For robotic systems to automatically plan and execute manipulation tasks involving intermittent contact, one must be able to accurately predict the motions of the manipulated objects. Not surprisingly, many of the important manipulation problems that could yield to closed-form analysis have been solved and studied thoroughly. Problems characterized by intermittent contact are one particularly important type of robotics problem for which research must rely on simulation techniques.;Due to the intermittency of contact and the presence of stick-slip frictional behavior, dynamic models of such multibody systems are inherently (mathematically) nonsmooth, and are thus difficult to integrate accurately or quickly. Commercially available software tools have a difficult time simulating systems with unilateral constraints, that is constraints where touching bodies are allowed to touch or separate, but not interpenetrate. Users expect to spend considerable effort in a trial-and-error search for good simulation parameters to obtain believable, not necessarily accurate, results. Even the seemingly simple problem of a sphere rolling on a horizontal plane under only the influence of gravity is challenging for commercial simulators. The correct handling of unilateral contact constraints is one of the most difficult challenges left for many commercial simulation software packages.;This thesis relates to the use of simulation for planning and design of robotics systems with intermittent contact. As previously noted, such systems arise in many applications, including automated manufacturing, health care, and personal robotics. The relationship between these seemingly unrelated application areas is forged by the desire of interactive robotic devices situated in an unstructured world. A better understanding of the dynamics, especially the contact dynamics, will allow us to improve the autonomy of these systems. In the first part of this work, we introduce four new time-stepping methods, which were constructed for a variety of reasons, including accuracy, performance, and design. Next, we developed a simulation software package (dubbed daVinci Code) that implements these new methods. This software tool facilitates the simulation, analysis, and virtual design of multibody systems with intermittent frictional unilateral contact. Next, a study on the applicability of our time-stepping method is presented. We performed a numerical study on the accuracy of our methods, and experimentally validated our time-stepper on a system composed of a vibrating rigid plate and interacting part. With the accuracy of our time-stepper verified for this system, we were able to study the inverse problem of designing new plate motions to generate a desired part motion. Lastly, we present our initial results of a new non-recursive nonlinear filter using our model of these systems. This filter allows us to estimate the system's parameters, which is a necessary requirement for using simulation for planning and design. The filtering problem is particularly challenging, since the underlying mathematical model is nonsmooth.