Computer simulation of the kinematic and dynamic behaviors of mechanical assemblies has become a very important tool in design and manufacturing, because the designer can foresee how a product is going to perform before the product is actually fabricated. However, up to now, the most current simulation modules are based on analysis from another kinematic or dynamic module by specifying the mating conditions between components, and then displaying the motion on the screen. This computer simulation actually performs similarly to a movie, and can only provide visual checking. The drawback of this simulation approach is that designers are forced to use the available joint models, and may lose their creativity. In part I of this paper, general mathematical modeling of the multi-body system is presented, while part II of this paper, a prototype convex-feature modeling system is presented with which a designer can interactively create an assembly of mechanical components ready for dynamic analysis. It can provide a state-of-the-art technology for real simulation of any mechanical systems, and act as a cost-effective test bed for concepts, final design, and control algorithms.