Convex surfaces and associated negative curvatures

I am talking mainly about convex surfaces, today.

However, before doing that I should perhaps define
some of my terminology. Illustrayted below are
curvatures.



Straight lines with A and B are typically belt-sander
surfaces, agaist which curvatures are depicted. A refers to
+tive curvatures, and B -tive curvatures.

In reality, however, you rarely find a single combination
of concave ad convex surfaces, except, perhaps with dishes
and the like.

In most cases, as shown in C, you have a little more
complicated situations. For instance, both small and large humps
have +tive curvaures, but, inevitably, you may have

a dip for ornamental purposes. The dip in this case has a
-ve curvature. How do you go about it? All that comes shortly.

OK, back to convex surfaces. I have given some thought to this
subject. My guess is that it is probably more difficult to
create convex surfaces.

The illustration above is about straight stem spoons,
but even bent stem spoons have negative curvatures. Concave
surfaces are single entities and can be worked out

independent of everything else. I short, there is no complication
in forming concave surfaces. Whereas, convex surfaces seem
always associated with negative curvatures.

This is true with both straight and bent stem spoons.
C's dip has a negative curvature, which is a pain
in the neck, really.

So, realistically speaking, convex surfaces are
just about how to combat these negative curvatures,
and how to go about them. I order to do that, I need

another illustration, as per below.



With this illustration, A refers to the side view of a
belt sander, against which the dip (negative curvature)
is pressed around the round corner of the sander.

This is fine, to remove the mass you do not want.

However, B is telling you the end result. The dip
as well as quite a lot of the stem and the convex
surface is littered with flat surfaces,

separated by the red lines as shown. Of course, you may say
to me that I should do more careful work, but, in reality,
even this belt sander has quite a lot of abrasive power,

and it is awefully difficult to control the sanding process.
So, these days, I am finding myself more and more dependent
on a tiny machine as shown below.



Effectively, the red lines in the previous illustration are
ridges, formed as a result of plainer surfaces side by side.
I could remover them by paper sanding, but it is a lot

quicker to use one of these tools. The drum sander (tiny!) is
attached to the end of a mini flexible shaft. I can easily
remove red lines (ridges) and furthermore, I can even

remove a little amount of the mass I left unattended during
my earlier grinding process! Such a versatile tool, this is!

The photo below is today's output. What was I doing?
Well, I was experimenting with the idea of very shallow
concaves, for tea leaves scooping.

For mass production, I need to establish optimum concave
depth. In the photo, two different depths are present. And,
I still have a lot of thinking to do.

So
much for concave suraces and associated issues. Now, take
a look at the follwing two photos.





The first of these shows the chopsticks for a female friend
of mine, already matt and ready to be given. Next one is reflecting
my current thinking. This photo has been shown before.

I just do not like the idea of having chopsticks being placed
anti-pararell in the container. If I find smaller disk magnets,
then I can go for smaller holders.

I diverted part of my today's thought to the toast holders, supporters,
as shown below.



These were fabricated using my milling machine.
My questioning to myself was, "Can I simplify this?"

I think I can, by striking either copper or brass
nails into a square plate. One problem there is how to chop off
sharp ends. I probably need 100 nails and the prospect

of chopping off 100 ends is daunting! But, If I manage to find
an easy way, these might even serve as soap holders!
The selling price? 1000 JPY!

So much for today and I go now.