I've read around a bit, and found this to be the web's general take on : Elliptical & non-round Chainrings. There has been development into shaft driven bicycles, but the ?cog & chain? drive remains the most effective transmission system to date. With a chain-driven bicycle the possibility exists to vary the mechanical advantage of pedalling according to the position of the cranks, by using elliptical and non-round chainwheels. 1) Elliptical Chainrings. The idea centres on the fact that the large radius of the elliptical chainwheel can 'drive' the chain when the cranks are horizontal, with the small radius 'pulling' the chain when the cranks are vertical. As a result you will be able to 'push a higher gear' when the cranks are vertical whilst you are reaping the benefit of a smaller radius of the chainwheel during the 'dead spot' in pedalling motion. Accordingly - so the argument goes - the pedalling stroke becomes (overall) more efficient. It has always looked great in principle, but does not work in practice. The high gear (with the cranks being horizontal) encourages the rider to push too hard - a common cause of knee problems - and the low gear (cranks being vertical) means that the knees are moving extra fast when they are changing direction (from going up or down (a "whiplash" effect). Over time elliptical chainwheels have been re-invented and abandoned - for the same reason - every ten or fifteen years. 2) Shimano's Biopace? was a patented, computer-aided 'non-round' chainwheel design. It looked like a traditional elliptical chainring, but wasn't. It worked diametrically opposed to the 'traditional' elliptical chainwheel, as the small radius of the chainring was engaged when the cranks were horizontal, the large radius when the cranks were vertical. The Biopace? design was different from the elliptivcal chainwheel/ring, based on analysis of the motion and momentum of moving cranks and legs, unlike the static, geometric analysis that produced the first elliptical chainrings. The theory behind Biopace? was that during the power down-stroke - the cranks being horizontal - you would be using the power of your legs to accelerate your feet, and the momentum of your feet, legs and cranks can carry you through the "dead spot" (when the cranks are near vertical). Since the rider doesn't push as hard during the Biopace?'s power phase of the stroke, and motion is slower when the leg is changing direction, the design is substantially gentler on the knees than a normal chainwheel! Generally speaking, the slower motion at top and bottom means that as legs change direction from upward to downward/ vice versa, they will do so at a slightly slower speed. The increased leg speed near the middle of the stroke is the result of a more gradual acceleration / deceleration with the leg moving in the same direction. Thus, as Biopace? makes it easier on your knees, it may also help you 'spin' better without bouncing, as 'bouncing in the saddle' results from the changes in the legs' direction. Biopace? chainwheels (and their derivatives) are particularly suitable for touring cyclists / any application that involves a steady, constant cadence, and they tend to allow more efficient pedalling at slower cadences than what is possible with round chainwheels. They are especially suitable for triathletes (the motion of 'transition' is a little bit closer to that of running, making it a bit easier) and mountain bikers (the design seems to somewhat smoothe out the delivery of power to the rear wheel) as traction can be increased. Non-round chainwheels can be of real value to the majority of non-racing cyclists, but do not work well with high cadence application. It is possible to mix Biopace? and round chainwheels on the same crankset - usually a small Biopace? chainwheel coupled with a round bigblade - taking advantage of Biopace?s? superior (climbing) performance at low cadence, whilst having the ?big blade' available for flatland spinning. Shimano has discontinued Biopace? chainwheels. It should also be noted that within the bicycle industry the term "biopace" has come to represent slang for any "new product" which revolutionizes a certain aspect of cycling, yet - on closer inspection - does not really perform as advertised.