Machine with Minifig
Many artists make kinetic sculptures. Arthur Ganson, for example, has a permanent exhibit at the MIT Museum in Cambridge, Massachusetts, of his kinetic works of art. One of my favorite pieces is "Machine with Concrete" (see Figure 11.30).
Figure 11.30 Arthur Ganson's "Machine with Concrete"
In a lot of Mr. Ganson's work, he solders and bends metal in intricate ways, including making his own gears, to achieve the desired movements in a piece. Other works, like "Machine with Concrete," use manufactured gears and can easily be duplicated with LEGO building elements (see Figure 11.31).
Figure 11.31 A piece that I call "Machine with Minifig"
Mr. Ganson's design uses 12 pairs of worm gears meshed with 50-tooth gears. The motor turns at 212 RPM. The first 50-tooth gear therefore turns at 212/50 RPM or 4.24 RPM. The second 50-tooth gear turns at 4.24/50 or 0.0848 RPM or 0.0848 3 60 5 5.088 revolutions per hour! At this rate, Mr. Ganson calculates, the last gear will turn around once in 2.191 trillion years!
Figure 11.32 Using the data log, the speed of the motor can be calculated with the angle sensor.
Mathematical Aside: Major Gear Ratios
Here's how to calculate how long it will take for the last gear in the gear train to turn around once:
If the first gear pair of worm gear and 50-tooth gear slows the rotation rate down by a factor of 50, then the very last axle is slowed down by 12 factors of 50.
(1/50) 3 (1/50) 3 (1/50) 3 (1/50) 3 (1/50) 3 (1/50) 3 (1/50) 3 (1/50) 3 (1/50) 3 (1/50) 3 (1/50) 3 (1/50) 5 (1/50)12
(1/50)12 5 0.000000000000000000004096 5 4.096 3 10-21 revolutions of last gear per one revolution of motor.
212 RPM of the motor 3 4.096 3 10-21 revolutions of last gear per revolution of motor 5 8.68352 3 10-19 revolutions of last gear per minute
8.68352 3 10-19 revolutions per minute 3 60 minutes in an hour 5 5.210112 3 10-17 revolutions per hour
5.210112 3 10-17 revolutions per hour 3 24 hours in a day 5 1.25 3 10-15 revolutions per day
1.25 3 10-15 revolutions per day 3 365.25 days in a year 5 4.57 3 10-13 revolutions per year
By taking the inverse of this number (dividing it into the number 1), we can figure out how many years per revolution instead of revolutions per year:
(1/4.57 3 10-13) 5 2.19 3 1012 years per one revolution 5 2,190,000,000,000 years for one revolution!!!
The same analysis can be applied to the Machine with Minifig. The speed of the motor can be estimated, or calculated, by attaching an angle sensor and using the data log (see Figure 11.32). See Chapter 20 for details on data logging.
Alternatively, you can watch the first 40-tooth gear spin, figure out its speed, and then multiply by 40 to get the speed of the motor. The calculated speed of the motor in Figure 11.32 is 300 RPM. (The official published speed from LEGO is 350 RPM without any loading.) Using the same method as before, it can be calculated that the Minifig will move one full rotation in 106.3 billion years.
The next time that you are visiting a museum, playing with a kinetic toy, or passing by a publicly displayed work of art, stop and think if it can be made out of LEGO. The best part about the LEGO Mindstorms system is that the kinetic sculptures that you make can be interactive as well. Not only can your kinetic sculptures move in funny and interesting ways, they also can be triggered to move by the light sensor detecting motion or the touch sensor detecting a press. A LEGO kinetic sculpture can be set up in your house for a party or even in a local art museum.