Forward kinematic calculation of parallel link manipulators

The authors propose a method to calculate the forward kinematics of parallel link manipulators. They introduce a virtual parallel link mechanism, having the same kinematic structure as the original parallel mechanism. It is assumed that the moving platform of the virtual mechanism is directly driven by actuators and the limbs connecting both platforms have no actuators. A control system is presented 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. The forward kinematics are calculated by numerically simulating the control system. The position and orientation of the moving platform of the virtual mechanism are a solution for given displacements of limbs, when the tracking error of limbs converges to zero. The method is effective for time varying displacements of limbs as long as the displacements are differentiable about time. The position/orientation of the moving platform is obtained without error, once the tracking error converges to zero. The simulation results illustrate the method