Even as I posted it I wasn’t satisfied with my Mood-O-Meter post from a few days ago. I knew intuitively that in order for the gears to display all possible “moods” the ratio of eye expressions to mouth expressions must be in its simplest form but I couldn’t quite describe mathematically why this was the case. The images below attempt to convey this relationship between the expression ratio and the gear ratio both mathematically and visually.
Essentially, to find how many “moods” will be displayed the numerator is multiplied by the simplified denominator. If the ratio is already in its simplest form, then this is obvious. For the ratio of 6:5, the viewable moods will be 6 x 5 = 30. But in the case of 6:4 (which can be reduced to 3:2), the viewable moods will be 6 x 2 = 12. In the more extreme example a ratio of 4:4, this is reduced to 1:1 so the viewable moods are limited to 4 x 1 = 4.
Now I’m satisfied.
6 mouths x 5 pairs of eyes = 30 different moods.
A few weeks ago I volunteered to lead a make and do session for a staff team building “fun day.” Two nights before the event I started prototyping this “Mood-O-Meter” which actually presented an interesting mathematical problem: what combination of gear teeth and multiples of eye and mouth expressions will display all possible mood options?
For example if I had two 12 tooth gears it wouldn’t matter if I put four eye expressions on one and four mouth expressions on the other because only four expressions out of a possible of sixteen would ever display.
If I printed four expressions on one 12 tooth gear and three on the other this would be even worse as only one mood would be displayed. The other eleven options would always be out of sync.
I settled upon a 18 tooth and 15 tooth with six eye expressions and five mouth expressions respectively to produce 30 individual moods.
My colleagues at Texas Performing Arts cutting out gears to make their Mood-O-Meters. They may have lacked the exuberance of my elementary aged students but when they meshed their gears for the first time they were positively giddy.
I’ve spent perhaps 150 hours working on this in CAD and less than 30 in the studio prototyping. Once all the patterns are printed and stuck to the double thick cereal boxes I think my students will have a shot at building their own in 12 hours of class time.
Materials include cereal box chip board, corrugated cardboard, wood dowel, hand-rolled paper tubes, recycled #1 plastic sheet, and brass grommets. Hot glue and quick set white glue are used for bonding as well as spray adhesive to mount the patterns. Tools include scissors, utility shears, snap blades, flush trim side cutters, sand paper, and a pull saw to cut dowels and paper tube. Class begins on Monday.
I finally have a complete design. There has been a lot of back and fourth between CAD and studio: design an element, build a prototype, redesign, tinker, second prototype, sketch, think about it for a while, third prototype. So even though I have yet to build a complete clock I do have some confidence that it will work.
But first a vacation back to the Fatherland to celebrate my Dad’s 70th Birthday!
Moments after I took this video the escapement stopped. Then I made “improvements” which made it worse. Likely the whole thing needs to be scrapped but it only took me 30 minutes to make so no big deal. You can’t get too precious with cardboard.
This June I’ll be teaching a summer camp class to 4th and 5th graders titled “Gears and Gravity.” In my proposal I claimed, “We will explore the history and science of time keeping (horology) by hands on experimentation with simple machines and then construct our own real working mechanical clocks from paper and wood.” Now I have to design said clock.
My first challenge is to design a gear train (“going train” in horology parlance) with the simplest possible tooth profile that is easy to cut out and error tolerant.
Did I mention that my class budget is $125?
Pierced globe Incense Burner, Mamluk period (1250–1517), late 13th–early 14th century. Syria, Damascus. British Museum.
Zayn al-Din. Incense Burner or Handwarmer. 15th – 16th c. gilded brass with silver inlay. Walters Art Museum.
Knowing my interests, my friend and remarkable scholar, Dr. Stephennie Mulder sent me the image of the gimbaled censer above. The link to the British Museum (which seems to be dead now) stated that the gimbals keep the incense cup from spilling its contents while swinging but this seems overly fussy to me considering the centrifugal forces of swinging itself solve that problem.
Another site suggested that these type of censers were used in games and rolled from one guest to another. I suppose this would work if it were a very low impact game but any amount of velocity or impact and I think the host’s carpet would suffer some damage from errant embers.
The description of “hand warmer” makes a lot more sense to me. In this case the mechanism would function perfectly. Unfortunately, I can’t confirm that the Walters object is also gimbaled though it must have some kind of suspension for without it the orb would certainly be too hot handle with bare hands.
All these pragmatic issues aside, both of these objects are virtuosic expressions of master metal smiths and are a delight to they eyes. What a pleasure it would also be to hold one of these in my hands!