Mobiles

I grew up with mobiles made by my mother in the late 40's and early 50's where the items being hung might be seashells, leaves or metal representations of leaves, or almost anything.  These were mounted with threads on longish rods or thin branches and each was free to pivot completely around.  While at Iowa State University in the mid - 60's, I built a mobile as a stage set for a synchronized swimming show (below)

Making a mobile with glass pieces involves dealing with the weight of the glass.  One can make a bold statement with heavier pieces of wire, use wood shapes, or add a yoke as with the stage piece.  Notice the truss structure of the supports for the Calder clouds unit above, consider how much heavier it would look if the beam side were filled in.  Or one can intentionally use a light pieces of glass as will produce the effect.

  Building a mobile is a matter of arranging the pieces in a pleasing layout, perhaps on a piece of paper, sketching in the support rods, then building from the bottom up, making each pair balance then each group balance against the counter item.  With practice, noticing the very heavy that will balance against several items becomes obvious, but at first it is likely that a layout will be attempted that can not be made to balance and also be attractive.
  Very light items - origami, real leaves, dried butterflies - have little momentum - a draft may make them move, but they stop quickly. Heavy items may not move in a draft at all but will keep moving if touched.  One solution is to put a heavy item on a support close to the balance and a light item way out - the light item moving in a slight breeze or draft and the momentum of the heavy part keeping it moving.  The weight of the supports may provide momentum - I have one made of artificial leaves with thin branches for supports that is pleasing in movement from central heating vents.
  Not fitting the usual definition of a mobile, the seashell handing form at right, strips of light fabric hung like banners to move in drafts, and paper hangings like the origami cranes on thread at the Crow oriental museum can make for attractive units.

  I use carpet thread most often and use a basic slip knot for fastening so I can adjust for balance and appearance, coming back with a touch of glue to fix the location and knot in place.  Using monofilament fishing line will make a less visible line but one that is harder to knot and less free to twist.  Thin wire is even less free to twist and may be difficult to keep completely straight as it holds its own bends.  With enough size and weight in the items and supports, coarser string or light rope may make an attractive line, provide necessary visual confidence to viewers, and flex enough to transmit torque to the other pieces to enhance overall rotation.
  I have found that I like a denser arrangement of pieces in most cases - that is, I like to have all the pieces forming a closely related visual group that shifts within the group.
  There are two other alternatives.  One is a very sparse arrangement - Calder used, during WWII, 3 or 4 wood shapes a few inches across that were spaced over several feet, the hanging wires being lines connecting the pieces..  The other is in between - an arrangement that is closely related at times but some or all of the elements swing out well away from the concentrated area - this requires a hanging arrangement of short arms and long arms so the piece unfolds from the most compact position.
  I prefer to hang a mobile from a fishing swivel, some come with ball bearings, so that it does not always come to rest in the same rotational direction which tends to happen with a firm hanger connection.  Some mobiles, such as Calder's Clouds above require a motor to provide movement and high quality bearings to provide rotation below.

 The guy who invented the mobile, Calder, as sculpture also created the stabile, which was supposed to be firmly on the ground. Calder's stabiles don't move much because most of them are pretty heavy and we aren't supposed to touch them (the sign says.)
Here are a bunch of pictures (Google search) many of which show pieces with no moving parts. I like them better when they do.
Now the Nasher, here in Dallas, has one of each type  and they say the stabiles have no moving parts. (click on images) which confuses me. And I swear they have a heavier one than the Spider shown on that page.
If you look at the Spider, you will see that like many of his mobiles, it consists of wire (or rods) with a loop at the hanging point and fairly rigid connections (not the strings used on craft mobiles) So the wire and the shapes make line and form combinations.
To make a moving mobile/stable, you lay out the cutout shapes that will be on the wires/rods, and then you start from the bottom making a piece with shapes on each end and finding the balance point. Then you use that whole unit as one end of the next wire up and put a shape out at the end and balance that (like hold it with needle nose pliers and loosen the grip and slide the wire till it balances on one jaw, taking a grip if it starts to tilt too far.