Proposed in this paper is a paradigm for the qualitative synthesis of simple kinematic chains that is based on the concept of complexity. Qualitative synthesis is understood here as the number and the type stages of the kinematic-synthesis process. The formulation hinges on the geometric complexity of the surface associated with lower kinematic pairs. First, the geometric complexity of curves and surfaces is recalled, as defined via the loss of regularity (LOR). The LOR, based in turn on the concept of diversity, measures the spectral richness of the curvature of either the curve or the surface under study. The paper closes with a complexity analysis of all six lower kinematic pairs, as a means to guide the mechanical designer into the conceptual stage of the design process. The paradigm is illustrated with the computation of the complexity of the four-bar linkage in all its versions, planar, spherical, and spatial, as well as that of a transmission for the conversion of a rotation about a vertical axis into one about a horizontal axis.