Over the last two decades, extensive work has been conducted to study the dynamic effect of the joint clearances in multibody mechanical systems. In contrast, little work has been devoted to optimize the performance of these systems. In this study, analysis of revolute joint clearance is formulated in terms of a Hertzian-based contact force model. For illustration, the classical slider-crank mechanism with a revolute clearance joint at the piston pin is presented, and a simulation model has been built through the analysis/design code MSC.ADAMS. The clearance is modeled as a pin-in-a-hole surface-to-surface dry contact, with appropriate contact force model between the journal and the bearing surfaces. Different simulations are performed to demonstrate the influence of the joint clearance size and the input crank speed on the dynamic behavior of the system with the clearance joint. An innovative DOE-based method for optimizing the performance of a mechanical system with the revolute joint clearance for different range of design parameters is then proposed. Based on the simulation modeling results from sample points, which are selected by a Latin hypercube sampling method, a polynomial function Kriging meta-model is established instead of the actual simulation model. The reason to build the meta-model is to bypass a compute-intensive simulation computer model for different values of design parameters to a more efficient and cost-effective mathematical model. Finally, numerical results obtained from two application examples, considering the different design parameters, including the joint clearance size, crank speed and contact stiffness, are presented for further analyzing and optimizing the dynamics of the revolute clearance joint in a mechanical system, thus accurately predicting the influence of the design parameters changes for the purpose of minimizing the contact forces, accelerations, and power requirements due to the clearance.