Who here likes to fiddle with their stationary while at school, college, work or home?
And who's teacher/lecturer/boss/wife get's annoyed at this (when you drop it)?

Well, there's me, and I'm sure a few others.

To solve this problem I came up with a small metal object that you can make that keeps your fingers busy while listening, but you won't accidentally drop.
And thus the undroppable was born.
This is just one of many possible designs

Step 1: Design

You can toy with a normal pen for only a few minutes before you get bored with it. I guessed this to be because it's shape is regular, and your hands quickly become associated with it's shape. Thus, you lose interest and move on to something else in your box of stationary.
Accordingly I came up with a set of design principles.

Must not be too regular
Different parts of it should have different "feels"
Should have moving parts (not always possible, but hey)
Must be small
Must be durable
Must not be able to tear/break something else.

Regularity.
No, it can, and should be symmetrical, but there must be corners, different sorts of corners.
On the one I made I has:
Two cylinders (of differing radius')
A Square
A tapered pyramid
The joints between these sections, as well as the edges of the shapes provide irregularities that keep your fingers interested.

Different feels:
When you work with metals, you can get different textures.
If you polish the metal you get a smooth surface
If you grind the metal without polishing at all you get a directional grain
If you use sandpaper you can get a sort of cross-hatch
Those are just the surfaces. For edges:
Edges can be sharpish
Edges can be rounded
Again this increases the irregularity, to keep you amused longer.

Moving parts:
Things that move work better too. This is evident by the fact you click pens, spin them, and end up dropping them. By giving the undroppable a moving part, you prevent yourself from dropping it to much. The more movement a part has, the less likely you are to drop it. I used a nut on a threaded section, which you can spin in and out. It is prevented coming off by deforming the thread at the end. A nut is a good choice as it not only rotates, but moves in and out as well. it also has a good selection of edges to toy with.

Sizing:
As you may be able to guess, it is good to be able to carry it with you in a pocket, pencil case or just in your hand. For this reason it is good to keep it to about 5cm x 1.5cm x 1.5cm. Not so small you will drop it, but not so large as to distract others, annoy teachers, or be inconvenient to carry with you.

Durable:
Assuming you're are at college or school you'll be touching it for a couple of hours a day, and plastics would tend to break after a couple days constant fiddling (look at your pens and count how many aren't missing the bit to latch over a pocket). So, metal or stone it is. I've never worked with stone before, so I decided on metal.

Mustn't tear or break anything else:
Because it would be just great if you put it in your pocket or pencil case, it tore a hole, and vanished. So edges can be somewhat sharp (gives a nice feel to it), but I don't want any edges to be "sharper" than about 60 degrees: an equilateral triangle.

Below is the design I ended up making.

Step 2: Materials and Tools

In short, use what you have. You could make a simple undroppable with nothing more than a piece of metal, hacksaw and sandpaper. Here's what I used:

1) Segment of metal with a thread at one end. You could use a lathe, and a die to add this thread, or drill a hole, tap it, and use a bolt.
2) Hacksaw
3) Bench grinder
4) Sandpaper
5) 45 minutes overall.

Step 3: Shape It

Obviously the first thing to do is figure out how it will fit into the metal you have.
Then it's time to shape.
The first thing I do is cut the metal to slightly over the length I want it.
For this you can either grind it, or you can use the hacksaw.

The second thing to do is to clean up the metal. While you will be grinding much of it away, cleaning it up makes it easier to think, and means that you don't have to go around later to tidy up the bits you don't cut down (for me, the edge of the square bit).
Using sandpaper later will round off the edges, and a little sharpness is what we are looking for.
So sand it. Shouldn't take that long, just a few minutes.

I don't have any photos of the construction I'm afraid.

Step 4: Shape It 2

Put away the hacksaw and sandpaper, you shan't need those again.
Time to dust off one of my favourite tools, the bench grinder.

The first thing I did was make those curves at the non-screw threaded end.
I did this by holding the metal against a hand rest, and letting the curvature of the grinder's disc regulate the curve. This worked well, but you had to make really sure that the metal was held perpendicular to the angle of the blade. Even a few degrees off was visible in the line at the base, where the grinder stopped and the straight metal continued on.
I left the roughness from the grinder on the metal, as part of the "feel"

Now you round it off. Hold the metal horizontally, and use the corner of the blade to make a 45 degree bevel to the end of the metal.
Once you've done that on all four corners, rotate it until you have a smooth-ish curve. If you have a lathe, you can use that here.
It doesn't have to be perfect, as imperfections and lack of regularity are the whole point of this.

As per normal:
- Wear safety glasses/googles
- Wear ear protection
- Don't touch the grinder's disc
- Don't burn yourself , keep a tan of water and frequently dunk whatever you're grinding.

Step 5: Done!

Put on your nut, deform the thread to lock it there and....
Tada, done. I didn't polish mine at all, but kept the texture.

Step 6: Use

Pretty straight-forwards really.

1) Put it in your non-writing hand (so you can still write, duh), and grip it between thumb, first and second fingers.
2) Feel the weight of the metal
3) Turn it so the tapered bit is facing your fingers.
4) Squeeze the metal, so it moves away from the taper
5) Move it back and turn it around so the nut is facing out.
6) Rotate it along it's length (axial), gripping the round part.
7) Spin the nut till it stops, then spin it back.
8a) Repeat steps 2-7 as necessary. If done correctly it requires only one hand.
8b) Do variations of the above.
9) Feel the sharp corners of the tapered bit
10) Feel the points where the round bit turns square
11) Continue until your lecture/class is over.

While you do this, notice how the whole piece is over the palm of your hand, as you are only touching the end bit. This means that if you drop it, it lands in your palm, doesn't make a sound, and you can pick it up without embarrassing yourself.
Also, after a while you don't have to think to fiddle with it, so you can still put all your concentration on the class.

Show me what other designs you come up with....