A systematic analytical method for PKM stiffness matrix calculation

The purpose of this work is to propose a new approach for the calculation of PKM stiffness matrix by using an analytical method based on matrix structural analysis. This method has as the main advantage to be systematic and it also can be applied to hyper-static PKM stiffness analysis. The implementation of the proposed method is fast and convenient and it can easily be involved during PKM design optimization. Moreover, as the stiffness matrix is obtained in a close form, it can be implemented directly on the robot controller. In other words, the proposed method could be used to reduce the gap existing between actual PKM and those that have to meet the high accuracy specifications required for machining applications. At first this paper presents the proposed analytical method that is applied to calculate the stiffness matrix of a delta parallel structure. Then the experimental results that have been done to evaluate and validate its efficiency are presented