Due to the difficulty of dynamical modelling of constrained flexible ropes for the closure process caused by the presence of non-smooth contacts and rigid-flexible coupling problem, a simplified model is provided. The contacts between the ropes and the rings or the separators are considered as slip joints, and the dynamical studies are conducted using the constraint method. Considering the collision of the slip joint, the contact stiffness is introduced and the contact dynamics equations of the slip joint are established. The absolute nodal coordinate formulation is used to describe the motion of rope element, and the dynamics model of which can then be established through the principle of virtual work. For rigid bodies such as separators, the quaternion description is used to establish the dynamics equations. The simulation of closure process is performed to obtain the motion law of the rope and the traction mass block, and the closure time and the degree of closure are compared under different numbers of rings. It is found that an increase in the number of rings will result in a more compact contraction of the rope, but considerable rings will prolong closure time and reduce closure efficiency.