Fast Numerical Solution to Forward Kinematics of General Stewart Mechanism Using Quaternion

The forward kinematics of the general Stewart mechanism is studied and a fast numerical method is presented.Quaternion is utilized to model the forward kinematics and the equations are merely a system of quadratic ones.The numerical method is a nice simplification of the Newton-Raphson method when applied to this system.A simulation of the movement control of the Stewart mechanism is accomplished,confirming the effectiveness of the proposed algorithm in real-time conditions.     

Aircraft Electric Anti-skid Braking System Based on Fuzzy-PID Controller with Parameter Self-adjustment Feature

The principle of electric braking system is analyzed and an anti-skid braking system based on the slip rate control is proposed. The fuzzy-PID controller with parameter self-adjustment feature is designed for the anti-skid braking system. The dynamic model of aircraft ground braking is established in the simulation environment of MATLAB/SIMULINK, and simulation results of dry runway and wet runway are presented. The results show that the fuzzy-PID controller with parameter self-adjustment feature for the electric anti-skid braking system keeps working in the state of stability and the brake efficiencies are increased to 93% on dry runway and 82% on wet runway respectively.     

Experiment on a Semi-Active In-Car Crib with Joint Application of Regular and Inverted Pendulum Mechanisms Using Scale Model

To reduce the collision shock and risk of injury to an infant in an in-car crib(or in a child safety bed)during a car crash,it is necessary to limit the force acting on the crib below a certain allowable value.To realize this objective,we propose a semi-active in-car crib system with the joint application of regular and inverted pendulum mechanisms.The crib is supported by arms similar to a pendulum,and the pendulum system itself is supported by arms similar to an inverted pendulum.In addition,the arm acting as a regular pendulum is joined with the arm acting as an inverted pendulum through a linking mechanism for simplicity,and the friction torque of the joint connecting the base and the latter arm is controlled using a brake mechanism,which enables the proposed in-car crib to gradually increase the deceleration of the crib and maintain it at around the target value.This system not only reduces the impulsive force but also transfers the force to the infant′s back using a spin control system,i.e.,the impulse force is made to act perpendicularly on the crib.The spin control system was developed in our previous work.The present work focuses on the acceleration control system.A semi-active control law with acceleration feedback is introduced using the sliding mode control theory.Especially,a feedback system of the crib acceleration relative to the vehicle is proposed for the high-vibrational environment.Further,a control experiment using scale model is conducted to confirm the effectiveness,and some results are reported.     

General Solutions of Thermoelastic Plane Problems of Two-Dimensional Quasicrystals

The thermoelastic plane problems of two-dimensional decagonal quasicrystals(QCs)are systematically investigated.By introducing a displacement function,the problem of thermoelastic plane problems can be simplified to an eighth-order partial differential governing equation,and then general solutions are presented through an operator method.By virtue of the Almansi′s theorem,the general solutions are further established,and all expressions for the phonon,phason and thermal fields are described in terms of the potential functions.As an application of the general solution,for a steady point heat source in a semi-infinite quasicrystal plane,the closed form solutions are presented by four newly induced harmonic functions.     

LEO AUTONOMOUS NAVIGATION BASED ON IMAGE MOTION

A method of LEO autonomous navigation is presented based on the nonlinear satellite velocity relative to the earth. The velocity is detected by a high-speed camera, with the attitude information detected by a star sensor. Compared with traditional autonomous navigation by landmark identification, the satellite velocity relarive to the earth is obtained by correlativity analysis of images. It does not need to recognize ground objects or views. Since it is not necessary to pre-store the database of ground marks, lots of memory space can be saved.The state and observation equations are constructed, and the filtering is processed by the Kalman filter. Simulation results show that the system has high autonomous navigation precision in LEO autonomous navigation.     

IN-FLIGHT ALIGNMENT OF INERTIAL NAVIGATION SYSTEM BY CELESTIAL OBSERVATION TECHNIQUE

This paper presents an in-flight alignment technique for a strapdown inertial navigation system (SINS) and employs a star pattern recognition procedure for identifying stars sensed by a CCD electrooptical star sensor.Collinearity equations are used to estimate sensor frame star coordinates and the conventional least square differential correction method is used to estimate the unknown orientation angles. A comparison of this attitude with the attitude estimated by the SINS provides axis misalignment angles. Simulations using a Kalman filter are carried out for an SINS and the system employs a local level navigation frame. The space stabilized SINS is discussed in conjunction with the celestial aiding. Based on the observation of the Kalman filter, the estimating and compensating gyro errors, as well as the position and velocity errors caused by the SINS misalignments are calibrated by celestial attitute information.     

Dynamical Model Updating Based on Modal Tests with Changed Structure

A new approach to modifying the stiffness and mass matrices of finite element models is presented to improve the calculation precision. By measuring the mode frequencies and shapes of both of the original and the new structures with changed stiffness and mass, the stiffness and mass matrices of the finite element model can be updated through matrices calculation and solving algebra equations. Taking a multi-freedom model as an example, the relation between the number of the modes and the correction precision of stiffness and mass matrix elements is researched. The facility and precision of the method are totally confirmed especially when the modeling error is known limited to a definite local range. The feasibility of the approach is proven by an effective engineering application to the model updating of a wing piece used in flutter test.     

Modeling and Simulation for Refueling Boom and Receiver in Coupled Mode

In coupled mode,the major problem of boom refueling system is undesirable nozzle loads.An automated load alleviation system(ALAS)is needed to alleviate nozzle loads.In order to simulate dynamic of the system and to validate ALAS,dynamic model is developed.Two models are established,which are the static model and the moving model,named after the two relative states between the fixed boom and the extension boom.Kane method is employed as main method considering system′s multi-body characteristics.D′Alembert′s principle is used to calculate nozzle loads.Simulation is conducted to research the effects of position disturbance and velocity disturbance on nozzle loads.Results indicate that position disturbance plays a more significant role in inducing nozzle loads.A fuzzy control law based ALAS is validated using the formulated model.It is concluded that this model can simulate system dynamic and validate ALAS.     

MAC Models in Thermoelasticity

There are two types of singularities in the linear thermoelasticity.The first one arises in the field of stresses if a force is applied to one point of the body.This singularity is physical and should be accepted.The second type of singularities is nonphysical and they arise in the fields of displacements and temperatures.There exist the nonlocal theories and gradient theories which have the goal to introduce the finite stresses instead of the infinite ones.The MAC model of the thermoelasticity is created to avoid the nonphysical singularities and it accepts the infinite stresses.MAC is the method of additional conditions,which allows introducing the new model to use the classical model,plus additional condition of the physical nonsingularity and/or condition of the good behavior of the solutions at infinity.The MAC Green′s functions for the heat conduction and for the elasticity could be introduced using the differential MAC models.The infinite and finite bodies are considered.The principle of superposition is applied to obtain the integral equations to solve the boundary value problems.The strength criteria based on finite stresses could be changed in this model because the infinite stresses are allowed.The strength criteria based on deformations are applicable.Classification of MAC models is given.     

Modeling and Simulation of Pipeline Security Monitoring System Based on Line-Structure Sagnac Interferometer with 3×3Coupler

The third damage action,human disruption behavior,is one of the major threats to pipeline operation.It is necessary to monitor and locate the perturbation behavior that may threat pipeline safety in real-time.Therefore,a new pipeline security monitoring system is designed by using line-structure Sagnac optic fiber interferemeter with the characteristic of 3×3coupler that can modulate the phase of optic signal,with no need for phase modulation and demodulation.The optic structure of the new system is simplified,the signal processing accuracy is improved,and the polarization effect is reduced.The working principle of the monitoring in ideal condition is described,the phase demodulation is analyzed and the location of the possible damage action point is formulated.By using simulink,the optic signal propagation and interference is simulated and interference signals in different frequencies are obtained.The results validate the feasibility of the monitoring system and indicate that the low frequency signal less than 1kHz resulting from the human damage action can be detected.The disturbance set at 10 km can be located by calculating the demodulation signal accurately over a long monitoring distance.     

Quadcopter UAV Modeling and Automatic Flight Control Design

The mathematical model of quadcopter-unmanned aerial vehicle(UAV)is derived by using two approaches:One is the Newton-Euler approach which is formulated using classical mechanics;and other is the Euler-Lagrange approach which describes the model in terms of kinetic(translational and rotational)and potential energy.The proposed quadcopter′s non-linear model is incorporated with aero-dynamical forces generated by air resistance,which helps aircraft to exhibits more realistic behavior while hovering.Based on the obtained model,the suitable control strategy is developed,under which two effective flight control systems are developed.Each control system is created by cascading the proportional-derivative(PD)and T-S fuzzy controllers that are equipped with six and twelve feedback signals individually respectively to ensure better tracking,stabilization,and response.Both proposed flight control designs are then implemented with the quadcopter model respectively and multitudinous simulations are conducted using MATLAB/Simulink to analyze the tracking performance of the quadcopter model at various reference inputs and trajectories.     

HYBRID CARTESIAN GRID/GRIDLESS METHOD FOR CALCULATING VISCOUS FLOWS OVER MULTI-ELEMENT AIRFOILS

A hybrid Cartesian grid/gridless method is developed for calculating viscous flows over multi-element airfoils. The method adopts an unstructured Cartesian grid to cover most areas of the computational domain and leaves only small region adjacent to the aerodynamic bodies to be filled with the cloud of points used in the gridless methods, which results in a better combination of the computational efficiency of the Cartesian grid and the flexi- bility of the gridless method in handling complex geometries. The clouds of points in the local gridless region are implemented in an anisotropic way according to the features of the thin boundary layer of the viscous flows over the airfoils, and the clouds of points at the vicinity of the interface between the grid and the gridless regions are also controlled by using an adaptive refinement technique during the generation of the unstructured Cartesian grid. An implementation of the resulting hybrid method is presented for solving two-dimensional compressible Navier-Stokes （NS） equations. The simulations of the viscous flows over a RAE2822 airfoil or a two-element airfoil are success- fully carried out, and the obtained results agree well with the available experimental data.     

Critical Length of Double-Walled Carbon Nanotubes Based Oscillators

The critical lengths of an oscillator based on double-walled carbon nanotubes （DWCNTs） are studied by energy minimization and molecular dynamics simulation. Van der Waals （vdW） potential energy in DWCNTs is shown to be changed periodically with the lattice matching of the inner and outer tubes by using atomistic models with energy minimization method. If the coincidence length between the inner and outer tubes is long enough, the restoring force cannot drive the DWCNT to slide over the vdW potential barrier to assure the DWCNT acts as an oscillator. The critical coincidence lengths of the oscillators are predicted by a very simple equation and then con- firmed with energy minimization method for both the zigzag/zigzag system and the armchair/armchair system. The critical length of the armchair/armchair system is much larger than that of the zigzag/zigzag system. The vdW po- tential energy fluctuation of the armchair/armchair system is weaker than that of the zigzag/zigzag system. So it is easier to slide over the barrier for the armchair/armchair system. The critical lengths of zigzag/zigzag DWCNT- based oscillator are found increasing along with temperature, by molecular dynamics simulations.     

MULTIGRID TECHNIQUE APPLIED TO LINEAR TIME-DEPENDENT HYPERBOLIC SYSTEMS

A system of linear time-dependent hyperbolic partial differential equations in the form of the time-domain Maxwell＇s equations is numerically solved using a geometric multigrid method. The multilevel method is an adap- tation of Ni＇s cell-vertex based multigrid technique, originally proposed for accelerating steady state convergence of nonlinear time-dependent Euler equations of gas dynamics. We discuss issues pertaining to the application of the geometric multigrid method to a system of equations where the major issue is of accurately propagating linear waves over large distances leading to major constraints on the required grid resolution in terms of points-per-wave- length.     

An Algorithm for Labeling Stable Regions of a Class of Time-Delay Systems with Abscissa

Stability is usually in the sense of Lyapunov′s asymptotical stability,thus the solutions starting from points close to a stable equilibrium may have a very long transient.In the applications of time-delayed feedback controls,it is important not only to determine the stable regions in the gain plane or gain space,but also to find out the abscissa that can be used as an index of stability.Based on the D-subdivision method,this paper proposes a simple algorithm for finding and labeling the stable regions in feedback gain plane with abscissa.The labeled sub-regions with smaller abscissa are better in applications.The main results are presented for the controlled pendulum or inverted pendulum under a delayed feedback,and are illustrated with two case studies.     

STRAIGHTFORWARD MULTI-SCALE BOUNDARY ELEMENT METHOD FOR GLOBAL/LOCAL MECHANICAL ANALYSIS OF ELASTIC HETEROGENEOUS MATERIAL

A straightforward multi-scale boundary element method is proposed for global and local mechanical analysis of heterogeneous material.The method is more accurate and convenient than finite element based multi-scale method.The formulations of this method are derived by combining the homogenization approach and the fundamental equations of boundary element method.The solution gives the convenient formulations to compute global elastic constants and the local stress field.Finally,two numerical examples of porous material are presented to prove the accuracy and the efficiency of the proposed method.The results show that the method does not require the iteration to obtain the solution of the displacement in micro level.     

CONCISE SOLUTION OF FORWARD KINEMATICS ANALYSIS OF PARALLEL MECHANISM IN 6-SPS SIMILAR PLATFORM

The forward kinematics analysis of a special 6-SPS Stewart platform is presented, in which both the base and the mobile platforms are hexagon and similar to each other. The forward kinematics of the parallel mechanism is a complicated nonlinear problem, however. there exists a class of parallel kinematics platforms that have the simplest forward kinematics. By introducing quaternion to represent the rotary transformation matrix and applying dual space method to eliminate the high degree polynomials, the forward kinematics can be expressed by a set of quadratic algebra equations, which decouple the position and the orientation of the mobile platform. The approach only requires solving one-variable quadratic equations. Besides, spurious complex roots are automatically avoided. Eight possible solutions are obtained from the approach. It discovers the inner symmetry relationship between the solutions of the forward kinematics.     

Identification of Time-Varying Modal Parameters for Thermo- Elastic Structure Subject to Unsteady Heating

A time-varying modal parameter identification method combined with Bayesian information criterion （BIC） and grey correlation analysis （GCA） is presented for a kind of thermo-elastic structures with sparse natural frequencies and subject to an unsteady temperature field. To demonstrate the method, the thermo-elastic structure to be identified is taken as a simply-supported beam with an axially movable boundary and subject to both random excitation and an unsteady temperature field, and the dynamic outputs of the beam are first simulated as the meas- ured data for the identification. Then, an improved time-varying autoregressive （TVAR） model is generated from the simulated input and output of the system. The time-varying coefficients of the TVAR model are expahded as a finite set of time basis functions that facilitate the time-varying coefficients to be time invariant. According to the BIC for preliminarily determining the scope of the order number, the grey system theory is introduced to determine the order of TVAR and the dimension of the basis functions simultaneously via the absolute grey correlation degree （AGCD）. Finally, the time-varying instantaneous frequencies of the system are estimated by using the recursive least squares method. The identified results are capable of tracking the slow time-varying natural frequencies with high accuracy no matter for noise-free or noisy estimation.     

Three-Dimentional Surface Light Irradiance Reconstruction in Bioluminescence Tomography

Reconstruction of 3D surface irradiance distribution using multiple views captured by charged coupled device(CCD)camera is the basis of solving the light source in bioluminescence tomography(BLT).A simple and convenient mapping technique based on the pin-hole imaging model and Lambert′s cosine law was presented to establish the relationship between gray levels and irradiance intensities.Compared with previous integrating sphere camera calibration used in BLT,the proposed method can effectively avoid heavy burden of simulation experiment to obtain the corresponding relationship of gray levels and irradiance intensities.The accuracy and feasibility of the proposed method are validated with no more than 1mm location error by different types of phantom experiments.The mapping approach is also applicable to other noncontact optical imaging system.