Kinematic and dynamic analysis of Stewart platform-based machine tool structures

In this paper, an analytical study of the kinematics and dynamics of Stewart platform-based machine tool structures is presented. The kinematic study includes the derivation of closed form expressions for the inverse Jacobian matrix of the mechanism and its time derivative. An evaluation of a numerical iterative scheme for an on-line solution of the forward kinematic problem is also presented. Effects of different configurations of the unpowered joints on the angular velocities and accelerations of the links are considered. The Newton-Euler formulation is used to derive the rigid body dynamic equations. Inclusion of models for actuator dynamics and joint friction is discussed.