Mood-O-Meter Math

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 than 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 is reduced to 1:1 so the viewable moods are limited to 4 x 1 = 4.

Now I’m satisfied.

Mood-O-Meter_math_18-15

Mood-O-Meter_math_18-12

Mood-O-Meter_math_12-12

Mood-O-Meter

6 mouths x 5 pairs of eyes = 30 different moods.

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.

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.

Gears and Gravity: Finished Clocks (Day 13)

All eight clocks on display for the final day of camp.

All eight clocks on display for the final day of camp.

Wow, took me long enough to post this. The last day of DEEP camp on June 28 and I learned so much from my students that I’ve been completely absorbed in revising the clock design that I haven’t taken time to post the photos of my student’s truly excellent work. Can’t wait for next year.

The video below shows six cardboard clocks running (mostly) all at once. What a lovely sound.

The recent purchases of a large shoe order and a new vacuum turned out to be quite helpful to the class.

The recent purchases of a large shoe order and a new vacuum turned out to be quite helpful to the class.

Parents and students watch the closing ceremony and show while the clocks wait to be taken home.

Parents and students watch the closing ceremony and show while the clocks wait to be taken home.

The escape wheel reads: "Genius is eternal patience." – Michelangelo

The escape wheel reads: “Genius is eternal patience.” – Michelangelo

The escape wheel read: "Play is the highest form of research." – Albert Einstein

The escape wheel read: “Play is the highest form of research.” – Albert Einstein

Gears and Gravity, Day 7: Gluing Wheels to Arbors

In standard clock construction a clock wheel (aka: gear) is attached to an arbor and the arbor in turn is attached to a pivot. The same methods apply to the Cereal Box Clock except the wheels and arbors are made of paper and the pivots are wood.

Hot glue helps the wheel go round.

Hot glue helps the wheel go round.

Gears and Gravity, Day 6: Wheel Cutting

Trimming the outer edge of the Hour Wheel.

Trimming the outer edge of the Hour Wheel.

Using flush jaw wire cutters to cut wheel teeth is methodical yet enjoyable work.

Using flush jaw wire cutters to cut wheel teeth is methodical yet enjoyable work.

Using a "Japanese" pull saw to cut arbor material. These saw work like butter.

Using a “Japanese” pull saw to cut arbor material. These saw work like butter.

Using a pull saw to cut dowels for pivots. These saws are so sharp that some students could cut through a dowel in one pull!

Using a pull saw to cut dowels for pivots. These saws are so sharp that some students could cut through a dowel in one pull!

Gears and Gravity, Day 5: Pinion Assembly

Assembling pinions is a lot of work and all of the students worked hard. Three eight leaf pinions are required for each clock.

The drilled holes are a little undersized so we must use this very sophisticated pointy stick to increase the diameter.

The drilled holes are a little undersized so we must use this very sophisticated pointy stick to increase the diameter.

Five of eight pins inserted.

Five of eight pins inserted.

They don't have to be straight.

They don’t have to be straight.

Little smears of hot glue hold the pins in place.

Little smears of hot glue hold the pins in place.

Love the pink hot glue guns.

Love the pink hot glue guns.

Gears and Gravity, Day 4: Arbor Tube Rolling

Each wheel and pinion must be secured to a paper arbor before being attached to the 1/4″ dowel pivot. The arbor is 1/4″ ID and 3/8″ OD. As I was designing the clock, I looked for off-the-shelf tubes that I could purchase but what I found seemed expensive and I wanted to ensure a consistent size so I decided that I’d have to roll my own. This video presented and excellent solution. Still, these are a challenge to roll consistently and I had to experiment for quite a while before I found the best technique to teach my students.

Applying glue thinned with water and a little rubbing alcohol to prevent wrinkling.One person holds the paper on the steel rolling-pin to prevent the two from getting glued together.

Applying glue thinned with water and a little rubbing alcohol to prevent wrinkling.One person holds the paper on the steel rolling pin to prevent the two from getting glued together.

Glue applied, starting the roll. A helper tries to keep wrinkles from forming.

Glue applied, starting the roll. A helper tries to keep wrinkles from forming.

Slow and steady.

Slow and steady.

All most there.

All most there.

A finished arbor tube.

A finished arbor tube.