Hi Non-Twisty Puzzles fans,
Extreme Reduction is an ultra-compact gearing system with an extreme reduction. The
gear ratio is 11.373.076 : 1, that is, over eleven million to one!!! That extreme reduction is achieved in three stages.
-Stage 1: Two sets of planetary gears with a reduction of 24 : 1 and 25 : 1, respectively.
-Stage 2: Two subtractions, 26×26-25×27=1 and 25×25-24×26=1, respectively.
-Stage 3: Another subtraction, namely (25×26+1×25)-(24×27+1×26)=1.
The gear ratio of this mechanism scales to the 5th power with the number of gear teeth. That is, for ×2 times the number of teeth, you get ×32 times the gear ratio. Here are some exaple gear ratios:
-Teeth = 4, gear ratio = 2.185
-Teeth = 9, gear ratio = 87.220
-Teeth = 16, gear ratio = 1.322.209
-Teeth = 25, gear ratio = 11.373.076
-Teeth = 36, gear ratio = 67.320.649
-Teeth = 49, gear ratio = 305.880.100
-Teeth = 64, gear ratio = 1.141.624.705
The number of teeth of a gear needs to be an integer square plus or minus one because of the subtracting mechanism.
Whereas high reduction radios are typically achieved with
worm gears, a planetary gear system like this is much more compact. The gears have a limited number of teeth, which makes the system very robust. Also unlike worm gears, this planetary gears system is
coaxial, which makes it easier to place.
The application of this type of extreme reduction gears is unclear. A patient person could use it to move a heavy
train locomotive with a
dental dril.
Watch the
YouTube video.
Buy the gears at
my Shapeways Shop.
Read more at the
Non-Twisty Puzzles Forum.
Check out the photos below.
Enjoy!
Oskar
