Dynamic Analysis of 4-SPS/CU Parallel Mechanism Considering Three-Dimensional Wear of Spherical Joint With Clearance

The dynamic performance of 4-SPS/CU (spherical joint, prismatic joint, cylindrical joint, and universal joint) parallel mechanism considering spherical joint with clearance is developed, and the three-dimensional (3D) wear property of the socket is based on the Archard's wear model. First, the kinematics model of spherical joint with clearance is established, and the updated procedure pertaining to the contact mechanics and wear state is explained via a flowchart. An improved contact force model was proposed by Flores et al. contact force model through a revised contact stiffness coefficient. The normal and tangential contact forces between ball and socket are calculated using the improved contact force model and a modified Coulomb friction model. Second, the dynamic model of the parallel mechanism considering spherical joint with clearance is formulated based on the multibody equations of motion. In order to obtain the 3D wear property of spherical joint with clearance, the contact force is decomposed into three components in the global coordinate system. The three components of sliding distance are computed based on the 3D revolute property of the parallel mechanism. Finally, the contact pressures in three different directions are calculated by the corresponding contact force and approximate contact area components for the sake of predicting the 3D wear depth of socket based on the Archard's wear model. The simulation results show that the wear depth in different directions along the socket surface is nonuniform, which affects the performance of 4-SPS/CU parallel mechanism.