We propose a formulation capable of measuring the complexity of kinematic chains at the conceptual stage in robot design. First, the complexity of the three basic lower kinematic pairs, the revolute, the prismatic and the cylindrical pairs, is proposed. Then, a formulation of the complexity of kinematic chains is introduced. Next, the complexity of the basic displacement subgroups generated by the lower kinematic pairs is established. Finally, as an example, two realizations of the Schönflies displacement subgroup are compared.