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This paper presents an efficient modular algorithm for the dynamic simulation of robots constrained through a single contact. Such configurations include single robots with closed-loop topologies, as well as, multiple robots with simple series, parallel, and bracing topologies. The modular nature of the algorithm enables the incorporation of existing open-chain models for the individual robots without significant reprogramming, while a general contact model extends the range of possible contact conditions to include both holonomic and nonholonomic constraints. The algorithm is validated through the simulation of two robots cooperating in parallel. This paper establishes an accurate framework for simulating simple robot systems with single contacts, which can be extended to multi-robot, multi-contact systems performing general tasks.