Dynamic Modeling And Simulation Of The Stewart Platform As One Of 6-DOF Parallel Mechanism

The Stewart platform, which is a 6-DOF (degrees of freedom) parallel mechanism with two bodies connected together by six extensible legs through the joints, is generalized from the flight simulator proposed by Stewart (1965). The lower platform of a general Stewart platform is referred to as the base-platform and the upper platform is known as the payload-platform, which is always referred to as the work platform. The Stewart platform can not only let its payload-platform move with 6-DOF in the workspace through the extension and contraction of the six legs, but also possesses the high stiffness, high precision, high load, and excellent dynamic characteristics. In this case, the Stewart platform is widely used to realize the mechanical machining, the precision positioning, and the vibration isolation. In the last two decades, the mechanical machining and the precision positioning based on Stewart platform are relatively mature to the vibration isolation based on Stewart platform. Some parallel machines and precision positioning platforms based on Stewart platform have been commercially available. However, the application of Stewart platform for the vibration isolation is developed latterly and the theoretical research in this field is incomplete up to now. The essential reason is the base-platform of Stewart platform for the application of vibration isolation is kinetic. Nowadays, some dynamic formulations of Stewart platform have been established. Miller (1992) built a dynamic formulation of Stewart platform through Lagrange approach; Dasgupta and Mruthyunjaya (1998) deduced a closed-form dynamic formulation of the Stewart platform successfully through Newton-Euler approach; Codourey and Burdet (1997), Wang and Gosselin (1998), and Tsai (2000) solved the inverse dynamics for the Stewart platform through the principle of virtual work principle. However, all the above mentioned models are proposed and built assuming the base-platform of Stewart platform is static. Therefore, it is difficult to use the existing models of Stewart platform when the base-platform is kinetic because of the following reasons: 1. The existing models can not be used to analyze the dynamic characteristics of the payload-platform of the Stewart platform with kinetic base-platform. 2. The existing models can not be used to direct the development and design of the Stewart platform with kinetic base-platform. 3. Regarding the feedback control of Stewart platform with kinetic base-platform, the existing models can not be used to realize the theoretical and simulation research of the feedback control algorithm. In this dissertation, inheriting the existing models of Stewart platform with a static base-platform, a closed-form dynamic model of the Stewart platform with kinetic base-platform through Newton-Euler approach is proposed and established. Base on the dynamic model of Stewart platform with kinetic base-platform, a simulation system under the Matlab/Simulink is built and some simulations are implemented for several concrete applications of Stewart platform with kinetic base-platform. The major research works completed in this dissertation includes: 1. Under the Matlab/Simulink, a closed-form dynamic simulation system based on the closed-form dynamic model of the Stewart platform by Dasgupta and Mruthyunjaya is built for the dynamic analysis of Stewart platform with static base-platform. 2. Two groups of simulation results by feedback of the motion state in task-space and in actuation-space are given, which offers a method to solve the inverse and forward kinematics and dynamics of Stewart platform. 3. Based on the closed-form dynamic model of Stewart platform with static base-platform, a new closed-form dynamic model of Stewart platform with kinetic base-platform is proposed and built. The newly established model does not only perfect the dynamics of Stewart platform, but also can be used to analyze the vibration damping, the vibration isolation, and the positioning when the base-platform exerts an outside excitation. 4. Based on the addressed closed-form dynamic model of Stewart platform with kinetic base-platform, the simulation system under the Matlab/Simulink is built successfully for the dynamic analysis of Stewart platform with kinetic base-platform. 5. Based on the addressed closed-form dynamic model of Stewart platform with kinetic base-platform, some simulations about the vibration damping, the vibration isolation, and the positioning with Stewart platform when the base-platform exerts an outsider excitation are implemented. Therefore, the configuration parameters and the control parameters for the Stewart platform can be optimized through the theoretical analysis and the simulation.The research work in this dissertation establishes a theoretical foundation for the development and design of Stewart platform with kinetic base-platform.