An Inverse Dynamic Model of Over Constrained Parallel Kinematic Machine Based on Newton–Euler Formulation

Abstract

It has been known that redundant constrains in a mechanism can improve the rigidity and stiffness of the mechanism. Some Parallel Kinematic Machines (PKMs) have adopted redundant constraints to enhance their performance and stability. However, limited studies have been conducted on the dynamics of overconstrained mechanisms. While a dynamic model is not essential to machine control, a clear understanding of the dynamic behavior of the system can be useful in identifying the weakest components, optimizing the overall structure, and improving the quality of control. In this paper, the dynamic characteristics of an overconstrained PKM are investigated for the first time. The Newton–Euler formulation is extended to develop the dynamic model of the machine. It is shown that the compliance of deformations of the redundant constraints needs to be taken into account to build a complete and solvable dynamic model since the number of equations derived from the force and moment equilibrium of the PKM components is insufficient to determine all unknown variables. The proposed approach is generic in sense that it can be applied to model dynamic behaviors of other overconstrained machines with a combination of the Newton–Euler formulation and compliance conditions. Its effectiveness has been verified by the dynamic model established for Exechon PKM. The developed dynamic model has its potential to be integrated with control systems to improve accuracy and dynamic performance of realtime control.