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A parallel manipulator is a closed kinematic structure with the necessary rigidity to provide a high payload to self-weight ratio suitable for many applications in manufacturing, flight simulation systems, and medical robotics. Because of its closed structure, the kinematic control of such a mechanism is difficult. The inverse kinematics problem for such manipulators has a mathematical solution; however, the forward kinematics problem (FKP) is mathematically intractable. This work addresses the FKP and proposes a neural-network-based hybrid strategy that solves the problem to a desired level of accuracy, and can achieve the solution in real time. Two neural-network (NN) concepts using a modified form of multilayered perceptrons with backpropagation learning were implemented. The better performing concept was then combined with a standard Newton-Raphson numerical technique to yield a hybrid solution strategy. Simulation studies were carried out on a flight simulation syystem to check the validity o the approach. Accuracy of close to 0.01 mm and 0.01° in the position and orientation parameters was achieved in less than two iterations and 0.02 s of execution time for the proposed strategy.