Dynamic Modeling and Simulation of Stewart Platform

Since a parallel structure is a closed kinematics chain, all legs are connected from the origin of the tool point by a parallel connection. This connection allows a higher precision and a higher velocity. Parallel kinematic manipulators have better performance compared to serial kinematic manipulators in terms of a high degree of accuracy, high speeds or accelerations and high stiffness. Therefore, they seem perfectly suitable for industrial high-speed applications, such as pick-and-place or micro and high-speed machining. They are used in many fields such as flight simulation systems, manufacturing and medical applications. One of the most popular parallel manipulators is the general purpose 6 degree of freedom (DOF) Stewart Platform (SP) proposed by Stewart in 1965 as a flight simulator (Stewart, 1965). It consists of a top plate (moving platform), a base plate (fixed base), and six extensible legs connecting the top plate to the bottom plate. SP employing the same architecture of the Gough mechanism (Merlet, 1999) is the most studied type of parallel manipulators. This is also known as Gough–Stewart platforms in literature. Complex kinematics and dynamics often lead to model simplifications decreasing the accuracy. In order to overcome this problem, accurate kinematic and dynamic identification is needed. The kinematic and dynamic modeling of SP is extremely complicated in comparison with serial robots. Typically, the robot kinematics can be divided into forward kinematics and inverse kinematics. For a parallel manipulator, inverse kinematics is straight forward and there is no complexity deriving the equations. However, forward kinematics of SP is very complicated and difficult to solve since it requires the solution of many non-linear equations. Moreover, the forward kinematic problem generally has more than one solution. As a result, most research papers concentrated on the forward kinematics of the parallel manipulators (Bonev and Ryu, 2000; Merlet, 2004; Harib and Srinivasan, 2003; Wang, 2007). For the design and the control of the SP manipulators, the accurate dynamic model is very essential. The dynamic modeling of parallel manipulators is quite complicated because of their closed-loop structure, coupled relationship between system parameters, high nonlinearity in system dynamics and kinematic constraints. Robot dynamic modeling can be also divided into two topics: inverse and forward dynamic model. The inverse dynamic model is important for system control while the forward model is used for system simulation. To obtain the dynamic model of parallel manipulators, there are many valuable studies published by many researches in the literature. The dynamic analysis of parallel manipulators has been traditionally performed through several different methods such as