用旋量矩阵解空间4杆低副机构运动的研究

本文运用旋量矩阵来建立空间4杆低副机构(不含球铰副)运动的解法。为解决空间机构运动分析,提出了一种简便方法。

一种机器人动力学的旋量—矩阵方程

旋量—矩阵方程是将经典力学中的旋量概念以矩阵形式表示的一种动力学方法。结合R W的图论工具 ,可以将旋量—矩阵方法推广到多体系统。利用旋量—矩阵方法进行了四自由度机器人动力学方程的推导。全部推导过程思路简洁 ,便于程式化 。

空间机构运动分析的旋量—矩阵方法

本文将旋量概念以矩阵形式表示,采用矢量和矢量矩的结合形式,可使空间机构运动分析中的算法公式书写得更为简洁。这种旋量——矩阵方法能保留旋量融矢量与矢量矩于一体的优点,却避免以往对偶数记法的缺点。文中以空间机构作为具体算例。

用旋量理论对平行对称齿轮曲柄滑块机构的力学分析

本文用旋置理论导出了受空间力系作用的刚体旋量动态潜力学方程，其形式简洁，内函却十分丰富。作为一个特例用以推导平行齿轮曲柄滑块机构的动力学方程式，所得结果与传统的方法是完全一致的，且前者比后者在表达方式上夏简单、规范。

Schur Forms and Normal-Nilpotent Decompositions

Real and complex Schur forms have been receiving increasing attention from the fluid mechanics community recently,especially related to vortices and turbulence.Several decompositions of the velocity gradient tensor,such as the triple decomposition of motion(TDM)and normal-nilpotent decomposition(NND),have been proposed to analyze the local motions of fluid elements.However,due to the existence of different types and non-uniqueness of Schur forms,as well as various possible definitions of NNDs,confusion has spread widely and is harming the research.This work aims to clean up this confusion.To this end,the complex and real Schur forms are derived constructively from the very basics,with special consideration for their non-uniqueness.Conditions of uniqueness are proposed.After a general discussion of normality and nilpotency,a complex NND and several real NNDs as well as normal-nonnormal decompositions are constructed,with a brief comparison of complex and real decompositions.Based on that,several confusing points are clarified,such as the distinction between NND and TDM,and the intrinsic gap between complex and real NNDs.Besides,the author proposes to extend the real block Schur form and its corresponding NNDs for the complex eigenvalue case to the real eigenvalue case.But their justification is left to further investigations.

基于配合约束的几何公差分配方法

当公差原则为相关原则时,如何建立相关尺寸公差到几何公差的定量转换关系,实现几何公差的精准分配,是该领域亟待解决的问题。通过几何公差自顶向下分配的定性分析与定量计算,提出一种基于配合约束的几何公差分配方法。根据配合公差、互参照公差和自参照公差之间的约束,构建了基于配合约束的公差关联模型;基于上述关联,构建了与产品结构同步的几何公差设计过程模型;将装配接点作为配合公差传递的基本载体,根据装配接点的顺序和表面类型,提出了相关配合表面旋量矩阵的分析方法,并基于旋量矩阵生成相关表面的几何公差约束;以基于旋量矩阵的公差约束、加工精度约束和互参照公差对自参照公差的约束为约束条件,以最小总公差成本为目标函数,利用遗传算法实现了几何公差数值的优化。最后,以曲轴活塞机构为实例进行了几何公差的分配,经与经验法对比,验证了该方法的经济性与有效性。

Digital Acousto-optic Matrix Computer

Acousto-optic system for performing basic operations of vector-matrix multiplication with digital(16-bit)accuracy are described.The system comprised of two multi-transducer Bragg cells that can perform at least 1×10 8 operation/s of basic vector-matrix multiplication with digital (16-bit ) accuracy and which is simple and compact.

Note on Implementation of Three-Qubit SWAP Gate

In this paper, the synthesis and implementation of three-qubit SWAP gate is discussed. The three-qubit SWAP gate can be decomposed into product of 2 two-qubit SWAP gates, and it can be realized by 6 CNOT gates. Research illustrated that although the result is very simple, the current methods of matrix decomposition for multi-qubit gate can not get that. Then the implementation of three-qubit SWAP gate in the three spin system with Ising interaction is investigated and the sequence of control pulse and drift process to implement the gate is given. It needs 23 control pulses and 12 drift processes. Since the interaction can not be switched on and off at will, the realization of three-qubit SWAP gate in specific quantum system also can not simply come down to 2 two-qubit SWAP gates.

Augmented Spinor Space

In this paper, based on the Pauli matrices, a notion of augmented spinor space is introduced, and a uniqueness of such augmented spinor space of rank n is proved. It may be expected that this new notion of spaces can be used in mathematical physics and geometry.