In order to obtain direct solutions of parallel manipulator without divergence in real time,a modified global Newton-Raphson(MGNR) algorithm was proposed for forward kinematics analysis of six-degree-of-freedom(DOF) parallel manipulator.Based on geometrical frame of parallel manipulator,the highly nonlinear equations of kinematics were derived using analytical approach.The MGNR algorithm was developed for the nonlinear equations based on Tailor expansion and Newton-Raphson iteration.The procedure of MGNR algorithm was programmed in Matlab/Simulink and compiled to a real-time computer with Microsoft visual studio.NET for implementation.The performance of the MGNR algorithms for 6-DOF parallel manipulator was analyzed and confirmed.Applying the MGNR algorithm,the real generalized pose of moving platform is solved by using the set of given positions of actuators.The theoretical analysis and numerical results indicate that the presented method can achieve the numerical convergent solution in less than 1 ms with high accuracy(1×10-9 m in linear motion and 1×10-9 rad in angular motion),even the initial guess value is far from the root.
The current research of electro-hydraulic servo valves mainly focuses on the vibration, pressure oscillating and source of noise. Unfortunately, literatures relating to the study of the influence of the magnetic reluctances of the magnetic elements are rarely available. This paper aims to analyze the influence of the magnetic reluctances of the magnetic elements on torque motor. Considering these magnetic reluctances ignored in previous literatures, a new mathematical model of servo valve torque motor is developed and proposed based on the fundamental laws of electromagnetism. By using this new mathematical model and the previous models, electromagnetic torque constant and magnetic spring stiffness are evaluated for a given set of torque motor parameters. A computer simulation by using AMESim software is also performed for the same set of torque motor parameters to verify the proposed model. The theoretical results of electromagnetic torque constant and magnetic spring stiffness evaluated by the proposed model render closer agreement with the simulation results than those evaluated by the previous models. In addition, an experimental measurement of the magnetic flux densities in the air-gaps is carried out by using SFL218 servo valve torque motor. Compared with the theoretical results of the magnetic flux densities in the air-gaps evaluated by the previous models, the theoretical results evaluated by the proposed model also show better agreement with the experimental data. The proposed model shows the influence of the magnetic reluctances of the magnetic elements on the servo valve torque motor, and offers modified and analytical expressions to electromagnetic torque constant and magnetic spring stiffness. These modified and analytical expressions could provide guidance more accurately for a linear control design approach and sensitivity analysis on electro-hydraulic servo valves than the previous expressions.
In this paper, taking two degrees of freedom on the armature–flapper assembly into account, a seventh-order model is deduced and proposed for the dynamic response of a two-stage electro-hydraulic servo valve from nonlinear equations. These deductions are based on fundamental laws of electromagnetism, fluid, and general mechanics. The coefficients of the proposed seventhorder model are derived in terms of servo valve physical parameters and fluid properties explicitly.For validating the results of the proposed model, an AMESim simulation model based on physical laws and the existing low-order models validated by other researchers through experiments are used to compare with the seventh-order model. The results show that the seventh-order model can reflect the physical behavior of the servo valve more explicitly than the existing low-order models and it could provide guidance more easily for a linear control design approach and sensitivity analysis than the AMESim simulation model.
A new simple and effective inertial parameter identification method based on sinusoidal vibrations of a six-degree-of-freedom parallel manipulator is proposed. Compared with previously known identification algorithms, the advantages of the new approach are there is no need to design the excitation trajectory to consider the condition number of the observation matrix and the inertial matrix can be accurately defined regardless of the effect of viscous friction. In addition, the use of a sinusoidal exciting trajectory allows calculation of the velocities and accelerations from the measured position response. Simulations show that the new approach has acceptable tolerance of dry friction when using a simple coupling parameter modified formula. The experimental application to the hydraulically driven Stewart platform demonstrates the capability and efficiency of the proposed identification method.
