I'd like to understand the new SRI "Abacus" transmission, recently reported at http://spectrum.ieee.org/automaton/robotics/robotics-hardware/sri-demonstrates-abacus-rotary-transmission
I haven't been able to find any information on it that doesn't seem derivative of the IEEE story.
I'm curious about how one determines the reduction ratio, and what the "grooves" look like mathematically (for example, the function from angle to width).
Judging from the pictures, this one seems to have 6 setscrews on the inner race, 7 "beads", and 8 setscrews on the outer race.
It's hard to tell the number of cycles for the grooves, but the ones in the outer race seem to be aligned with the setscrews.
They say the beads can have any profile you like; it seems that must then determine the groove profiles, but how would you get from one to the other?
I've tried to reason out the relationship between number of groove cycles on each race, diameter profile of the beads, offset of the driveshaft's attachment to the inner cam, and the resulting reduction ratio. But my intuition is failing even after watching the video many times.
Can anyone explain the relationships involved here?