Abstract: The existing Newton-Raphson iterative method used for the forward kinematics of parallel mechanisms has a strong dependency on the initial value with a slow iteration convergence speed,and thus the instantaneity can- not be satisfied.In order to solve these problems,a combinatorial method of a new improved BP Neural Network model based on the Levenberg-Marquardt algorithm and the high-order modified Newton-Raphson (HMNR) itera- tion method is proposed to achieve the forward kinematics of Redundancy parallel mechanism.Then,by taking a test bench for bogie parameters (TBBP) as the example,the track spectrum is converted to the displacement of the actuator with the help of the invert kinematics.Hydraulic system received the instruction of displacement to propel the test bench's coupling motion,which is used to simulate the running status of the real vehicle or bogie on real tracks.By using a mass of actual data as the training material,the initial value of the forward kinematics of the test bench is thus determined,which is then compared with those obtained through the neural network models respec- tively based on the quasi-Newton algorithm BFGS and the scaled conjugate gradient (SCG) algorithm.Experimen- tal results show that the L-M algorithm model is obviously superior to the BFGS algorithm model and the SCG algo- rithm model in terms of the error performance analysis,with a predicted angle value of less than 4 ×10 －7 and a dis- placement error of less than 8 ×10 －4 .In addition,the predicted value is taken as the initial value of the HMNR method to perform an iterative calculation,which causes a 41% reduction in the required iterations and a 23% re- duction in the iteration time in comparison with the Newton-Raphson (NR) method.Finally,by applying the hy- brid strategy on the TBBP for testing the relative position and attitude of adjacent vehicles,the effectiveness of the hybrid strategy is further validated.

Key words: railway vehicle, forward kinematics, redundancy, 6-DOF parallel mechanism, Levenberg-Mar- quardt algorithm, higher-order convergence