Geometric Condition of 3UPS-S Parallel Mechanism in Singular Configuration

The existing researches on singularity of parallel mechanism are mostly limited to the property and regularity of singularity locus and there is no further research into the geometric relationship between uncontrolled kinematic screw and parallel mechanism in singularity. A 3UPS-S parallel mechanism is presented which fulfils 3-DOF in rotation. The regularity of nutation angle singularity is analyzed based on the Jacobian matrix, and the singularity surface of 3UPS-S parallel mechanisms is obtained. By applying the concept of reciprocal product in screw theory, the singular kinematic screw is derived when 3UPS-S parallel mechanism is in singularity. The geometric relationship between singular kinematic screw and singular configuration of 3UPS-S parallel mechanism is investigated by using programs in MATLAB. It is revealed that there are two kinds of situation. Firstly, the three limbs of 3UPS-S parallel mechanism intersect the singular kinematic screw in space simultaneously; Secondly, two limbs cross the singular kinematic screw while the third limb parallels with that screw. It is concluded that the nutation angle singularity of 3UPS-S parallel mechanism belongs to the singular linear complexes. This paper sheds light into and clarifies the geometric relationship between singular kinematic screw and singular configuration of 3UPS-S parallel mechanism.

On the Preconditioning Properties of RHSS Preconditioner for Saddle-Point Linear Systems

In this paper,for the regularized Hermitian and skew-Hermitian splitting(RHSS)preconditioner introduced by Bai and Benzi(BIT Numer Math 57:287–311,2017)for the solution of saddle-point linear systems,we analyze the spectral properties of the preconditioned matrix when the regularization matrix is a special Hermitian positive semidefinite matrix which depends on certain parameters.We accurately describe the numbers of eigenvalues clustered at(0,0)and(2,0),if the iteration parameter is close to 0.An estimate about the condition number of the corresponding eigenvector matrix,which partly determines the convergence rate of the RHSS-preconditioned Krylov subspace method,is also studied in this work.

2D Minimum Compliance Topology Optimization Based on a Region Partitioning Strategy

This paper presents an extended sequential element rejection and admission(SERA)topology optimizationmethod with a region partitioning strategy.Based on the partitioning of a design domain into solid regions and weak regions,the proposed optimizationmethod sequentially implements finite element analysis(FEA)in these regions.After standard FEA in the solid regions,the boundary displacement of the weak regions is constrained using the numerical solution of the solid regions as Dirichlet boundary conditions.This treatment can alleviate the negative effect of the material interpolation model of the topology optimization method in the weak regions,such as the condition number of the structural global stiffness matrix.For optimization,in which the forward problem requires nonlinear structural analysis,a linear solver can be applied in weak regions to avoid numerical singularities caused by the over-deformedmesh.To enhance the robustness of the proposedmethod,the nonmanifold point and island are identified and handled separately.The performance of the proposed method is verified by three 2D minimum compliance examples.

Novel high-performance element in the electromagnetic finite-element method——node-edge element

It is known in the computational electromagnetics （CEM） that the node element has a relative wellconditioned matrix, but suffers from the spurious solution problem; whereas the edge element has no spurious solutions, but usually produces an ill-conditioned matrix. Particularly, when the mesh is over dense, the iterative solution of the matrix equation from edge element converges very slowly. Based on the node element and edge element, a node-edge element is presented, which has no spurious solutions and better-conditioned matrix. Numerical experiments demonstrate that the proposed node-edge element is more efficient than now-widely used edge element.

Stability of GM(1,1) power model on vector transformation

The morbidity problem of the GM（1,1） power model in parameter identification is discussed by using multiple and rotation transformation of vectors. Firstly we consider the morbidity problem of the special matrix and prove that the condition number of the coefficient matrix is determined by the ratio of lengths and the included angle of the column vector, which could be adjusted by multiple and rotation transformation to turn the matrix to a well-conditioned one. Then partition the corresponding matrix of the GM（1,1） power model in accordance with the column vector and regulate the matrix to a well-conditioned one by multiple and rotation transformation of vectors, which completely solve the instability problem of the GM（1,1） power model. Numerical results show that vector transformation is a new method in studying the stability problem of the GM（1,1） power model.

An advanced integrated framework for moving object tracking

This paper first introduces the concept of a geogram that captures richer features to represent the objects. The spatiogram contains some moments upon the coordinates of the pixels corresponding to each bin, while the geogram contains information about the perimeter of grouped regions in addition to features in the spatiogram.Then we consider that a convergence process of mean shift is divided into obvious dynamic and steady states,and introduce a hybrid technique of feature description, to control the convergence process. Also, we propose a spline resampling to control the balance between computational cost and accuracy of particle filtering. Finally, we propose a boosting-refining approach, which is boosting the particles positioned in the ill-posed condition instead of eliminating the ill-posed particles, to refine the particles. It enables the estimation of the object state to obtain high accuracy. Experimental results show that our approach has promising discriminative capability in comparison with the state-of-the-art approaches.