In order to study the influence of compliance parts on spatial multibody systems, a rigid-flexible coupling dynamic equation of a spatial crank-slider mechanism is established based on the finite element method. Specifically, absolute node coordinate formulation (ANCF) is used to formulate a three-dimensional, two-node flexible cable element. The rigid-flexible coupling dynamic equation of the mechanism is derived by the Lagrange multiplier method and solved by the generalized α method and Newton–Raphson iteration method combined. Comparison of the kinematics and dynamics response between rigid-flexible coupling system and pure rigid system implies that the flexible part causes a certain degree of nonlinearity and reduces the reaction forces of joints. The elastic modulus of the flexible part is also important to the dynamics of the rigid-flexible multibody system. With smaller elastic modulus, the motion accuracy and reaction forces become lower.

The rigid-flexible coupling cable system under large deformation is studied, and the beam element from absolute node coordinate formulation is used to establish flexible cable body of the system. Different numerical integral algorithms are discussed for solving the rigid-flexible cable system and an integration strategy which combines Implicit Euler with Minimum Residual Method (MINRES) is proposed. The influence of the position and number of rigid components and different the lengths of the flexible elements on the system dynamics are analyzed. With constant total mass of the system, higher number of rigid components and their uniform distribution contribute to stabilization of the swing of the flexible cable body. When the total length of the cable is constant, increasing the number of beam elements enhances the nonlinear characteristics of the swing motion and damages the stability. The influence of different factors on the movement of large deformation flexible cable body is obtained through modeling and simulation of the rigid-flexible coupling cable system.

As a high-precision motion mechanism, the kinematics and dynamics of cascade thrust reverser are sensitive to the changes of nonlinear factors which are rarely considered in traditional dynamic modeling and optimization. In order to study the effect of nonlinear factors on the dynamics behavior of cascade thrust reverser mechanism, the dynamic model considering joint clearance and flexible component is established. Lankarani–Nikravesh and modified-Coulomb model are used to establish the contact force at the clearance, and the flexible component in the mechanism is modeled by the absolute node coordinate method. The effects of joint clearance value, clearance position, flexible component, and driving speed on the dynamic response of the mechanism are studied. Specifically, the nonlinear characteristics of the mechanism increase with the clearance value, and the joint clearance near the mobile fairing has greater influence on the kinematics and dynamics of blocker door. For the mechanical system with clearances, the flexible component can partially reduce the vibration of the system. The analysis of the motion synchronization of the thrust reverser actuators indicates that the asynchronous movement of actuators may increase the driving forces of actuators especially for the middle actuator.