Kinetostatic modeling of Exechon parallel kinematic machine for stiffness analysis

Exechon machines are a new type of parallel kinematic machines, which have been proven experimentally to be competitive in terms of accuracy, reliability, and operation speed. The proven performance is partially contributed by its unique layout of three prismatic legs; its kinematic structure is overconstrained. Higher accuracy is a primary goal for the use of an Exechon machine; accuracy relies on system stiffness and rigidity. However, the works on the stiffness analysis of Exechon machines has been limited to some numerical results from finite element analysis; no correlation between the motions and stiffness change has been studied systematically. To gain a thorough understanding of the impact of the overconstraints on system stiffness, the kinetostatic method is used for stiffness analysis. Jacobian matrices of kinematics have been derived, and they are used to develop the system stiffness model of the machine. The Exechon X700 model has been used as a case study to illustrate the process of stiffness analysis. The stiffness model is established and quantifiable comparison has been made between simulation and test data to verify the effectiveness of the stiffness model. The developed stiffness model can be applied to optimize machine structure or trajectory planning based on the specified task.