This past season, I've been doing a good amount of testing with Osymetric's (http://osymetricusa.com) non-round (read "eccentric") chainrings. The theory behind most non-round chainring design is that the effective size of the ring decreases in the minimal power phase of the pedal stroke (the "dead spot"), making it easier to pedal, while it increases during the maximal phase, when pedaling is at its most effective.
There is a good amount of debate regarding the efficacy of eccentric change rings. For some varying perspectives, see:
My initial observations and thoughts regarding eccentric chainrings--in this case, Osymetrics--are as follows:
1. I mounted the 56t Osymetric with a 44t round inner ring; normally, I just run a single ring, but I wanted to see how well the Osymetric shifted. It was a little fiddly getting the front derailleur set, but nothing all that challenging. Shifting was fine, only marginally slower/rougher than with standard round rings. I did space my front derailleur back behind its mount (DuraAce); those with fixed front hangers may have difficulty raising the derailleur high enough for clearance when using Osymetrics bigger than 53 or so.
2. The ring is plenty stiff--no flex or other issues while shifting or while under power.
3. The ring's eccentricity fades into the background relatively quickly; it is very disconcerting to see the chain oscillating front and back when one glances down.
4. The ring's eccentricity is most noticeable at higher cadences, say 90-95 rpm, plus; the eccentricity is much less noticeable at lower cadences, <80. As my optimal TT cadence is in the low eighties, I didn't really notice much of an impact, positive or negative, associated with the Osymetric. At higher cadences, there definitely was a sensation of variable effort during the pedaling cycle, much as what I recalled from my experiments with Rotor's crankset several years ago. Obviously, all of this is subjective.
5. I experienced no notable muscle soreness or fatigue, other than what I'd normally feel after a long TT event. I suspect that any adaptation process will not negatively impact on performance.
6. Now, there are a couple schools of thought regarding how eccentric chainrings work. One is that they benefit riders with slower cadences, as one is in the low power phase longer than riders with higher cadences; the ring's smaller axis during this phase helps one move more quickly through it. Another is that eccentric rings benefit riders with high cadences/low torque, making it easier for them to get through the low power phase.
7. It is possible that properly designed eccentric rings might be of most value for riders who don't efficiently unweight their pedal during the upstroke. There's been a number of studies that indicate that the fastest, strongest riders don't actually "pedal in circles"; rather, they are really, really good at stomping really, really hard on the pedals, while retaining the ability to minimize negative force on the upstroke. Eccentric rings might help compensate for negative force when pedaling with inefficiently.
8. Will I continue to use them? While I don't have any definitive conclusions. I am comfortable in saying, though, that the Osymetric does not hurt my performance; I also can say that I did experience a lower perceived effort with non-round rings on long climbs, while PE (along with watts) remained largely unchanged on fast flats.
The other major manufacturer of eccentric chainrings is Rotor (http://www.rotorbike.com/) . Rotor's chainrings have less eccentricity than Osymetrics; also, unlike Osymetrics, Rotor's Q-Rings do allow some fine tuning of their position.
Experiments with eccentric chainrings have been recorded as far back as the early 1900s. Pedaling a bike is not a simple activity, as is comprised of a combination of multiple levers, vertical movement, and circular motion. Today's eccentric chainrings take advantage of complex mathematical modeling to develop products far more sophisticated than the simple oval chainrings in the past. Eccentric chainrings are not a magic bullet, but this said, they are worth investigating if one is interested in exploring variables that can impact positively on-the-bike performance.
How Eccentric Chainrings Work
(Click on image for enlarged view)