We introduce computational support tools for the analysis and design of systems with multiple frictional contacts, with a focus on applications to part feeding and assembly processes. The tools rely on dynamic models of the processes. We describe two approaches to modeling, the Stewart-Trinkle model [1] and the Song-Pang-Kumar model [2], that allow the designer to experiment with different geometric, material and dynamic properties and optimize the design for performance. In order to accomodate contact transitions, we introduce a smooth cone model for friction. We illustrate the models and the design process by describing the design optimization of a part feeder.