Modeling of Configuration-Dependent Flexible Joints for a Parallel Robot

This paper provides a method to determine the variable flexible joint parameters which are dependent on configurations for a PRS Parallel Robot. Based on the continuous force approach, virtual springs were used between the joint components to simulate the joint flexibility. The stiffness matrix of the joint virtual springs was derived. The method uses system dynamic characteristics in different configurations to set the virtual spring stiffness for all the joints in the system. Modal testing was conducted on a set of selected robot configurations to determine the system natural frequencies and mode shapes along with their variation. To obtain the virtual spring stiffness, the system was condensed at the joint nodal coordinates. Then eigen-sensitivity analysis was conducted on the condensed system matrices with respect to the stiffness parameters of the joint virtual springs. Thus, the virtual spring parameters in the model can be set to match the variation of the system dynamic responses with the robot configuration changes. The virtual spring parameters between the selected robot configurations were obtained by interpolation. The research indicates that the method is effective and relatively easy to conduct, compared to other methods. The variable flexible joint model is applicable to flexible multibody systems with variable configurations.