The conceptual design of robotic architectures, the subject of this paper, pertains to the topology of the underlying kinematic chain. Schoenflies Motion Generators (SMGs) are robots capable of a special class of motions---three independent translations and one rotation about an axis of fixed direction. In this paper, synthesis rules are proposed to obtain a complete minimum set of serial topologies capable of producing Schoenflies motions. Only revolute (R), prismatic (P), helical (H) and $Pi$ joints are considered, as any multi-degree-of-freedom lower kinematic pair can be produced as a combination of R, P, H and $\Pi$ joints. Next, the concept-evaluation framework, proposed in an earlier work, is used to organize the topologies obtained in an ascending order of complexity, hence completing the conceptual design phase of the subject motion generators.