Wednesday, April 23, 2008

How to solve it

My apologies to George Pólya for quoting the title of his jewel of a book, but "How to solve it" made an indelible impression on me when I read it decades ago. I wish I had had him as my math teacher instead of the monster that expelled me from his class for having the nerve to record his "lectures" (which I did not understand) in what must have been one of the earliest portable recorders (the size of a worker's box lunch) that my dad, a very forward thinking man gave me as a present so I could use technology to help me in my studies. This wicked teacher foamed (he became redder than he was and I remember his veins bulging in his neck) that my intent was to make money with his awful expositions, when my only intention was to listen to it again at home and review the parts that were unintelligible to me. Remember it was the time (1960's) of slide rulers and solving logarithms, square roots etc. with pen and paper! and teachers which threw solid wooden rulers at students if they failed to pay attention.

In any case, this is how I went about it:

The two control strings for the head (1 and 4) allow it to not only turn left and right, but as I said before to tilt sideways and bow as well. In a traditional marionette these strings are played like an instrument, varying the tension, twisting and plucking.

When the marionette needs to kneel or jump etc. you are not really concerned with this since the entire body, head and all is balanced by your hand, which uses your own personal embedded experience as a subject of gravity to effect movements which prove extremely hard to program convincingly. Imagine for example that you want the character to tilt his head slightly in an inquisitive way while bowing and kneeling at the same time. If you try to break that into individual movements performed by individual muscles of your hand, fingers and arm you will picture the complexity of the apparent simplicity. Don't forget that I said tilt his head in an inquisitive way!

So, in my dream I must have followed some of the principles Pólya suggests to poor souls in distress, like for example:
  • Look for a pattern
  • Draw a picture
  • Solve a simpler problem
  • Use a model
  • Work backward
  • Use a formula
  • Be ingenious
The 'head' strings reach the horn which would turn the head left and right and you would think that is where the strings should end. Then I visualized (and this is what comes from the dream) that the strings at that point corresponded to my left hand fingers twisting them while my right hand controlled the other movements in unison.

So I let the strings continue on to the other 'hand' which would pull or let go to let the gravity do its thing. The combination of these elements (including the most important, gravity) give you a very rich and expressive palette of head "language". This of course I cannot convey simply by pictures, but I will eventually post a video of the movements.

The 'other hand'

I continued raiding my wife's sewing supplies and used this perfect and beautiful spool, which I epoxied to the servo horn (you can still see behind the spool the gray irregular shape of the rock hard Apoxie that I used. Need to refine that.)

There was another problem, which because of its apparent simplicity tends to be forgotten until it is too late. Remember the analogy with a string instrument. So it is that you must tune the strings of your marionette to the perfect tension which allows precise control while at the same time giving gravity and inertia room to infuse the movement with the illusion of life.

Easier said than done. First of all the strings are very thin and usually waxed or Teflon coated to prevent fraying. That makes tying and untying knots practically impossible. Then consider the awkward and tight places where the strings are connected. Finally, size. Things that are very easy at a human scale become wickedly difficult in Lilliput.

Bowl of Sushi by Hiroshige (Edo Period)

My love of sushi came to the rescue. Chopsticks! the bamboo sticks have the right diameter, are pleasant to touch and sight (and taste) and its transversal structure provides the friction necessary to prevent the 80 lb. Teflon string from sliding. This was my prototype but although it stopped that string diameter from sliding, my preferred string is .006" Fireline, which is a braided bead thread very strong and resistant to abrasion (it is used to weave the smallest glass beads). This string just went through my tensioner like a water snake.

So I refined my prototype incorporating an opposing path that effectively holds it in place. And what is more important and the reason for this exercise, it is easy to adjust as needed, to tune the strings of the instrument.

Tension is good when needed

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