I've read repeatedly that a small sprocket will cause a reduction in transmission efficiency, especially at very small sizes. My question is, is it the small size of the sprocket or the limited number of teeth that matters more?
I ask because I have a unique bicycle with an expanding front sprocket. It's called the "Yankee Bicycle" and was featured in Popular Science about 20 years ago. The sprocket consists of six segments, two of which have teeth and four of which are idlers. The segments expand and retract along arms that radially extend from the bottom bracket axle. It can approximate the sizes of traditional sprockets ranging from 32 to 56 teeth, but it does so in shape of a hexagon, rather than a circle. It only touches the chain at a few points (at the points of the hexagon), unlike a traditional sprocket.
Here's a link (not mine). In addition, here's an image:
I presume that there's some transmission efficiency lost because of the design, but can't figure out whether it's to the same degree as for a traditional small sprocket.