This paper presents a method for designing mechanisms composed of Revolute-Binary state prismatic-Revolute (RBR) chains for rigid body guidance. Where a prismatic joint allows for any distance between two revolute joints, a binary state prismatic joint reaches two distances precisely. A single RBR chain can be designed to reach six positions. A parallel arrangement of three RBR chains can be assembled at the six positions but, in general, is not a viable kinematic solution. By requiring the arrangement of three RBR chains to share specific fixed and moving pivots, called an N-type arrangement, four positions are reachable. Further, the design space is quickly searchable for singularity-free solutions. Examples illustrate a solution to a four position synthesis problem and a ten position problem using a serial assembly of these mechanisms.