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 an elongate first island disposed thereon. The first island can have a body with a volume generally defined between front and rear surfaces that are spaced apart. The front and rear surfaces can lie in a plane parallel to a radial axis R. The perimeters of the front and rear surfaces can define a curved perimeter surface therebetween. The disclosure further provides embodiments having stationary islands and casings that rotate about the island.