Eigentwists and eigenwrenches capture the stationary stiffness behavior of compliant mechanisms and can be related to a mechanism’s primary kinematic behavior. The nature of concatenation of multiple mechanism building blocks is not well understood. In this paper, we consider the mechanics of concatenation and develop design rules that capture the geometric nature of concatenation in terms of eigenwrenches and eigentwists. The rules are illustrated through mechanisms from the literature and an example design problem. The design rules have potential to provide intelligent guidance for systematic building block synthesis of compliant mechanisms.