A new recursive algorithm for real-time, interactive dynamic simulation, animated graphics, and design variation analysis is presented for mechanical systems with closed loops. State vector kinematic relations that represent translational and rotational motion are defined, to simplify the formulation and to relieve computational burden. Recursive equations of motion are first derived for a single loop multi-body system. Faster than real-time performance is demonstrated for a closed loop robot, using an Alliant FX/8 multiprocessor. The algorithm is extended to multi-loop, multi-body systems for parallel processing real-time simulation in companion papers [1,2]. Performance of the algorithm on a shared memory multi-processor is compared with that achieved with other dynamic simulation algorithms. A vehicle example is used to demonstrate efficiency of the algorithm for real-time simulation and graphics rendering in a network environment, for use as an interactive design tool.