Algebraic Solution for the Forward Displacement Analysis of the General 6-6 Stewart Mechanism

The solution for the forward displacement analysis（FDA） of the general 6-6 Stewart mechanism（i.e., the connection points of the moving and fixed platforms are not restricted to lying in a plane） has been extensively studied, but the efficiency of the solution remains to be effectively addressed. To this end, an algebraic elimination method is proposed for the FDA of the general 6-6 Stewart mechanism. The kinematic constraint equations are built using conformal geometric algebra（CGA）. The kinematic constraint equations are transformed by a substitution of variables into seven equations with seven unknown variables. According to the characteristic of anti-symmetric matrices, the aforementioned seven equations can be further transformed into seven equations with four unknown variables by a substitution of variables using the Grobner basis. Its elimination weight is increased through changing the degree of one variable, and sixteen equations with four unknown variables can be obtained using the Grobner basis. A 40th-degree univariate polynomial equation is derived by constructing a relatively small-sized 9 × 9 Sylvester resultant matrix. Finally, two numerical examples are employed to verify the proposed method. The results indicate that the proposed method can effectively improve the efficiency of solution and reduce the computational burden because of the small-sized resultant matrix.

Separation of closely spaced modes by combining complex envelope displacement analysis with method of generating intrinsic mode functions through filtering algorithm based on wavelet packet decomposition

One of the important issues in the system identification and the spectrum analysis is the frequency resolution, i.e., the capability of distinguishing between two or more closely spaced frequency components. In the modal identification by the empirical mode decomposition （EMD） method, because of the separating capability of the method, it is still a challenge to consistently and reliably identify the parameters of structures of which modes are not well separated. A new method is introduced to generate the intrin- sic mode functions （IMFs） through the filtering algorithm based on the wavelet packet decomposition （GIFWPD）. In this paper, it is demonstrated that the CIFWPD method alone has a good capability of separating close modes, even under the severe condition beyond the critical frequency ratio limit which makes it impossible to separate two closely spaced harmonics by the EMD method. However, the GIFWPD-only based method is impelled to use a very fine sampling frequency with consequent prohibitive computational costs. Therefore, in order to decrease the computational load by reducing the amount of samples and improve the effectiveness of separation by increasing the frequency ratio, the present paper uses a combination of the complex envelope displacement analysis （CEDA） and the GIFWPD method. For the validation, two examples from the previous works are taken to show the results obtained by the GIFWPD-only based method and by combining the CEDA with the GIFWPD method.

An Inverse Analysis of the Comprehensive Medium Parameters and a Simulation of the Crustal Deformation of the Qinghai-Tibet Plateau

Based on the theory of finite element analysis, an inverse analysis model for the comprehensive medium parameters of the Qinghai-Tibet Plateau is set up. With the help of GPS velocity field, the comprehensive crustal medium parameters of the plateau are inversely analyzed and the characteristics of the related movement macroscopically simulated. It is then concluded that the tectonic deformation of the plateau is mainly in the form of a N-S compression accompanied by an E-W stretching, and the present tectonic setting of the plateau should be the result of the collision between the Indian and the Eurasian continents during the Cenozoic.

Forward Displacement Analysis of a Class of the 6-6 Stewart Platforms

A special form of the Stewart platform is presented in which the top platform and base platform are similar and corresponding vertices are connected by six prismatic joints.A closed-from solution for the forward displacement analysis of this mechanism is developed.When the six vertices of the top platform are in a quadratic curve,this mechanism becomes singular.This new theoretical result is confirmed with a numerical example.

Large Displacement Analysis of Tapered Beam Structures

A Bernoulli-Euler beam mechanism for static analysis of large displacement,large rotation but small strain planar tapered beam structures is proposed using the Updated Lagrangian formulation and the moving coordinate method.The object beam is the tapered one whose profile is assumed to be varying linearly.From the governing differential equation of lateral deflection including second-order effects by beam-column theory,the geometric nonlinear tangent elemental stiffness matrix is derived.The nonlinear effect of the bending distortions on the axial action is considered to manifest itself as an axial change in length.The aforementioned stiffness matrix is amended,by developing the auxiliary stiffness of bowing effect.The moving coordinate method is employed for obtaining the large displacement total equilibrium equations,and the hinged-hinged moving coordinate system is constructed at the last updated configuration.The multiple load steps Newton-Raphson iteration is adopted for the solution of the nonlinear equations.The validity and efficiency of the proposed method are shown by solving various typical numerical examples.

Inverse displacement analysis of the general six degree-of-freedom serial robot based on optimization method

The paper presents a new solution of inverse displacement analysis of the general six degree-of-freedom serial robot.The inverse displacement analysis of the general serial robot is transformed into a minimization problem and then the optimization method is adopted to solve the nonlinear least squares problem with the analytic form of new Jacobian matrix.In this way,joint variables of the general serial robot can be searched out quickly under the desired precision when positions of the three non-collinear end effector points are given.Compared with the general Newton iterative method,the proposed algorithm can search out the solution when the robot is at the singular configuration and the initial configuration used in the optimization method may also be the singular configuration.So the convergence domain is bigger than that of the general Newton iterative method.Another advantage of the proposed algorithm is that positions of the three non-collinear end effector points are usually much easier to be measured than the orientation of the end effector.The inverse displacement analysis of the general 6R(six-revolute-joint) serial robot is illustrated as an example and the simulation results verify the efficiency of the proposed algorithm.Because the three non-collinear points can be selected at random,the method can be applied to any other types of serial robots.

Theoretical analysis on the deformation characteristics of coal wall in a longwall top coal caving face

Against the background of analyzing coal wall stability in 14101 fully mechanized longwall top coal caving face in Majialiang coal mine,based on the torque equilibrium of the coal wall,shield support and the roof strata,an elastic mechanics model was established to calculate the stress applied on the coal wall.The displacement method was used to obtain the stress and deformation distributions of the coal wall.This study also researched the influence of support resistance,protective pressure to the coal wall,fracture position of the main roof and mining height on the coal wall deformation.The following conclusions are drawn:(1) The shorter the distance from the longwall face,the greater the vertical compressive stress and horizontal tensile stress borne by the coal wall.The coal wall is prone to failure in the form of compressive-shear and tension;(2) With increasing support resistance,the revolution angle of the main roof decreases linearly.As the support resistance and protective force supplied by the face guard increases,the maximum deformation of the coal wall decreases linearly;(3) As the face approaches the fracture position of the main roof,coal wall horizontal deformation increases significantly,and the coal wall is prone to instability;and(4) The best mining height of 14101 longwall face is 3.0 m.

A back-propagation neural-network-based displacement back analysis for the identification of the geomechanical parameters of the Yonglang landslide in China

Xigeda formation is a type of hundredmeter-thick lacustrine sediments of being prone to triggering landslides along the trunk channel and tributaries of the upper Yangtze River in China. The Yonglang landslide located near Yonglang Town of Dechang County in Sichuan Province of China, which was a typical Xigeda formation landslide, was stabilized by anti-slide piles. Loading tests on a loading-test pile were conducted to measure the displacements and moments. The uncertainty of the tested geomechanical parameters of the Yonglang landslide over certain ranges would be problematic during the evaluation of the landslide. Thus, uniform design was introduced in the experimental design,and by which, numerical analyses of the loading-test pile were performed using Fast Lagrangian Analysis of Continua(FLAC3D) to acquire a database of the geomechanical parameters of the Yonglang landslide and the corresponding displacements of the loadingtest pile. A three-layer back-propagation neural network was established and trained with the database, and then tested and verified for its accuracy and reliability in numerical simulations. Displacement back analysis was conducted by substituting the displacements of the loading-test pile to the well-trained three-layer back-propagation neural network so as to identify the geomechanical parameters of the Yonglang landslide. The neuralnetwork-based displacement back analysis method with the proposed methodology is verified to be accurate and reliable for the identification of the uncertain geomechanical parameters of landslides.

Numerical scheme for elastoplastic parameter identification and finite element analysis of wall-slope of the Fushun West Open Pit Mine

The elasto brittle plastic finite element analysis has been taken on the prediction for the deformation of the northwall of an open pit of Fushun, China. Numerical simulation has been made on the reinforcement measures of the slope structure. Using parameter identification techniques and connecting with elasto brittle plastic finite element program, the displacement back analysis has been made on the material parameters of the rockslope. The equivalent parameter values of the real slope structure have been obtained. The process of the rapid increment of the slope′s deformation caused by open mining during 1987～1990 has been reappeared through the numerical simulation.

Stability analysis of the moving interface in piston- and non-piston-like displacements

From the macroscopic point of view, expressions involving reservoir and operational parameters are established for investigating the stability of moving interface in piston- and non-piston-like displacements. In the case of axisymmetrical piston-like displacement, the stability is related to the moving interface position and water to oil mobility ratio. The capillary effect on the stability of moving interface depends on whether or not the moving interface is already stable and correlates with the wettability of the reservoir rock. In the case of non-piston-like displacement, the stability of the front is governed by both the relative permeability and the mobility ratio.

A Model of Shield Jack Thrust to Shield Attitude

The attitude of the shield tunneling machine (or "shield" for short) during tunneling is important to tunnel excavation and construction quality, which results from a combination of jack thrust, ground displacement around the shield, and ground mechanics parameters, etc. A shield attitude model involving elements above was proposed. In this model, ground displacement was taken to calculate the load around the shield. Ground mechanics parameters were involved. Based on the shield load model, the needed jack thrust for shield desired attitude was derived. The proposed method is validated using engineering data, and lays reliable foundation for shield attitude control.

Inverse Displacement Analysis of a Hyper-redundant Elephant＇s Trunk Robot

This paper deals with inverse displacement analysis of a Hyper-redundant Elephant＇s Trunk Robot （HRETR）. The HRETR is connected in series with n modules of 3UPS-PRU parallel mechanism where the underline P denotes an active prismatic joint. Based on the idea of differential geometry, backbone curve of the robot is formulated by using a parametric fimction consisting of sub-fimctions and control parameters. A general algorithm for generating a backbone curve and fitting the modules to the backbone curve is proposed. In this way, the inverse displacement analysis of the robot can be carried out by solving the inverse displacement problem of each parallel mechanism module and taking into account the length limits of the links. A HRETR with 6 modules is taken as an example to demonstrate the applicability of the algorithm.

THE PHENOMENON ON COLLAPSIBLE TUBE DISPLACEMENT OSCILLATION AND ITS THEORETICAL ANALYSIS

In this paper,the phenomenon on collapsible tube displacement oscillation,a new behavior of the collapsible tube puisatile flow has been studied.The experiments show that the collapsible tube,in which the flow is periodic puisatile in the upstream,will oscillate as a simple supported beam when it is collapsed to certain extent,and that if the tube is collapsed continue,this oscillation will tend to weak and completely disappear lastly.An analytical model corresponding to the collapsible tube displacement oscillation and its governed equations are set up from the experiment background.By analysing the model and solving the equations, the collapsible tube displacement oscillation pattern and the oscillation occurring or disappearing criterion are obtained.The results predicted by this study are in agreement with those observed from experiment phenomena.