What is a nutating engine?

Answer 1

a nutating engine is a new, though slightly similar to the wankel engine, where "a disk spins on a Z-shaped shaft that makes the disk oscillate. In a Wankel engine, a (roughly) triangular-shaped rotor spins on a straight shaft." (Corrected below)

source: http://blog.wired.com/cars/2008/06/pistons-we-dont.html

Correction: Actually, the disk doesn't spin at all. Only the shaft spins. If you look at the diagrams in the reference link, there's actually an "anti-rotation pin" sticking out of the disk to prevent that!

The above should read: "a disk wobbles (like a spun coin coming to a stop) because it's riding on a z-shaped shaft." Its edge sweeps the spherical wall of the chamber, and its conical sides meet the conical ends of the chamber.