Abstract: A positive displacement rotary machine includes a piston rotor rotatable about a first axis and including a number of pistons equally spaced about the first axis and rotatably mounted about their axes on the piston rotor; a chamber rotor rotatable about a second axis spaced from the first axis, including a central common chamber and a number of radial fluid chambers arranged in diametrically opposed pairs across the common chamber, and guide tracks extending between opposing pairs of radial chambers across the common chamber for kinematically constraining each of the pistons as they move from one of their associated radial chambers to the other through the common chamber, and intake and exhaust ports for introducing and exhausting fluid from the radial chambers.