The disclosure provides rotary machines that include, in one embodiment, a rotatable shaft defining a central axis A, the shaft having a first end and a second end. The shaft can have a first hub disposed thereon with a plurality of cavities. At least one contour is slidably received into an arcuate cavity in an exterior surface of the hub. The contour has a convex outer surface that cooperates with an inwardly facing curved surface of a housing to form a working volume.