In this paper we propose a formulation capable of measuring the complexity of robotic architectures at the conceptual-design stage. The motivation lies in providing a tool to the robot designer when selecting the best alternative among various candidates generated at the early stages of the design process, when a parametric design is not yet available. While the performance evaluation of a robot includes many criteria, we focus on: the kinetostatic, the elastostatic and the elastodynamic performances; workspace volume; actuation complexity and the life-cycle cost. Within the realm of conceptual design, characterized by the absence of a mathematical model, it is not possible to optimize the performance at hand using classical mathematical programming methods. In this paper, a set of rules derived from robotics knowledge is outlined. These rules are then used to formulate a complexity measure used to filter-out less promising architectures at the conceptual stage. The complete formulation is applied to the development of a six-degree-of-freedom robot with low topological complexity, high performance and low actuation-system complexity. A complexity-comparison between the proposed architecture, the DIESTRO and the PUMA robots, is also provided.