Continuous stiffness modeling of 3-RPS parallel kinematic machine with special composite spherical joints

A comprehensive continuous modeling methodology of 3-RPS parallel machine under dynamic load condition was developed and presented by considering the stiffness of legs and joints. The variational Jacobian matrix was used through vector differential and equivalent mechanism technique. Based on the screw theory, the force equation between the dynamic load on the mobile platform and its reaction forces on the legs and joints of the 3-RPS parallel machine was investigated and analyzed. The relationship between the pose (position and orientation) distortion of the mobile platform and the elastic deformation behavior of the legs and joints on 3-RPS parallel machine was established and analyzed by vector differential. A comprehensive dynamic stiffness model of the machine was developed by adding the total differential of the residual forces on the machine system. To validate the methodology, a numerical simulation was carried out. The result shows that the stiffness model of the parallel machine is affected by the outside load and the pose of the mobile platform. There is a large difference between the simple stiffness model and the integrate stiffness model near the workspace boundary of the parallel machine.