Dynamic analysis of a mechanism with clearance joints and flexible links is a research focus in the field of multibody dynamics. In this study, a general modular dynamic modeling approach based on Lagrange multiplier method for planar closed-loop mechanisms is proposed in order to improve the modeling efficiency and reusability of a structure having same topology. With this approach, dynamic analysis considering clearance joints and flexible links can be performed conveniently. A novel mathematical model to determine the relative motion modes between the two components of a clearance joint is developed based on the previous contact detection method. A complete dynamic effect evaluation system, which measures the influence of clearance joints and flexible links on the dynamic performances more conveniently and intuitively, is established. A planar 3-RRR parallel mechanism that is a closed-loop system including imperfect joints and flexible links is studied as an example. The dynamic model of this mechanism is established and its dynamic characteristics are investigated. The couple effects of clearance joints and flexible links for a parallel mechanism are investigated first. The contact forces existing in the clearance joints can cause system vibration and thus reduces the dynamic stability of the whole mechanical system. Meanwhile, the simulation results indicate that the flexible links can damp the vibration of the moving platform caused by clearance joints is certain.