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.
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.
Last edited by Patrick Chase; 09-13-2017 at 1:52 AM.
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.
Mine were made using a pattern found online:
Fibonacci Gauge.png
The rivets came from Lee Valley:
http://www.leevalley.com/us/hardware...=3,41306,41327
jtk
"A pessimist sees the difficulty in every opportunity; an optimist sees the opportunity in every difficulty."
- Sir Winston Churchill (1874-1965)
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.
Last edited by Patrick Chase; 09-13-2017 at 6:00 AM.
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-compassDi...aightedge.html
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.
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.
Last edited by Brian Holcombe; 09-13-2017 at 9:33 AM.
Bumbling forward into the unknown.
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.
Golden Rectiangle.jpg
Beranek's Law:
It has been remarked that if one selects his own components, builds his own enclosure, and is convinced he has made a wise choice of design, then his own loudspeaker sounds better to him than does anyone else's loudspeaker. In this case, the frequency response of the loudspeaker seems to play only a minor part in forming a person's opinion.
L.L. Beranek, Acoustics (McGraw-Hill, New York, 1954), p.208.
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
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)"
Last edited by Jim Koepke; 09-13-2017 at 12:41 PM. Reason: Also the points weren't cut...
"A pessimist sees the difficulty in every opportunity; an optimist sees the opportunity in every difficulty."
- Sir Winston Churchill (1874-1965)