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.

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 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.

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.

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

sedonthetheoryoffiniteelementanalysis,aninverseanalysismodelforthecomprehensivemediumparametersoftheQinghai-TibetPlateauissetup.WiththehelpofGPSvelocityfield,thecomprehensivecrustalmediumparametersoftheplateauareinverselyanalyzedandthecharacteristicsoftherelatedmovementmacroscopicallysimulated.ItisthenconcludedthatthetectonicdeformationoftheplateauismainlyintheformofaN-ScompressionaccompaniedbyanE-Wstretching,andthepresenttectonicsettingoftheplateaushouldbetheresultofthecollisionbetweentheIndianandtheEurasiancontinentsduringtheCenozoic.

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.