

[James Pallas]

Something tells me you have never tried the methods you suggest.

If my dividers were .001 off, then after seven repetitions, going around the turning, it would be .007 off, something I could easily see. Reminds me of the time I marked off 1/32 on a board with a marking gauge, then counted shavings until I got down to the gauge line. Maybe more accurate than trying to measure a very thin shaving with a micrometer. They used to teach this stuff in school.
Warren you got me laughing with your last sentence. In school the shop teacher was also the chemistry teacher. Good combination for learning about measuring. Tough combination for examinations:).
Jim

[steven c newman]

Wonder how hard it would be to buy some Brass bar stock.....and make your own dividers?

[Pat Barry]

Warren you got me laughing with your last sentence. In school the shop teacher was also the chemistry teacher. Good combination for learning about measuring. Tough combination for examinations:).
Jim
Yesh, it was super funny. LOL. Thing is, when I went to school we used sliderules, not dividers. We certainly didn't use dividers in any drafting class, although we did use a compass, but never to do division. I suspect that back in the really old days, before "new math" they might have covered ancient techniques. I haver never seen a machinist use a dividers although they all use calipers. I have never seen dividers used in an industrial setting. I think if you are happy using the dividers then more power to you.

[Jim Koepke]

Wonder how hard it would be to buy some Brass bar stock.....and make your own dividers?

It would depend on the quality you want.

I made some Fibonocci divider/gauges out of wood:

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Dividers wouldn't be any more difficult.

jtk

[steven c newman]

Maybe start a "build thread" about how to make one? I'm sure someone here can do that? I'll look around this weekend, and see what metal I can scrounge up. maybe some Brass knobs to dress it up a bit? Quandrant might be just a plain flat piece, have a brass knob to lock it in place? Hmmmm....

[Mel Fulks]

Pat makes some valid points. But besides engineering there is the consideration of how things look. Columns and other architectural features need to be done with dividers. Yes, there are different systems ,dividers are needed with all of them
at the custom shop level. I'd rather listen to condescending comments about how my work is accomplished than be guilty of turning out the schlock now seen in the nuttier post modern dreck. I concede that the mass produced factory millwork could be designed with a slide rule. But I don't want to assign blame to useful methods.

[James Pallas]

It would depend on the quality you want.

I made some Fibonocci divider/gauges out of wood:

367755

Dividers wouldn't be any more difficult.

jtk
Those look very nicely done Jim. I've never used any. Thought about making or buying them. What ratios did you use to make them?
Jim

[James Pallas]

Maybe start a "build thread" about how to make one? I'm sure someone here can do that? I'll look around this weekend, and see what metal I can scrounge up. maybe some Brass knobs to dress it up a bit? Quandrant might be just a plain flat piece, have a brass knob to lock it in place? Hmmmm....
Steven from the work you have shown you are more than capable of making dividers. Two points and a way to hold the setting is about it. I'll be watching to see what you come up with.
Jim

[William Fretwell]

I remember a year of drafting classes many years ago, before they let us loose on machines or tools. I also remember how boring it was, the equipment was rather good however. I blame the teacher as good teachers left their mark on their subject.
As the need arises we learn things and methods, often the simple things prove most useful and more accurate. I love 'clever' ways of working. Story sticks, patterns and jigs improve my accuracy and productivity, I work to a ruler on a large scale more than small scale.
I will look for a large pair of dividers to expand my range.

[Patrick Chase]

Yes, you can see a hair. I don't think you could see a spread of .003" between points of a divider. Let's face it, the points aren't .001" diameter.

Let's use Warren's example to look at what sorts of errors you can accumulate with a tape measure. Turned finials typically have always-varying diameter (i.e. there are no significant cylindrical sections), so the obvious gotcha is that your tape will always be trying to "walk" in one direction or the other as it wraps around the piece, causing the effective circumference to change. I don't know about you, but I don't find it very easy to keep a tape perfectly perpendicular to the piece's long axis under those conditions. In contrast it's pretty easy to mark a circumference on the piece while turning, and use that to guide your dividers as you walk them around.

I would guess that the dividers' accuracy advantage would be measured in hundredths rather than mils in that case. Warren picked that example for a reason.

[John Gornall]

An accurate tape - Lufkin W606P - only 1/4" wide and 6 feet long - we have a dozen or so and use them everyday in out shop - no clip error as there is no clip as zero is 3 inches from the end - no burning an inch which eliminates many errors. Backside reads diameter when wrapped around. Dimensions on tape are precise. Fits nicely in pocket.

[Jim Koepke]

Those look very nicely done Jim. I've never used any. Thought about making or buying them. What ratios did you use to make them?
Jim

Mine were made using a pattern found online:

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The rivets came from Lee Valley:

http://www.leevalley.com/us/hardware/page.aspx?p=40386&cat=3,41306,41327

jtk

[Patrick Chase]

Mine were made using a pattern found online:

367770

The rivets came from Lee Valley:

http://www.leevalley.com/us/hardware/page.aspx?p=40386&cat=3,41306,41327

jtk

The other lengths are really easy to derive from the length of the two long legs.


Let the length of the long legs be called 'AF' (AF = 340 mm in yours example)
In your drawing the length BG must be AF/golden_ratio = AF/1.62. (so BG = 340/1.62 = 210 mm in your example)
For the linkage to work the polygon ABEC must be a Rhombus. That tells us a couple things:

BF = BG (from rhombus angle equalities)
AB = BE = EC = CA = AF - BF = AF - BG (340 - 210 = 130 mm in your example)


From that alone we have all of the dimensions. Note that you can create a divider for any ratio you want by replacing the number "1.62" in the second step.

[Stanley Covington]

Here is a link to an interesting website with instructions and pictures for basic techniques using dividers and compass. His precision could be better, but the technique is solid.

http://toolbytool.com/ch07-compassDividersStraightedge.html

[Todd Stock]

In addition to dividers and compass, we use so-called 10 point (actually 11 points and 10 spaces) and both standard and universal proportional dividers in the shop. The 10 points are available in larger sizes, which reduces the stepwise accumulation of errors, but I've never see a set of universals ( outside one of those 4' long mocked-up teaching aids) in anything other than 10", so will require a step or two with a standard divider for large projects (e.g., a hendecagon...11-sided table)...as Warren suggested, a little math and trial and error is usually faster where direct layout is not possible. We have a smaller set of proportionals for really small stuff like laying out string nuts or bridges. Available on eBay, although use caution as prices fluctuate wildly for quality drafting and layout tools. My dividers come mostly from a student formerly employed as a government map maker...lovely stuff tossed as useless as the job moved to digital media.

Even if not using dividers for open shape layouts, they are handy for checking the final result.

[Pat Barry]

The other lengths are really easy to derive from the length of the two long legs.


Let the length of the long legs be called 'AF' (AF = 340 mm in yours example)
In your drawing the length BG must be AF/golden_ratio = AF/1.62. (so BG = 340/1.62 = 210 mm in your example)
For the linkage to work the polygon ABEC must be a Rhombus. That tells us a couple things:

BF = BG (from rhombus angle equalities)
AB = BE = EC = CA = AF - BF = AF - BG (340 - 210 = 130 mm in your example)



From that alone we have all of the dimensions. Note that you can create a divider for any ratio you want by replacing the number "1.62" in the second step.
Of course, you will need to MEASURE precisely to the specified dimensions in order to create a tool that performs as expected.

[Brian Holcombe]

Maybe more accurate than trying to measure a very thin shaving with a micrometer. They used to teach this stuff in school.

Hah!

Thank you Stan! Great thread! Thank you Warren also, wonderful insights.

I use dividers a fair bit, not as often as I should but good habits take time. I use them for shoji just as Stan mentioned in the previous thread.

Tape measures are not especially accurate, mostly due to the moveable end piece, but they can repeat fairly well. I use mine for rough cutting stock and for measuring corner to corner to check squareness.

We had a tape measure at the machine shop, and truly I can't recall it being used for anything other than building a crate to ship a finished motor. Even in scenarios where it may have been practical to use one we would usually default to a steel rule. I recall my mentor being appalled by the thought of using a tape measure for anything really, anytime I use one in my shop I can feel the same hairy eyeball I would receive if I were reaching for it in the machine shop, as if he is looking in on me and shaking his head. :D

[David L Morse]

Of course, you will need to MEASURE precisely to the specified dimensions in order to create a tool that performs as expected.

It can be done without measuring anything. A compass and straightedge can be used to construct a Golden Rectangle and the appropriate dimensions transferred from there with dividers.
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[James Pallas]

To me the most important thing in measuring is portability. We use it all of the time. Marking gauges, calipers, set up blocks,etc, etc. Rulers and tapes do the same except for the fact that the human element comes into play, our eyesight, memory, steadiness of hand and such. Dividers do double duty by dividing and transferring. We even make things to make rulers and tapes better, ruler stops and all kinds of fancy rulers with preset markings. Dividers are a good part of the kit.
Jim

[Pat Barry]

It can be done without measuring anything. A compass and straightedge can be used to construct a Golden Rectangle and the appropriate dimensions transferred from there with dividers.
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Yes, I see that you can use the divider to construct golden ratio / rectangle.

I'm not so sure that it can be used to create the dimension Patrick indicated (210 mm) from the 340 mm starting point however per Patrick: "the length BG must be AF/golden_ratio = AF/1.62. (so BG = 340/1.62 = 210 mm in your example)"

[Pat Barry]

Hah!

Thank you Stan! Great thread! Thank you Warren also, wonderful insights.

I use dividers a fair bit, not as often as I should but good habits take time. I use them for shoji just as Stan mentioned in the previous thread.

Tape measures are not especially accurate, mostly due to the moveable end piece, but they can repeat fairly well. I use mine for rough cutting stock and for measuring corner to corner to check squareness.

We had a tape measure at the machine shop, and truly I can't recall it being used for anything other than building a crate to ship a finished motor. Even in scenarios where it may have been practical to use one we would usually default to a steel rule. I recall my mentor being appalled by the thought of using a tape measure for anything really, anytime I use one in my shop I can feel the same hairy eyeball I would receive if I were reaching for it in the machine shop, as if he is looking in on me and shaking his head. :D
Yes - I agree - you won't find much use for a tape measure in a machine shop. You will however find many more uses in a sheet metal shop.

[Jim Koepke]

Of course, you will need to MEASURE precisely to the specified dimensions in order to create a tool that performs as expected.

Mine were laid out using a metric zig-zag rule and 'burning' the first centimeter.

Also the points weren't cut until after assembly.

jtk

[steven c newman]

Hmmm thinking some more on the home-made Brass divider project:

2 square sections of brass bar stock
1 section of the thicker brass plate stock ( quadrant)
Set screw to hold the fixed end of quadrant
Brass bolt, or thumbscrew to hold the moving leg to the quadrant...
Brass bolt to act as a "hinge" at the top.
2 hardened steel points....may use a couple of "scribe" pins from old combo squares.

Maybe a weekend , or two to complete? Depends on the cost of the parts....and how soon I can get to this.

Length of the "arms"? 6"? 8" or something else? Brass was chosen for it's ease to work with the few tools in my shop. It IS a woodshop, not a machine shop,after all.

[Pat Barry]

Hmmm thinking some more on the home-made Brass divider project:

2 square sections of brass bar stock
1 section of the thicker brass plate stock ( quadrant)
Set screw to hold the fixed end of quadrant
Brass bolt, or thumbscrew to hold the moving leg to the quadrant...
Brass bolt to act as a "hinge" at the top.
2 hardened steel points....may use a couple of "scribe" pins from old combo squares.

Maybe a weekend , or two to complete? Depends on the cost of the parts....and how soon I can get to this.

Length of the "arms"? 6"? 8" or something else? Brass was chosen for it's ease to work with the few tools in my shop. It IS a woodshop, not a machine shop,after all.
Of course you could make a very serviceable one out of wood as a prototype. I would suggest going for the 6 inch leg length as long as you are making one. You just need to be able to lock the arms - maybe a bolt, a couple of washers and a wing nut for example at the pivot point. You don't even need to make a saddle / bridle joint to get something that will work fine. If you need an adjustment screw it will add considerable complexity.

[steven c newman]

Will need a 5" non-ferrous scrollsaw blade....with pin ends. Makes it a bit easier to cut out the brass Quadrant. Have the taps and dies.....Hmmmm

[William Adams]

I did a similar tool a while back --- the file and notes on the hardware might help: http://www.sawmillcreek.org/showthread.php?235456-Locking-Register-Calipers-after-H-O-Studley

[Pat Barry]

Lest all think I don't fit in the neander section, or wouldn't know a divider if it poked him in the eye, I thought I would show you my woodworking dividers - OK one is an old compass, probably from high school, that I still use from time to time for drawing circles, marking arcs, etc. The middle dividers with the fine points is one originally used to measure heart waveforms, back from when we still had paper print-outs. The pair on the left is one I use most often but which needs some tip dressing.
367816

[Mel Fulks]

Pat, good start. Get a pair of hand made old ones and you will be collecting them. Beautiful and useful things.

[James Pallas]

Lest all think I don't fit in the neander section, or wouldn't know a divider if it poked him in the eye, I thought I would show you my woodworking dividers - OK one is an old compass, probably from high school, that I still use from time to time for drawing circles, marking arcs, etc. The middle dividers with the fine points is one originally used to measure heart waveforms, back from when we still had paper print-outs. The pair on the left is one I use most often but which needs some tip dressing.
367816
Pat be careful and don't stick yourself with the sharp end. You will soon be over your fear of the unknown past.
Jim

[Chris Parks]

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.

I believe that BMI are made to a certified standard http://www.bmi.de/en/products-pocket-tapes.php

I use this one at all times, notice no clip http://www.bmi.de/en/products-pocket-tapes-429-bmimeter.php

I use a standard measure rod in my workshop which I had made for all my machine fences and these tapes (I have several) measure spot on or as spot on as can be measured by eye with my machine fences.

[Jim Koepke]

There are a couple drafting sets of mine that have been misplaced. They could even still be in California. Drafting compass sets were a dime a dozen when everything was switching to CAD. Now they are starting to climb in price because they are "antiques." There are plenty compasses or dividers to work with in the shop:

367825

The fancy set is kept in the house:

367826

The beam points in this set have a knurled wheel to fine adjust the setting. They do the same job as a set of trammel points. There are also some fancy inking accessories in this set for various dashed or dotted lines.

Heck, just thought of another dividers stashed in a drawer not in the pictures above.

Just the same they seem to call my name and grab hold of my wallet if a set jumps out at me somewhere.

jtk

[Frederick Skelly]

Great thread guys! I second making it a stickie.

[Chris Parks]

The discrepancy is multiplied by the number of divisions. If after 7 steps there isn't a discernible discrepancy, then it is likely close enough.

Just for the heck of it one can train oneself to gauge small sizes by eye. Here is a training exercise I wrote years ago:



We also had some .003, .020, .025 and other odd sizes in the mix. My co-workers and I became fairly adept at keeping our spacing washers sorted after this training.

This not only helps at gauging sizes, it helps to train the eye to see small features like a nick in the edge of a blade.

Another training piece was on using known screw thread and the amount of rotation of a screw as a method of measurement. After all, that is all a micrometer is doing.

jtk

I did my trade as a hand compositor and one thing that it did was train your eye to measure quite accurately and reliably.

[Mel Fulks]

In the 1960s tape rules were pretty expensive and there were differences among brands. Companies often demanded all employees use the same brand. As has been noted before, they are much better now. Harbor freight has a 1/4 inch wide carabiner 10 ' tape; English on one edge and metric on the other. They have nice clear skinny marks and line up exactly with my two foot Starrette combination square blades. Ends are non slide-adjust but accurate. Cost is one dollar.

[Jim Koepke]

Is there a moderator who can link this thread in the Neanderthal wisdom/FAQs folder?

It would fit in right here:


4. Tool usage and maintenance/tuning
Hand planes
Block Plane selection and rehab, Bob Smalser
Spokeshave tune-up, Bob Smalser
Getting started in handplanes, James Koepke
Everything you ever wanted to ask about molding planes but were afraid to ask.
Chisel
Chisel names, types and uses, Bob Smalser
Saws
Sharpening a handsaw, Bob Smalser
Resawing using a frame saw, by Bob Easton
BowSaw resources: by Peter Cobb. This post includes articles and videos on various bowsaw related topics (how to make, sharpen, use etc.)
Files and rasps
Card scrapers
Tuning Card Scrapers, Bob Smalser
An interesting thread on card scrapers. See post #7 by Derek Cohen for a link to his article.
Vices
Other

A new category would have to be created.

jtk

[michael langman]

The use of dividers was taught and used by machinery repairmen in the navy. The concepts of geometrical construction in the machiney repairman book using dividers was common knowledge in the shop while I was in the navy.

[William Fretwell]

Well I bought the last display pair of big dividers from my not so local LV. Made in France! Perhaps they use them for wine barrels!
The points are somewhat square so will need careful honing unless they are designed to ream out the mark as you spin the compass.
Derek will know!

[Jim Koepke]

Well I bought the last display pair of big dividers from my not so local LV. Made in France! Perhaps they use them for wine barrels!
The points are somewhat square so will need careful honing unless they are designed to ream out the mark as you spin the compass.
Derek will know!

Maybe it is actually a mult-tool with built in bird cage awls for points?

jtk

[Patrick Chase]

Well I bought the last display pair of big dividers from my not so local LV. Made in France! Perhaps they use them for wine barrels!
The points are somewhat square so will need careful honing unless they are designed to ream out the mark as you spin the compass.
Derek will know!

FWIW I don't think there's any particular reason to buy dividers from a woodworking outlet. You can find plenty of very serviceable ones (with sharp points) anywhere that sells drafting tools. Mine are mostly Alvin (German made) FWIW.

[Ryan Mooney]

Mostly related is the clickspring video on laying out gears and making a dividing plate as part of his antikythera reconstruction process.

https://www.youtube.com/watch?v=BIUAdINXZmQ

Also Jim, the jeweling on that second set of drafting tools you have there is simply divine.

[William Fretwell]

This is Canada, we don't have a lot of shopping choices outside of the really major cities. You get used to it. These were a foot long. Postage rates here are also one of the highest in the world, add in crossing a border and it stops you buying much by mail.
The Alvin's I see on ebay are school size.

[Mel Fulks]

Ryan,that's a terrific video ,thank you. Always interested in the antithekera.

[James Pallas]

Ryan, Thank you for posting that video. Some very interesting info. Much of his set up could apply to woodworking as well as metal working. The part about expanding the fixture to make marking out easier is a good thing to remember.
Jim

[James Pallas]

This is Canada, we don't have a lot of shopping choices outside of the really major cities. You get used to it. These were a foot long. Postage rates here are also one of the highest in the world, add in crossing a border and it stops you buying much by mail.
The Alvin's I see on ebay are school size.
William, I have a large compass, about 12" I believe. I replace the pencil with an awl and use that if I have the need for a large divider. Works very well for me. As I recall it wasn't terribly expensive and does double duty.
Jim

[Patrick Chase]

This is Canada, we don't have a lot of shopping choices outside of the really major cities. You get used to it. These were a foot long. Postage rates here are also one of the highest in the world, add in crossing a border and it stops you buying much by mail.
The Alvin's I see on ebay are school size.

Yeah, with the Alvins you have to use an extension arm up to ~12" and then trammel points (or a "beam divider" as they call it) beyond that.

[Normand Leblanc]

A few years back while I was building this
367899

I wanted the drawers to be gradually thicker and the frame was already done. After some googling I found this site
https://www.popularwoodworking.com/techniques/graduated_drawers_woodworking_design
where dividers where used (no measuring).

It worked great.

[Chris Parks]

Ryan,that's a terrific video ,thank you. Always interested in the antithekera.

Any Clickspring video is worth watching, his layout skills are very good. Many hours have been spent watching in amazement at his skills and the clocks he makes.

[Stanley Covington]

Here is a very ancient and reliable technique to accurately make perpendicular (right angle) lines using just divider/trammel and straightedge or dryline/chalkline/inkline, but without using graduated linear measuring tools like a ruler or tape measure. This simple technique has been used since ancient times as a very accurate way to determine if an angle is 90 degrees, and for drafting and laying-out everything from furniture to the Great pyramid.

Assume you have a line (reference line) and want to make another line perpendicular to it.

1. The first step is to use your divider to divide the reference line into 5 equal-length segments. Let's call the starting point of these segments, the point where you want the perpendicular line to intersect the reference line, Point A. Make a mark at each of the 5 segments. Let's call the end point of the 4th (not 5th) segment Point B.

2. Set your divider to the distance of three of these segments.

3. Place one of the divider's points at Point A, and draw/scratch an arc.

4. Change the divider's setting to equal 5 segments, place one leg at Point B, and draw an arc intersecting the previous arc. Let's call the intersection of these two arcs Point C.

5. Draw a line with a ruler, snap a line with a chalkline or inkline, or pull a dryline from point A and either to, or through, Point C. The angle between A-B and A-C is 90 degrees.

This is called a "3-4-5 triangle" and was used as a real-world graphical method to layout/check right-angles long before Pythagoras figured out that Asquared+Bsquared=Csquared. There are many applications for this triangle beyond this single example, as you can easily imagine.

The larger the segments, the more precise your layout will be.

On a modern construction jobsite, chains and transits/theodolites/stations are the preferred method, but you may not always have such pricey equipment on-hand.

6" dividers are useless for laying out excavations on a jobsite of course. The divider can be replaced with a stout dryline trammel using 2 nails as points, but the line tends to stretch and accuracy may suffer. A more accurate but cumbersome method is make a trammel from a 2x4 with a spikes as heads/points. Drill/insert one spike through the far end of the 2x4's narrow edge, and use a C clamp to secure the other spike to the 2x4's side. This trammel is used to scribe the soil. It takes at least 2 guys and maybe 3 to operate this ancient tool, but I have used them up to 12' long with good accuracy. Make sure the ground is clear and will allow enough clearance to swing the trammel.

Of course, the 3-4-5 triangle works with a tape measure or surveying chain too, but it is hard to beat the precision of a good pair of dividers or a trammel.

Stan




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[James Pallas]

Interesting example of trusting the tool instead of a measurement. Years back I had a young man come to work for the summer. Put him to work with the framers. After a few weeks I asked him how he was doing. He told me that he had gained a lot of respect for the people he was working with. He said he had no idea how complicated the job was to do. What he found interesting was that the crew used higher math all of the time but had no idea what to call it. It was things like Stanley's example that caught his attention. The young man was a college math major.
Jim

[Todd Stock]

Excellent! The 3-4-5 is such a useful construction. Great tool for laying out deck and porch joists when the ledger board is a little less than perfectly straight!

Another construction for a perpendicular that does not require a walk-off and minimizes divider resets is:

- Mark the point of the perpendicular on the baseline (we will call it P)
- Use a dividers to swing a circle of arbitrary radius around the point, creating two additional points along the baseline on either side of P - we'll call these P' and P''
- Reset the dividers to a larger, still arbitrary radius (the larger, the better) and swing arcs off P' and P''
- The perpendicular of the baseline passing through P is the line between the intersections of those arcs (although with less accuracy, just one of the intersections and P may be used)

Once the perpendicular is constructed, two additional arcs can be swung off the baseline and perpendicular to find the 45 degree from P, and the same form of construction will bisect any angle.

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[Stanley Covington]

Excellent! The 3-4-5 is such a useful construction. Great tool for laying out deck and porch joists when the ledger board is a little less than perfectly straight!

Another construction for a perpendicular that does not require a walk-off and minimizes divider resets is:

- Mark the point of the perpendicular on the baseline (we will call it P)
- Use a dividers to swing a circle of arbitrary radius around the point, creating two additional points along the baseline on either side of P - we'll call these P' and P''
- Reset the dividers to a larger, still arbitrary radius (the larger, the better) and swing arcs off P' and P''
- The perpendicular of the baseline passing through P is the line between the intersections of those arcs (although with less accuracy, just one of the intersections and P may be used)

Once the perpendicular is constructed, two additional arcs can be swung off the baseline and perpendicular to find the 45 degree from P, and the same form of construction will bisect any angle.

367907

Another classic technique! Thanks, Todd.

[David Eisenhauer]

Thanks for the link Normand. I see the article was written by George Walker - one of the authors of "By Hand and Eye" that I have been going through lately. This is a good practical application of the design ideas presented in the book.

[Bob Glenn]

There are much simpler methods to divide a width using a sector or a ruler. I won't go into how to use a sector or where to get one, I had to make mine, but you can goggle it. The ruler method is related to the sector and easier to explain.

If you want to divide the width of a board into seven equal increments, just take a ruler and lay it across the width of the board with one end at the edge of the board and the seven mark on the other edge. The ruler should be at an angle across the board. Now make a tic mark at each one inch increment and you have just divided the board into seven even increments! No trial and error, no math. Try it, it's easy!

Now using this knowledge, think about how to make a marking guage that will scratch a center line down the width of a board with parallel edges. Bob

[Edwin Santos]

There are much simpler methods to divide a width using a sector or a ruler. I won't go into how to use a sector or where to get one, I had to make mine, but you can goggle it. The ruler method is related to the sector and easier to explain.

If you want to divide the width of a board into seven equal increments, just take a ruler and lay it across the width of the board with one end at the edge of the board and the seven mark on the other edge. The ruler should be at an angle across the board. Now make a tic mark at each one inch increment and you have just divided the board into seven even increments! No trial and error, no math. Try it, it's easy!

Now using this knowledge, think about how to make a marking guage that will scratch a center line down the width of a board with parallel edges. Bob

I use the angled ruler technique often and I might mention, you can use any even multiple of the desired segments i.e. if you want to divide the board into thirds, lay the angled ruler 0 one end and angled so 9 is on the other, make your marks at 3 and 6.

However if you are making a story stick which is only 3/4" wide, the angled ruler is no help but a sector is. The sector I made definitely works, but not to the precision of dividers so I use it to get in the ballpark, and if the task demands precision, I then walk it with dividers to fine tune the accuracy. A sector looks very impressive hanging on the wall but if you gave me the choice of a having a sector or a pair of dividers I'd take the dividers any day.

[James Pallas]

There are much simpler methods to divide a width using a sector or a ruler. I won't go into how to use a sector or where to get one, I had to make mine, but you can goggle it. The ruler method is related to the sector and easier to explain.

If you want to divide the width of a board into seven equal increments, just take a ruler and lay it across the width of the board with one end at the edge of the board and the seven mark on the other edge. The ruler should be at an angle across the board. Now make a tic mark at each one inch increment and you have just divided the board into seven even increments! No trial and error, no math. Try it, it's easy!

Now using this knowledge, think about how to make a marking guage that will scratch a center line down the width of a board with parallel edges. Bob
Bob, There are many ways to do things usually. Your way is a good method and I have used it. The only issue I have with it is you have to introduce another device to square your lines back to the end of the work if you need the marks at the end. Sectors are good also but again you have to introduce another device to transfer the marks.
Jim

[Ryan Mooney]

I've used the 345 trick like Stanley mentioned for laying out square foundation lines for farm buildings and fence corners using three wooden stakes and some baling twine. Basically you can just take a string as long as the side you want to reference off of, fold it into 3 or 4 segments (as is convenient.. depending on clearance/length of the other side) and then use that to measure the other two sides of the triangle. You can of course use any multiple of those numbers (6,8,10 or 9, 12, 15 for instance).

I would second that all of the Clickspring videos are quite good but I especially enjoy his tooling ones and the recent batch with the Antikythera repro he's been doing a good handful of what might be termed more "primitive" (or less heavily tooled anyway) techniques that I think are really relevant to a lot of folks here interests. I know at least one person is using a copy of his "jam vise" for a stitching pony (for stitching leather).

[steven c newman]

Guess I don't have to make one...now
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6" dividers, and an Inside caliper...$5 each, today.

These will go well with a $0.50 item I got a few weeks ago..
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Just about the same size. Works for me...

[steven c newman]

And....to "complete the set"....picked this little fellow up today..
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Even came with a pencil! Between a contractor pack of 180 grit sandpaper, and these three tools
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Spent $5 this morning at a Barn Sale...

[Stanley Covington]

I mentioned before using dividers/compass to scribe/layout around walls and columns.

The website linked below is about the restoration of a famous and wonderful wooden yacht. It shows an example of using a compass to layout curved planks for the yacht's hull. In the shipwright trade, this technique is called "spiling."

Take a look. I think you can see how useful this ancient method is, and can imagine many potential applications.

http://coronet1885.com/?p=1038

This example uses a thin wooden strip suited to planking, but for architectural purposes, a wider board or piece of cardboard is usually used.

Stan

[steven c newman]

Picked this one up today..
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A real "corker" at $3 + Tax...arms are just under 8" long. I'll need to get rid of that black paint....

[Mel Fulks]

Steven, last time I got one like that for 3$ was 40 years ago. And it was a great deal then!

[steven c newman]

Have since removed to black paint, and cleaned and oiled the moving parts....even sharpened the points. One leg has a "Made in USA" 8, the other has a Scioto Tool Co.

Can get a few more "shots" of it, IF anyone wants to see them..

BTW: I also picked a Stanley No. 4c, type 16 today, for $12. Should be here by the weekend....

Twas a very good walk-about, today..