Multibody dynamics plays the key role in the modeling, simulation, design, and control of many engineering problems. In practice, such problems may be encountered with the existence of uncertainty in the system's parameters and/or excitations. As the complexity of these problems in terms of the number of the bodies and kinematic loops (chains) increases, the effect of uncertainty in the system becomes even more significant due to the accumulation of inaccuracies. Therefore, considering uncertainty is inarguably a crucial aspect of performance analysis of a multibody problem. In fact, uncertainty needs to be propagated to the system kinematics and dynamics for the better understanding of the system behavior. This will significantly affect the design and control process of such systems. For this reason, this research presents a detailed investigation on the use of the Polynomial Chaos Expansion (PCE) method for both control and kinematic analysis of nondeterministic multibody systems.