Traditional Elliptical Chainweels
Around the turn of the century, shortly after the development of the chain driven bicycle, someone came up with the bright idea of elliptical chainwheels. The idea was that the large radius of the chainwheel would drive the chain when the cranks are horizontal and the small radius would pull the chain when the cranks are vertical.
The theory was that while the cranks are horizontal you can pedal more efficiently, and thus can push a higher gear. When the cranks are vertical, you get a lower gear due to the smaller effective radius of the chainwheel. The lower gear is easier to push, and you get through the dead spot sooner. This is the basis for the Q-Rings design.
Biopace is a patented non-round chainwheel design made and licensed by Shimano. It looks the same as Elliptical but it acutally is the exact opposite of the classical elliptical design. The product of extensive research and computer-aided design, Biopace chainwheels have the small radius engaged when the cranks are horizontal, the large when they are vertical. This is because the Biopace design is based on a dynamic analysis of the motion and momentum of moving cranks and legs, unlike the static, geometric analysis that produced classical ellipticals.
The theory is that during the power stroke, when the cranks are more or less horizontal, you are using the power of your legs to accelerate your feet, which get going quite fast in the lower gear provided for that part of the stroke. Biopace relies more on momentum to get around the pedal stroke instead of optimizing for the power of the user. Biopace is really a flawed theory and venture and have alienated many users from trying standard elliptical designs.