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This work presents a modular approach for the dynamic modeling and efficient simulation of complex robot systems composed of multiple robots constrained by multiple concurrent contacts. The modular nature of the algorithm enables existing open-chain models for individual robots and other mechanisms to be incorporated without significant reprogramming, while a general contact model allows both holonomic and nonholonomic constraints in the system. An example is provided to illustrate the algorithm's modularity and demonstrate its application. In addition to the development of the dynamic equations, this paper will discuss the implementation of the simulation algorithm in detail, including issues of computational complexity.