Abstract
This paper proposes a method to calculate the forward kinematics of a Stewart Plaftorm type of parallel link manipulators. The Stewart Platform consists of a base platform, a moving platform, and linear actuators connecting the both platforms. First we introduce a virtual parallel link mechanism, having the same kinematic structure as the original parallel mechanism. We assume that the moving platform of the virtual mechanism is directly driven by actuators and the limbs connecting both platforms have no actuators. A trajectory tracking control system is designed for this virtual mechanism based on the resolved motion rate control, so that the displacements of limbs are controlled by the actuators driving the moving platform. We calculate the forward kinematics by numerical simulation of the control system ; the position and orientation of the moving platform of the virtual mechanism is a solution for given displacements of limbs, when the tracking error of limbs converges to zero. The method is effective for a time varying displacements of limbs as long as the displacements are differentiable about time. The position and orientation of the moving platform is obtained without error, once the tracking error converges to zero. The simulation results illustrate the method.
