Numerical Methods for Computing the Forward Kinematics of a Redundant Parallel Manipulator

In this paper, different approaches are presented to solve the forward kinematics of a three DOF actuator redundant hydraulic parallel manipulator. It is known, that on the contrary to series manipulators, the forward kinematic map of parallel manipulators involves highly coupled nonlinear equations, which are almost impossible to solve analytically. The proposed methods are using mainly numerical computations, with different ideas to solve the problem. The accuracy of the results of each method are compared in detail and the advantages and the disadvantages of them in computing the forward kinematic map of the given mechanism is discussed in detail. It is concluded that the 4th order Taylor series approximation has the best acceptable prediction errors for robotic applications, compared to that of the different structures of neural networks and the quasi-closed solution method considered in this paper. KeywordsParallel Manipulator; Forward Kinematics; Taylor Series; Neural Networks; Numerical solution; Closed-Form solution; Performance comparison