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In recent times, there has been considerable interest in creating and deploying modular cooperating collectives of robots. Interest in such cooperative systems typically arises when certain tasks are either too complex to be performed by a single agent or when there are distinct benefits that accrue by cooperation of many simple robotic modules. However, the nature of both the individual modules as well as their interactions can affect the overall system performance. In this paper, we examine this aspect in the context of cooperative payload transport by robot collectives wherein the physical nature of the interactions between the various modules creates a tight coupling within the system. We leverage the rich theoretical background of analysis of constrained mechanical systems to provide a systematic framework for formulation and evaluation of system-level performance on the basis of the individual-module characteristics. The composite multi-degree-of-freedom (DOF) wheeled vehicle, formed by supporting a common payload on the end-effectors of multiple individual mobile manipulator modules, is treated as an in-parallel system with articulated serial-chain arms. The system-level model, constructed from the twist- and wrench-based models of the attached serial chains, can then be systematically analyzed for performance (in terms of mobility and disturbance rejection). A two-module composite system example is used throughout the paper to highlight various aspects of methodical system model formulation, effects of selection of active, passive or locked articulations on system performance, and experimental validation on a hardware prototype test bed.