This paper presents a design system for planar eight-bar linkages that adds three RR constraints to a user-specified 4R serial chain. R denotes a revolute, or hinged, joint. There are 100 ways in which these constraints can be added to yield as many as 3951 different linkages. An analysis routine based on the Dixon determinant evaluates the performance of each linkage candidate and determines the feasible designs that reach the task positions in a single assembly. A random search within the user-specified tolerance zones around the task specifications is iterated in order to increase the number of linkage candidates and feasible designs. The methodology is demonstrated with the design of rectilinear eight-bar linkages that guide an end-effector through five parallel positions along a straight line.