Abstract: A rotary fluid machine comprising a housing, a drive disk, a drive shaft, inner and outer cylindrical assemblies, and a plurality of vanes. The drive disk is supported within the housing for rotation about a first axis, and the drive shaft is connected to the drive disk to rotate that disk about the first axis. The inner and outer cylindrical assemblies extend within the housing, and the housing, the drive disk, and the inner and outer cylindrical assemblies form a working chamber that extends around, eccentric to, that first axis. The vanes are connected to the drive disc and are located in the working chamber to compress or to drive a fluid therein.