Dynamic modeling, identification and control of Stewart platform-based machine tools

The Stewart platform is a fully parallel link manipulator with six degrees-of-freedom (DOF). It has excellent mechanical characteristics, such as high stiffness and strength-to-weight ratio, that motivate its application as a machine tool. Research issues related to this application are addressed in this dissertation. The covered areas include kinematic and dynamic modeling of Stewart platform mechanisms, and motion control of Stewart platform based machine tools.; Solution of the inverse kinematic problem of the Stewart platform mechanisms is straightforward to obtain. The inverse Jacobian matrix and its time derivative are derived as part of solutions for the inverse rate kinematic and inverse acceleration kinematic problems. A numerical iterative solution based on the Newton-Raphson method for solving the forward kinematic problem on-line for controller implementation is developed and evaluated. Convergence after a few iterations is reached if a close enough initial guess is available. The effects of the different types of joints at the strut ends on the angular velocity and angular acceleration of the struts are discussed. For example, a strut can be attached to the base and to the platform through two spherical joints or through a spherical and a universal joint.; The Newton-Euler method and the Lagrange-Euler method are both used to derive the rigid body dynamic equations of the Stewart platform mechanism. A computer simulation that uses the Newtonian approach to compute the Coriolis, centrifugal and gravity force/torque vector, and the Lagrangian approach to compute the inertia matrix is developed. Actuator dynamic models, and models for friction at the spherical joints and for transmission compliance are also incorporated into the simulation. Inverse dynamic simulation is used to study the relative significance of different components of the rigid body dynamics, and frictional effects at the spherical joints.; Experimental modeling on a single strut test stand is presented. The dynamic model of the strut includes a model for the brushless DC motor powering the strut, rigid body and actuator dynamic effects, transmission compliance, and viscous and Coulombic frictional effects. The identified model agrees well with experiment at frequencies up to 100 Hz.; A comparative study of joint space control and task space based cross-coupling control is presented. The cross-coupling controllers exert more control effort on the more critical position and orientation control axes. The simulation study proves the superiority of cross-coupling controllers over the uncoupled joint space controller in both transient and steady state conditions for a variety of test contours.