This paper presents a framework to design mechanical models relying on a topological basis. Whereas naive topological models such as adjacency graphs provide low topological control, the use of efficient topological models such as generalized maps guarantees the quasi-manifold property of the manipulated object: Topological inquiries or changes can be handled robustly and allow the model designer to focus on mechanical aspects. Even if the topology structure is more detailed and consumes more memory, we show that an efficient implementation does not impact computation time and still enables real-time simulation and interaction. We analyze how a simple mass/spring model can be embedded within this framework.