## Wednesday, December 21, 2011

### A Bootstrapped Mobile

kw: art, mobiles

I created this mobile more than a year ago. I just moved it to my workplace because at home the cat keeps knocking it down. I call it "Upwardly Mobile". It is a prototype for a larger work I hope to produce. It helped me understand the parameters for a mobile that is supported from the bottom and does not clash.

The support is a finishing nail with the head ground into a sharp tip after being driven half into the wooden stake. The stake is held by a block of 2x4.

The three sections are cut from aluminum sheet; I used leftover flashing from a home maintenance project. The bottommost section is counterbalanced by a 3/8-inch hex nut. The sections weigh, from top to bottom, 0.55 g, 2.3 g, and 14.2 g. All three sections are 15 cm long. The assembled mobile rises 11 cm from the support tip, and can extend as far as 27 cm horizontally.

The weight ratios are the first crucial set of parameters. 2.3/0.55 = 4.18 and 14.2/(0.55+2.3) = 4.98. While it may be possible to tune up a mobile having weight ratios in the range of 3.0-3.5, let's analyze the more conservative value of 4.0, and see what it takes to design an upward-thrusting mobile with a minimum section weighing 1 gram, and a total mass of 20 kg or less.

The first two sections weigh 1 g and 4 g, totaling 5g, so the third is 20g. Continuing, we find the sections will weigh 100 g, 500 g, 2.5 kg and 12.5 kg. The total weight is 15.625 kg for all seven sections. To illustrate the power of the geometric sequence, if we were to design for ratios of 3.0, we could have eight sections totaling 16.384 kg, but if we went with ratios of 5.0, seven sections would total nearly 50 kg, and six would total 7,776 kg.

To get the most out of such a mobile, it makes sense to use thinner and lighter material for the longer sections of the arms. Perhaps it is best to use steel for the heavy ends and aluminum for the light ends.

This picture taken from above shows a little more detail about how the sections are balanced. I cut the first two sections freehand, and just rolled a piece of rod stock underneath to find the balance point, marked it, and drove a blunted nail partway through from the bottom side with the section lying on a block of wood. This made a dimple for the tip of the section below to stick into. I also made an aluminum counterbalance for the back end of the second section, which can be slid for tuning the balance point and angle.

The third, bottommost section was a bit trickier. I used a nut I had handy and cut the sheet metal piece extra-long by a centimeter. I attached the nut with folded tabs cut at the back of the piece. Then I found the approximate balance point—with the two upper sections lying across the tip—and made the dimple. I put the bifold in so the dimple would be horizontal when the section was rising steeply (it rises about 35°). I trimmed the tip back gradually until it was close enough to fold the last 5 mm for fine tuning.

The process could be continued, but a different way of attaching counterweights, or incorporating them in as thicker stock, must be devised, so the sections don't need to rise so steeply to keep out of one another's way. As with hanging mobiles, the more sections, the more complex and pleasing the motion.

Being light, Upwardly Mobile bounces and shifts with slight breezes I cannot feel. Too many sections, however, will yield a lower section or two that are impervious to "breeze" level air motion, and the mobile as a whole would be less pleasing. This has me leaning toward attempting a design with a ratio near 3.0, and maximum mass less than half a kilogram, perhaps in five sections total.