A rotary surgical reamer assembly for removing bone and tissue from a joint to facilitate the installation of a prosthetic device. The assembly includes a hollow reamer body having an opening and a base portion. The base portion includes a first pivoting link member, a wall with a surface defining a central cavity, and a plurality of spaced apart cutting sites defining apertures through said wall. A shaft is configured to be de-mountably attached to a rotary source of power. The shaft has a rotary axis and a second pivoting link member coupled to the first pivoting link member. The axis of the shaft forms an angle to the base portion. A mechanism adjusts the angle of the hollow reamer body from an un-deployed position to a deployed position.