Some goldsmiths wear their disdain for mathematics like a badge of
honor. Developing such an attitude should be avoided at all costs.
No serious work can be done without solid foundation in at least
elementary mathematics.
Leonid’s words are true, except I don’t know any successful
goldsmiths with a disdain of mathematics (meaning geometry here,
really). The problems many newbies have is with needing lifelines -
binding wire, third hands, mill products, various other things. My
bezels are MORE precise than measured ones, because I make them just
exactly how I want them. Of course, if I need 6 of them matching, I
cut matching strips to start. My rings are perfect because I make
them small and stretch them up to a perfect circle- I don’t WANT to
make it to the perfect size, that’s too big to start.
There’s nothing really wrong with measuring such things, but it
takes away your own input - the inherent craftsmanship that makes a
bezel YOUR bezel, just how you like it. It seems better to use math,
but it often distances you from the work. There are times when you
must use geometry - square and triangle bezels and others. Drawing
tubing… Don’t be afraid to be captain of your bench, though. Get
inside your work.
Some goldsmiths wear their disdain for mathematics like a badge of
honor. Developing such an attitude should be avoided at all costs.
No serious work can be done without solid foundation in at least
elementary mathematics.
I totally agree with Leonid here. Just try designing and making this
necklace without using mathematics.
I agree wholeheartedly with John. One thing I drill into my students
is to be sure there is enough metal…extra metal that is, because
it is easier to cut or file some away than it is to add some (?!).
Also, it is important to learn skills of enlarging things. A bezel
that is slightly too small is easily rolled up to fit perfectly the
way you want it to. If it is too large, you must waste time cutting,
squaring and re-soldering. Also, early on, a jeweler should have
learned that before cutting any wire etc, they should first square up
the one end so the other, when cut, can be easily squared and made to
fit. I have found that when one gets in a hurry, the basics sometimes
fly out the window. There are, in my view, some mathematical
procedures that can be routinely applied but most are done by rote!
Hi Roz, When you make a ring, position it on the mandrel so that the
centerof the shank is the desired size, never the leaing edge and
never the traiing edge and you won’t go wrong.
Thanks John - got it, loud and clear - 22 ga is too thin, will use
it rolling out thinner for bezels. Maybe some backplates too. But
16 ga? I can't cut it with my shears (you're going to tell me to
cut it with my saw, right?
Before John writes another novel you HAVE to learn learn to saw.
About as basic a jewellery skill as soldering although easier.
Personally I really like working with thicker metals, it is amazing
how many errors and mistakes secumb to a few file strokes.
One could counter that the problem is one of deficient math
skills. OK, show of hands here...who's willing to take remedial
math courses just so they can make ring blanks?
This reminds me. When my son was in 6 grade, he came from school one
day and sait that they were talking about jewellery in class and
that he would like to learn how it is done. I sat him down and sati
that the first thing is one must know how to do layout, and that
means ability to draw ellipse, divide circle in equal parts and so
on. In about 10 minutes, he lost all interest and that was the end of
his apprenticeship. So I am very much familiar with the problem.
Nevertheless, ignorance of the math is very limiting to a goldsmith.
Some things can be accomplished by trial and error, but there are
others that cannot.
When you make a ring, position it on the mandrel so that the
centerof the shank is the desired size, never the leaing edge and
never the traiing edge and you won't go wrong.
Reading to the center is guess work as you cannot see through the
ring. Using the leading edge will give you the correct diameter of
the ring. If you try to use the middle it will read differently on
different mandrels as the taper angle of the mandrel will determine
how far the middle is from the leading edge.
I'm one of those nasty people who use cnc..001 mm really does make
a difference, hand fab work and I eye ball it. Hammers etc cover
all sorts of stuff. No problems with eye balling, and an old habit
of jewellers which goes back forever.
I wound up using CNC myself to indirectly create some nice uniform
fine silver bezel which I made by hand. So I guess math works for me:
Last year I picked up a foot and a half of mining cart rail that
someone had carved into a very crude anvil. I applied my fly-cutter
over the top of it, th= en used various width carbide cutter to ground
in some lines across the top of various depths and thicknesses.
Voila, a bezel anvil, seen here (in Facebook).
My favorite line are the one I ground in at.06 inch wide at.1 inch
deep. Last week, after forging and annealing a tenth ounce of fine
silver ingot until it was slightly smaller than the line, then I fed
it through gradually, hammering and annealing as I went, to get me
almost a foot of nicely squared up bezel.
You’ll see some used in my current attempt, seen here (in Facebook).
I made a frame to enclose two pieces of ebony (based off a thread
someone was asking regarding using wood with gemstones). I had carved
a heart shaped recess into the ebony so that a piece of elk ivory I
that I carved into a heart which could fit into it.
So, I’m actually making again at long last, honest! I had a LOT of
fun using your jeweler’s saw for the first time to cut the bezel,
using a #2 blade from a pack from India which I got for Christmas. My
daughter put Play-dough handles on the files you sent me, per your
suggestion, and those came in handy for removing tool marks. The small
triangular file was lovely for making mitres in the corners.
One thing I drill into my students is to be sure there is enough
metal....extra metal that is, because it is easier to cut or file
some away than it is to add some (?!).
I am not arguing with the point as far as technique. There is
however another consideration. In hand fabrication from precious
metals (mostly 18k gold and platinum), there is also an economic
considerations. The average weight of completed item is only 30% of
starting metal, and that with very careful handling, or it could be
even less. Relying on filling rather than on precise shaping
increasing amount of lemel, and thereby amount of loss.
I took John’s comments that he has a natural ability to shape things
exactly. There are lucky individuals who can easily do things
difficult for others. Da Vinci could draw perfect circle freehand.
The astronomer, (don’t remember his name) who first compiled very
detailed star chars, did it without a telescope. He naturally had
very sharp eyesight. There is a guy in Israel Air Force ( I do not
know if he still flying ), who can see 20 miles away. He is known to
engage multiple combatants simultaneously, and I do not believe he
was ever shot down.
I have none of these talents, so I have to rely on mathematics and
other tools.
Just try designing and making this necklace without using
mathematics. http://www.ganoksin.com/gnkurl/6h
This is a great example, so let’s dig into it deeper.
Chocker type of necklace is always designed round, but necklaces with
a lot of mass in front will look ugly in the round, unless person is
very slim, and even then. Anything above 16 inches should be rather
oval, than round. It is not a big deal for thin necklaces, but heavy
graduated necklaces are difficult, not necessarily to make them, but
to insure that they sit evenly around the neck. When necklace has
relatively large mass, every movement of the head brings this mass in
motion and necklace bunches up, and exhibit another undesirable
artifacts. Large earrings have similar problems, as well as heavy
brooches.
To control necklace behavior designer employs several tools. First,
notice that number of links are increasing proportionate to decrease
in size. That is inertia damping device. Every link presents a unit
of friction, so designer by increasing number of links, increasing
friction of the section making it more difficult to follow motion of
section with larger mass, but less friction. There is mutual damping
between the sections, where larger section employ mass and smaller
ones use friction.
To make it work, a designer must insure that power transition is
smooth, and that requires elliptical form to be calculated correctly.
In most cases, we make ellipses by flattening round, which is fine
for small sizes. Large ellipses require different approach. An
ellipse circumference, mathematically speaking, composed of 2 pairs
of arcs. Each pair is oriented perpendicular to each other and having
a distinct radius. Those who interested in details should look up “4
point ellipse construction”. The outline of necklace should mimic
these arcs. Take another look at the necklace. You should see that
figures eight are not the same. Proportions between upper and lower
varies.
This needs to be understood in the following way. Take a figure
eight and draw lines on both sides, so each line is tangent to upper
and lower circles. ( mathematically figure eight is abstracted to
two circles ). If we continue these lines towards the center, they
will intersect (ideally in the center of necklace) forming a central
angle. In well designed necklace, the sum of the angles of each
group, will equal to central angle of one of the 4 arcs comprising
circumference of the ellipse, with each group corresponding to a
particular arc.
So now you have it. One can take an intuitive approach and later
having to explain to the client why thing just goes crazy at the
slightest motion, or take some time to study the issues, and design
it like an engineer.
P.S.
After re-reading the above, I realize that I utterly failed to
control the geek part of my personality. These concepts are much
easier to explain via drawings than relying on just verbal
descriptions. It is simpler than it appears, just require time and
desire to understand.
True, Jeff - sawing is important and a basic skill. I’m actually
learning to like my saw but still have trouble sawing very thick (to
me) sheet - I tend to want to cut long lengths in the sheet (so 9 mm
wide by 12 inches long…) and find that with the thicker sheet,
the portion being cut doesn’t want to curl out of the way and I can’t
pass the saw frame thru, so I have to stop, bend a piece back,
adjust and end up with wavy lines… Maybe I’m doing something
wrong?
Leonid and others, don’t give in, you are absolutely right about the
necessity for math skills in jewelry manufacture/fabrication. As an
old man of 74, one of my main regrets, is my insufficiency in math. I
have math skills, but not enough and my work would be so much easier.
For the sake of the young ones coming into this business, continue to
encourage them.There are times that eyeballing might be OK, but for
the most part, never as good.I’m still trying to find someone who can
teach me to find the center of an oval and the center of each of it’s
four quadrants, without doing it by trial and error. Makes it harder
in making oval belt buckles
I totally agree with Leonid here. Just try designing and making
this necklace without using mathematics.
http://www.ganoksin.com/gnkurl/6h
Well, Gary, calling that mathematics is calling a Big Mac gourmet
food. All you need is a ruler and some rudimentary knowlege of how
to use it. And it ~could~ be made without even that, but I wouldn’t,
either.
There are, in my view, some mathematical procedures that can be
routinely applied but most are done by rote!
Don has it right - arithmetic and geometry (mathematics is not
really the right word) are essential in jewelry making. What’s
important is knowing when it’s important and when it’s not. Newbies,
again. Calibrated round and oval stones, standard sizes, idealism.
If you are tied to calculating, what do you do with an
odd-proportion pear shape or (shudder!) a baroque stone. Yes, it can
be calculated, but I’ll have it done, delivered and paid for before
you finish the topological math. It’s a case of - yes, it can be
calculated, but why on Earth would you? Be a craftsman, learn how to
use your metal and train your eye.
Starting with the same stock, I’ll have my band ring bent and
soldered and sized in the time it takes you to calculate it. It’s
not necessary to calculate it, it’s slower and it’s LESS accurate.
I can always tell the school-taught makers - they want to measure
things that don’t need measuring and they have this thing about
gift-wrapping jewelry in binding wire. Both (and some other things)
are processes that actually do more harm than good. Be a
crafftsman…
Reading to the center is guess work as you cannot see through the
ring. Using the leading edge will give you the correct diameter of
the ring. If you try to use the middle it will read differently on
different mandrels as the taper angle of the mandrel will
determine how far the middle is from the leading edge.
I’ll second Jim’s comment. In addition, consider just what a ring
size is. It is a specific inside diameter to the ring, not
necessarily a postion on the mandrel. If you center the ring on the
marking, then the leading edge is too large. The center of the ring
would be right only if in finishing and polishing, you don’t remove
the slight taper left by shaping on the mandre. In many cases, the
inside surface of the ring is a straight cylindrical surface, not
tapered to be slightly tighter at the center line. In this case, the
leading edge is the right place to measure the size of the ring, IF
your mandrel is accurate. Not all mandrels are accurate. Be sure
yours is, by checking the diameter of the mandrel either with sizing
guages (themselves not always perfect) or with a micrometer at the
markings. You’d be surprised at how many purportedly accurate
mandrels are actually off by an 1/8th of a size or more, often more
at either the large or small end. One of the worst ones I ever
encountered was a supposedly high precision mandrel (made by Karat, I
think, and sold by Gesswein). It’s beautifully machined with crisp
clean markings and all that. But the markings were actually almost a
quarter of a size off over the whole length of the mandrel. So much
for paying almost double for a high precision mandrel… You can
still use an inaccurate mandrel so long as you know where and how
much it’s off.
Now, with all that said (ie, leading edge is “right”), you can fit a
ring however you like, leading edge, centered, trailing edge, IF and
only IF, whomever is making or sizing the ring (presumably you) and
the person who measured the finger or specified the size is also
using the same standard of measurment. But this can be tricky.
Standard finger sizers will fit “leading edge”. If the person
specifying the measurment intends the ring to be a tad looser, then
saying centered or trailing edge can convey by how much, but as Jim
points out, how much this actually is may vary according to what type
of mandrel (and it’s taper) is involved. Much better than saying a
size six trailing edge, would be to simply say size six and one
eighth, or whatever is desired…
Now there’s one big exception to all this leading edge stuff.
Comfort fit rings need to be measured on the mandrel where the inside
actually contacts the mandrel at it’s smallest diameter. Usually, but
not always, this will be centerline, or close to it.
and they have this thing about gift-wrapping jewelry in binding
wire.
haha, love the image, hate the wire. In my earliest years, I
struggled with binding wire. I mean its a genuine pain but I kept at
it because, you know, that’s what the book said (wayyyyy before
internet, not that its any more accurate). Then came an epiphany. The
Book Is Wrong.
.... and find that with the thicker sheet, the portion being cut
doesn't want to curl out of the way and I can't pass the saw frame
thru, so I have to stop, bend a piece back, adjust and end up with
wavy lines..... Maybe I'm doing something wrong?
You are probably going to hate me for this one, I told a friend and
she thought I was totally nutz
Grab your un mounted blade with smooth pliers maybe 1/2" from the
end (before the teeth start) another pair of pliers 1/8" away and
twist 90 degrees. Same on the other end of the blade. Mount the
blade. Saw frame totally out of the way for long cuts. It feels
rather strange and you will break more blades than average. It really
does work. Oh, and use good blades, none of those cheap Indian ones.
Some goldsmiths wear their disdain for mathematics like a badge of
honor. Developing such an attitude should be avoided at all costs.
No serious work can be done without solid foundation in at least
elementary mathematics
Agreed, but a good measure of art must be added to the equation.
Calculate the theoretical ideal and then add the art.
For example if the ring needs a hammered texture then allow for the
expansion caused by the hammering. Allow for some hammering to get
perfect roundness on the mandrel. Find the balance between the need
for hammering and preserving the profile of the ring blank.
Stretching the finished ring to final size can be better than
marring the profile with hammer marks. Hammer first and then form
the profile, or profile the blank and form it without any hammering?
Science and maths are the starting point and art is the refiner.
They must combine in harmony at the end.
Well, Gary, calling that mathematics is calling a Big Mac gourmet
food. All you need is a ruler and some rudimentary knowlege of how
to use it. And it ~could~ be made without even that, but I
wouldn't, either.
Bearing in mind the price of gold and the observations made by
Leonid on how the necklace should react with the wearer, perhaps you
could tell me (us?) how you would set about making it without the use
of mathematics. Granted it was only high school mathematics, but
maths is maths.
Here are some of the design considerations:
The necklace should nicely fit onto the conical area where the
neck starts to spread onto the shoulders. This implied that the inner
and outer lengths had to accurately match the corresponding neck
circumferences.
With these basic requirements, it was then necessary to determine
the number and size of the links, and then to devise a method of
making them. The wire thickness influences the number of links
required.
The price had to be known before it was made; in other words, the
length and thickness of the gold wire had to be known, together with
an estimate for the time to actually make it. The final price had to
match a known budget.
I'm still trying to find someone who can teach me to find the
center of an oval and the center of each of it's four quadrants,
without doing it by trial and error.
Well, John, I’ve studied the geometry, and especially the drafting
techniques, that Leonid and others are talking about here. (not
saying you don’t need them, just to know when), and I’m not aware of
any really precision way to do that - you’re supposed to keep those
centers from when you drew it to begin with, you see. What I would
do is pretty simple, though: An ellipse is two circles overlapping
each other - not exactly, of course, but all should understand that,
I’d think. Make two circles out of anything (cardboard) with the
centers marked, that are of a diameter that fits your oval. Meaning
the arcs of the circles should correspond with the arc of the ends
of your ellipse. Set them carefully on your ellipse, mark off the
centers of the circles onto your ellipse, and there you have it.
With those two centers marked you can do anything you want from
there with dividers and ruler. Near enough for government work,
anyway.
Let’s remember the context shall we? We’re cutting a ring blank. Its
kinda funny how sweeping generalizations are made, sides are chosen
and jewelry math becomes an existential question instead of a
practical one.
Ros, you may find over time that formulas are not always the perfect
answer we may wish them to be so its good to calibrate your
eyeballs. Comes with practice, don’t worry too much about it. Do what
it takes to get you thru present circumstances. Make note of just
exactly what works for you because in the end that’s all that
matters. What YOU do.
you HAVE to learn learn to saw.