基于旋量理论凯恩动力学方程的开链机器人动力学分析

简介了主动力旋量、惯性力旋量、偏速度旋量、偏速度旋量矩阵及开链机器人旋量理论凯恩动力学方程。以三连杆开链机器人为例分析了其动力学。

基于旋量理论Kane方程的挖掘机工作装置动力学分析

旋量是机器人研究中的重要工具,且其计算优势明显,建模过程几何意义突出。将挖掘机视作4自由度单开链机构,根据旋量理论建立了挖掘机动力学模型,旋量将挖掘机末端铲斗轨迹的位置与姿态变量分离,为提高控制精度奠定基础,且其计算简洁,利于实现挖掘机轨迹实时控制。文中根据旋量理论求取了挖掘机上部转台、动臂、斗杆与铲斗的物体雅可比矩阵,分别表示作用于挖掘机上部转台、动臂、斗杆与铲斗的主动力旋量与惯性力旋量,通过旋量形式Kane方程,建立了置于刚性水平土壤基上的挖掘机工作装置动力学模型。最后由相关挖掘机参数进行仿真,结果验证了所建模型的正确性。

空间机构的向量分析——Ⅳ空间机构动力学

本文用建立向量方程方法解决前述四种空间机构动力学的一般性问题.由于变换不同运动副的参考系,所以求解过程与位移矩阵完全无关.

平面索牵引机构工作空间解析求解与验证

为求解平面索牵引多体机构的力旋量封闭工作空间边界,提出矩阵零空间的方法.该方法通过对力的雅克比矩阵分析,推导出保证索力的非负条件,并根据此条件求解出力旋量封闭工作空间边界,找到力旋量可行工作空间.使用蒙特卡罗方法优化电机的位置和杆上牵索点的位置,使得力旋量可行工作空间最大,并保证机构的运行轨迹在力旋量可行工作空间的范围内.对平面串联两杆机构的一种构型进行参数优化求解和实验验证,结果表明参数优化后的构型可以保证预期轨迹在力旋量可行工作空间内,解析法可以准确地推导出力旋量封闭工作空间的边界.

绳牵引并联机构奇异性分析及无奇异机构设计

绳牵引并联机构是将驱动器的运动和力以绳为介质并行转换成动平台的运动和力的装置,其末端执行器的自由度数可定义为机构的结构矩阵的所有旋量正张成的实数空间的维数。指出绳牵引并联机构仅有过运动性的奇异类型,阐明该奇异是一种由于位姿几何的特殊导致动平台的力旋量集合的维数降秩的现象;以一个1R2T机构为例指出了机构的奇异性除了会导致机构失去控制,还会导致绳优化拉力分布的不连续性:以1-2-1型的1R2T 机构为例研究动平台的重力会对机构的奇异性所造成的影响,从而发现即便动平台重力无法消除机构的奇异点, 但却能使各根绳的拉力分布重新得以配置。提出用各个转动自由度相互解耦,而平动运动能得到完全控制的机构是无奇异的这个原理来构造无奇异性的1-2-1型的CRPM(1R2T)、2-3-2型的RRPM-7(2R3T)的方法;提出用对心抓取定理构造无奇异性的2-2型的CRPMs(1R2T)和3-3型的CRPM(2R3T)的方法;提出用3维力封闭抓取定理构造无奇异性的3-3-3型的RRPM-9(3R3T)的方法。

绳牵引并联机器人工作空间的判定条件与解析表达

研究6自由度完全和冗余约束绳牵引并联机器人力旋量封闭工作空间的性质,给出并证明在不同牵引绳根数下末端执行器位姿属于力旋量封闭工作空间的充要条件,分析满足矢量封闭原理的结构矩阵对应的几何特征。总结6自由度完全和冗余约束绳牵引并联机器人力旋量封闭工作空间的判定定理,即结构矩阵满秩,在结构矩阵中存在列矢量位于6个线性独立列矢量反方向张成的六维凸锥内,且满足相关系数之和大于0。基于以上定理和性质,推导6自由度完全和冗余约束绳牵引并联机器人力旋量封闭工作空间边界的解析表达式,提出力旋量封闭工作空间解析求解方法。数值算例验证了方法有效可行。

六自由度绳索悬挂式并联机器人工作空间和鲁棒性研究

六自由度绳索悬挂式并联机器人在机械加工、物料搬运和抢险救灾等方面具有广阔的应用前景。工作空间和抗外力扰动鲁棒性是这类欠约束绳索机器人的两项重要性能指标。在绳索长度、动平台尺寸和雅可比矩阵条件数等约束下,本文研究了工作空间的体积和基于运动旋量斜率的鲁棒性与动、定平台几何构型、半径比及动平台姿态之间的关系,首次得出了工作空间的形状及其变化规律。研究结论对这类机器人的设计和使用都具有较高的参考价值。

DYNAMICS ANALYSIS OF 2-DOF SPHERICAL PARALLEL MECHANISM

The analytical formulations of the velocity and the acceleration of a 2-DOF spherical parallel mechanism are derived by the screw theory. Based on building its dynamics model by the principle of virtual work and reciprocal product of the screw, the equation of the motor moment is obtained. Through the transformation of dynamics model, the configuration space method of the dynamics equation and the corresponding coefficients are presented. Finally, the result of an example shows that the inertia moment and the gravity play a more important role than the coriolis and centrifugal moment, and the former is ten times of the latter in the magnitude. So, the latter can be neglected only when the velocity of mechanism is very slow.

The kinematics modeling based on Spinor theory for CT-guided hybrid robot

This paper focused on a simplified method for solving the hybrid robot kinematics in CT-guided （computerized tomography, CT） surgery. By position constraint introduced, the hybrid robot can be transformed as a redundant serial 7-DOF robot. The forward displacement calculation was developed based on the product-of-exponential formula （POE）. Because of the kinematics complexity of the hybrid and redundant robot, the combination technique of Ulrich two-step iteration method and paul variables detachment method （UTI-PVD） was introduced to fulfill the inverse kinematics of redundant robot, the novelty of which lay in the flexibility of various robots structures and in high calculation efficiency for realtime control. The process of solving the inverse displacement was analyzed. The UTI-PVD method can be applicable to kinematics of many robots, especially for redundant robots with more than 6DOF. The kinematics simulation was provided, and robot dexterity analysis was presented. The results indicated that the hybrid robot could implement the minimally invasive CT-guided surgery.

Ising Transition in Dimerized XY Quantum Spin Chain

We proposed a simple spin-1/2 model which provides an exactly solvable example to study the Ising criticality with central charge . By mapping it onto the real Majorana fermions, the Ising critical behavior is explored explicitly, although its bosonized form is not the double frequency sine-Gordon model.

Coupling Between Spin and Gravitational Field and Equation of Motion of Spin

In general relativity, the equation of motion of the spin is given by the equation of parallel transport, which is a result of the space-time geometry. Any result of the space-time geometry cannog be directly applied to gauge theory of gravity. In gauge theory of gravity, based on the viewpoint of the coupling between the spin and gravitational field, an equation of motlon of the spin is deduced. In the post Newtonian approximation, it is proved that this equation gives the same result as that of the equation of parallel transport. So, in the post Newtonian approximation, gauge theory of gravity gives out the same prediction on the precession of orbiting gyroscope as that of general relativity.

Equation of Motion of a Spinning Test Particle in Gravitational Field

Based on the coupfing between the spin of a particle and gravitoelectromagnetic field, the equation of motion of a spinning test particle in gravitational field is deduced. From this equation of motion, it is found that the motion of a spinning particle deviates from the geodesic trajectory, and this deviation originates from the coupling between the spin of the particle and gravitoelectromagnetic field, which is also the origin of Lense-Thirring effects. In post-Newtonian approximations, this equation gives the same results as those of Mathisson-Papapetrou equation. Effect of the deviation of geodesic trajectory is detectable.

Effects of Arbitrarily Directed Field on Spin Phase Oscillations in Biaxial Molecular Magnets

Quantum phase interference and spin-parity effects are studied in biaxial molecular magnets in a magnetic field at an arbitrarily directed angle. The calculations of the ground-state tunnel splitting are performed on the basis of the instanton technique in the spin-coherent-state path-integral representation, and complemented by exactly numerical diagonalization. Both the Wentzel–Kramers–Brillouin exponent and the pre-exponential factor are obtained for the entire region of the direction of the field. Our results show that the tunnel splitting oscillates with the field for the small field angle, while for the large field angle the oscillation is completely suppressed. This distinct angular dependence, together with the dependence of the tunnel splitting on the field strength, provides an independent test for spin-parity effects in biaxial molecular magnets. The analytical results for the molecular magnet are found to be in good agreement with the numerical simulations, which suggests that even the molecular magnet with total spin is large enough to be treated as a giant spin system.

Entanglement Dynamics of Multipartite Systems Under Decoherence from a Spin Environment

The entanglement evolution of multipartite quantum states under a spin environment is analyzed. Due to interaction, the extent to which the entanglement vanishes depends not only on the size of system and the structure of quantum states, but also on the exchange couplings with environment. The decoherence-free subspaces have been identified by using the linear entropy.

Bell＇s Theorem Without Inequalities for Arbitrarily High-Dimensional Fermionic System

A generalized proof of Bell's theorem without inequalities via the singlet state of two spin-(2n + 1)/2 fermionic particles for two observers is proposed. It is a direct and meaningful extension of that presented by A. Cabello [Phys. Rev. A67 (2003) 032107] and the proof from A. Cabello is included in our proof as a special example.

Numerical analysis of thermal fluid transport behavior during electron beam welding of 2219 aluminum alloy plate

A two-dimensional mathematical model based on volume-of-fluid method is proposed to investigate the heat transfer,fluidflow and keyhole dynamics during electron beam welding(EBW)on20mm-thick2219aluminum alloy plate.In the model,anadaptive heat source model tracking keyhole depth is employed to simulate the heating process of electron beam.Heat and masstransport of different vortexes induced by surface tension,thermo-capillary force,recoil pressure,hydrostatic pressure and thermalbuoyancy is coupled with keyhole evolution.A series of physical phenomena involving keyhole drilling,collapse,reopening,quasi-stability,backfilling and the coupled thermal field are analyzed systematically.The results indicate that the decreased heat fluxof beam in depth can decelerate the keyholing velocity of recoil pressure and promote the quasi-steady state.Before and close to thisstate,the keyhole collapses and complicates the fluid transport of vortexes.Finally,all simulation results are validated againstexperiments.

A Note on Classification of Spatially Homogeneous Rotating Space-Times According to Their Teleparallel Killing Vector Fields in Teleparallel Theory of Gravitation

In this paper we classify spatially homogeneous rotating space-times according to their teleparallel Killing vector fields using direct integration technique.It turns out that the dimension of the teleparallel Killing vector fields is 5 or 10.In the case of 10 teleparallel Killing vector fields the space-time becomes Minkowski and all the torsion components are zero.Teleparallel Killing vector fields in this case are exactly the same as in general relativity.In the cases of 5 teleparallel Killing vector fields we get two more conservation laws in the teleparallel theory of gravitation.Here we also discuss some well-known examples of spatially homogeneous rotating space-times according to their teleparallel Killing vector fields.

Hydrodynamic Behavior in a Rotating Zigzag Bed

As a high gravity(HIGEE)unit,the rotating packed bed(RPB)uses centrifugal force to intensify mass transfer.Zigzag rotating bed(RZB)is a new type of HIGEE unit.The rotor of RZB consists of stationary discs and rotating discs,forming zigzag channels for liquid-gas flow and mass transfer.As in RPBs,some hydrodynamic behavior in RZB is interesting but no satisfactory explanation.In this study,the experiments were carried on in a RZB unit with a rotor of 600 mm in diameter using air-water system.The gas pressure drop and power consumption were measured with two types of rotating baffle for RZB rotors,one with perforations and another with shutter openings. The circumferential velocities of gas were measured with a five-hole Pitot probe.The pressure drop decreased rapidly when the liquid was introduced to the rotor,because the circumferential velocity of the liquid droplets was lower than that of the gas,reducing the circumferential velocity of gas and the centrifugal pressure drop.The power consumption decreased first when the gas entered the RZB rotor,because the gas with higher circumferential velocity facilitates the rotation of baffles.

The Antiferromagnetic Correlations in the Half—Filled Double—Exchange Model at Finite Temperature

We extend a previous result of ours [G.S. Tian, Phys. Rev. B63 (2001) 224413] on the antiferromagnetic spin correlations in the half-filled Hubbard model at finite temperature to the double-exchange model. To overcome the mathematical difficulty caused by the localized spin freedom in this model, we apply both Zener's argument and the finite-temperature spin-reflection-positivity method to show rigorously that, at any temperature , the spin correlations in the half-filled double-exchange model are predominantly antiferromagnetic. This conclusion is completely consistent with the experimental observations and the previous theoretical results by approximate methods.

Metric of Rotating Charged Spherical Mass in Vacuum for Vector Graviton Metric Theory of Gravitation

Based on the vector graviton metric theory of gravitation (VGM) suggested by one of the authors of this article, using the method of null tetrad and analytic continuation, this paper gives the metric of the rotating charged spherical mass in VGM. The result shows once again that a replacement of G by G* = G(1 - G M /2r) in general relativity will yield the corresponding result in VGM for the metric in vacuum.