As the coupler link of an RCCC linkage moves, its instant screw axis (ISA) sweeps a ruled surface on the fixed link; by the same token, the ISA describes on the coupler link itself a corresponding ruled surface. These two surfaces are the axodes of the linkage, which roll while sliding and maintaining line contact. The axodes not only help to visualize the motion undergone by the coupler link but also can be machined as spatial cams and replace the four-bar linkage, if the need arises. Reported in this paper is a procedure that allows the synthesis of the axodes of an RCCC linkage. The synthesis of this linkage, in turn, is based on dual algebra and the principle of transference, as applied to a spherical four-bar linkage with the same input–output function as the angular variables of the RCCC linkage. Examples of RCCC linkages are included. Moreover, to illustrate the generality of the synthesis procedure, it is also applied to a spherical linkage, namely, the Hooke joint, and to the Bennett linkage.