Singularities Analysis of Paradoxical Mechanism and Parallel Manipulators

Parallel manipulator is associated with a set of functions defined by its closure constraints. In this paper, using Lie algebra method, we provide a study on the singularities of parallel manipulators, their relations with the second order of the closure functions, and the tangent space of the configuration space of the manipulator. The transverse condition criterion is applied to analyze the behavior of the singularities. This gives a downright explication why the 6R paradoxical mechanisms work in their singular configurations, and allows to gain insight on configuration space singularities and to choose the adequate design parameters for the parallel manipulator.     

The generalized inverse of singular integral operators on an open arc and its applications

After choosing weight functions suitably, we define a Banach spaceH _ω ^μ (L) and discuss the generalized inverse of singular integral operators on an open arc. Using the generalized inverse, we obtain the solutions for the following singular integral equation

三维Minkowski空间中非类光曲线的球面达布像

本文主要给出了三维Mirdcow幽空间中非类光曲线的球面达布像的奇点的充要条件，并且建立了奇点和曲线几何不变量之间的联系，其中曲线几何不变量与曲线同螺线切触的阶数密切相关．     

任意大初值等温相对论欧拉方程组的奇性形成问题

主要证明了当初始值受到挤压以及初始流体向外流出时等温相对论欧拉方程组光滑解的奇性形成问题.通过引入与解有关的泛函,证明该泛函满足适当的微分不等式,同时证明该微分不等式的解会发生奇性,继而得到等温相对论欧拉方程组解的奇性形成结果.     

A-调和张量的奇点可去性

考虑微分形式的A-调和方程d*A(x,du)=0的弱解(即A-调和张量),通过建立A-调和张量的Caccioppoli估计,获得了A-调和张量的奇点可去性.     

一般二维奇异问题的间断时空有限元方法

将时间允许间断而空间允许连续的间断时空有限元方法应用于一般二维奇异问题,给出解的存在唯一性证明,并给出加权索伯列夫空间模意义下的有限元解的误差估计,包括在允许的时间间断点tn处,有限元解产生跳跃时的误差.     

Characteristic singular integral equations with solutions having singularities of higher order on the real axis

Under the appropriate hypotheses subject to the unknown function and the free term, by means of our Lemma, we prove the rationality of order at x = ∞ on two sides for the characteristic singular integral equations with solutions having singularities of higher order on the real axis X. We transform the equations into solving equivalent Riemann boundary value problems with solutions having singularities of higher order and with additional conditions on X. The solutions and the solvable conditions for the former are obtained from the latter. Biography: ZHONG Shouguo (1941–), male, Professor, research direction: singular integral equations and their applications.     

二维拟线性奇异抛物问题的时空间断有限元法

将时间允许间断而空间连续的时空有限元方法应用于二维拟线性奇异问题,利用线性化的方法,化为线性抛物方程予以处理,证明加权索伯列夫空间模意义下的有限元解的误差估计,包括在允许的时间间断点tn处,有限元解产生跳跃时的误差,最后再给出原方程的误差估计.     

平面V形切口双应力强度因子的光弹性实验研究

文章在分析具有双重应力奇异性平面 V形切口尖端应力场的基础上 ,提出了基于由光弹性实验获得的等差线确定与双重应力奇异性对应的双应力强度因子 K1 、K2 的光弹性实验方法 ,并通过对模型的光弹性实验 ,运用该方法较好地确定了均质材料 60°单应力奇异性 V型对称切口模型和均质材料 45°双重应力奇异性 V型非对称切口模型的应力强度因子 ,验证了该文中提出的方法的正确性     

R_1~3空间中特殊曲线和可展曲面的奇点分类

本文主要研究在指标数为1的3维伪欧氏空间(即三维Minkowski空间)中,我们给出Minkowski一般螺线、Minkowski斜螺线和Minkowski锥面测地线的定义及其所特有的性质,研究Minkowski一般螺线的等价条件,构造出三维Minkowski空间中的三类可展曲面,研究Minkowski斜螺线和Minkowski锥面测地线这两种特殊曲线和这些曲面的关系,给出R31中非类光曲线的达布型可展曲面和切达布型可展曲面的奇点分类。