Joints clearance are essential components of multi-body systems, and it gives rise to the impact forces between the joint elements, which induce increased vibration and noise, reduce component life ,and result in a loss of precision. Joint clearance of mechanical system is necessary to allow the relative motion of connected bodies. This paper presents a dynamic modeling of a novel vibration damping platform (4-SPS/CU parallel mechanism) with spherical joint clearance based on the continuous contact mode. One of the driving chains connected to the lower platform with spherical joint, and the clearance in this spherical joint isviewedasno-mass rigid link in the 4-SPS/CU parallel mechanism. Firstly, the mathematical model of spherical clearance and the position equations with clearance of the parallel mechanism are set up. Secondly, thekinetostatics equilibrium equations of the ideal parallel mechanism are successfully formulated via d'Alembert principle, and all of the joint reactions are induced by solving the kinetostatics equilibrium equations. On the basis of the above results, the position angles of the ideal mechanism’s joint reactions corresponding to the clearance kinematicpair are approximately equal to the orientation angles of the no-mass rigid link. Lastly, the dynamics equations with clearance are modeled by reopening force analysis of the driving chain with joint clearance. The driving forces, kinematics characteristicsand joint reactions of the parallel mechanism are analyzed respectively under with clearance or ideal joint by numerical calculation. These observations can provide useful information towards the design of the parallel mechanisms.