Dynamic behavior of mechanisms with clearance joints often exhibits nonlinear dynamic characteristics due to the collisions between the journal and bearing. However, previous studies could not quantify the complexity of the dynamic response. In this paper, based on the Poincaré map and correlation dimension, a fractal method is proposed to evaluate the complexity of nonlinear dynamic response of mechanisms with clearance joints. Motion equations of mechanical systems with clearance joints are described. A slider–crank mechanism is employed to demonstrate the efficiency of the fractal method and to discuss the influence of the clearance size and crank speed on the complexity of the dynamic response.