多机械臂抓取物的内力不变性

对多机械臂抓取物的受力分析表明，现有物体内力的定义不具备欧几里德直射变换下的不变性，导致模型化的内力与物体实际所受内力不符，基于这样的定义进行载荷分配并实施协调控制会造成物体或机械臂的损坏．本文定义了两投影算子，把手臂作用力分解成两部分，一部分只影响物体运动，另一部分不导致物体运动而产生内力效应．基于力分解定义的内力具备欧几里德直射变换下的不变性。

Form Invariance of Birkhoffian Systems

The form invariance of Birkhoffian systems is a kind of invariance of the Birkhoffian equations under the infinitesimal transformations. The definition and criteria of the form invariance are given, and the relation between the form invariance and the Noether symmetry is studied.

Form Invariance of Lagrange System

To study a form invariance of Lagrange system, the form invariance of Lagrange equations under the infinitesimal transformations was used. The definition and criterion for the form invariance are given. The relation between the form invariance and the Noether symmetry was established.

Form Invariance of Routh Equations

The form invariance of Routh equations in holonomic systems is studied. The definition and criterion for the form invariance under the infinitesimal transformations are given. The relation of the form invariance with the Noether symmetry and the Lie symmetry is discussed.

Conformal Invariance and Noether Symmetry, Lie Symmetry of Birkhoffian Systems in Event Space

This paper focuses on studying a conformal invariance and a Noether symmetry, a Lie symmetry for a Birkhoffian system in event space. The definitions of the conformal invariance of the system are given. By investigation on the relations between the conformal invariance and the Noether symmetry, the conformal invariance and the Lie symmetry, the expressions of conformal factors of the system under these circumstances are obtained. The Noether conserved quantities and the Hojman conserved quantities directly derived from the conformal invariance are given. Two examples are given to illustrate the application of the results.

Deformation inhomogeneity due to sample-anvil friction in cylindrical compression test

Finite element(FEM)analysis was used to systematically evaluate the inhomogeneity of deformation in cylindrical samples with various sample-anvil friction coefficients,m.It was found that the level of friction strongly influences the deformation homogeneity,which increases significantly with the friction coefficient although the overall geometry of the samples almost remains the same when m >0.4.The position,at which the effective strain along the maximum radial direction in a compressed sample is equal to the equivalent strain of the sample,does not vary greatly with respect to both equivalent strain of the sample and m.Hardness measurements of compressed cylindrical 5056B Al alloy samples revealed a change of effective strain distribution similar to that revealed by FEM analysis.There exists a quantitative relationship between the hardness and the effective strain if no recrystallization or recovery occurs during the compression process.

Orientation-dependent Hydrodynamic Instabilities from Chemo-Marangoni Cells to Large Scale Interfacial Deformations

The interplay between chemistry and interfacial-tension-driven hydrodynamic instabilities has been studied experimentally. The system on hand consists of two immiscible liquids separated along an initially plane interface at which an interfacial reaction takes place to produce in situ a surfactant. It is identified that the dynamics of the system depends on the orientation of the Hele-Shaw cell with respect to the vector of gravity. If the nele-Shaw cell is placed vertically, Marangoni cells with vigorous convection develop in both phases along a nearly planar interface. However, if the Hele-Shaw cell is tilted off the gravity, the instabilities in the system are characterized by the large scale interracial deformation with a spatio-temporal periodicity together with the chemo-Marangoni convection. The focus is on the exploration of the transition from the cellular mode to the large scale interfacial deformation.

Effect of key factors on cold orbital forging of a spur bevel gear

Cold orbital forging is an advanced spur bevel gear forming technology. Generally, the spur bevel gear in the cold orbital forging process is formed by two steps: the preforming step and the final step. Due to the great importance of the final step to gear forming and its complication with interactive factors, this work aims at examining the influence of key factors on the final step in cold orbital forging of a spur bevel gear. Using the finite element(FE) method and control variate method, the influence rules of four key factors, rotation velocity of the upper tool, n, feeding velocity of the lower tool, v, tilted angle of the upper tool, γ, friction factor between the tools and the billet, m, on the geometry and the deformation inhomogeneity of the cold orbital forged gear are thoroughly clarified. The research results show that the flash becomes more homogeneous with increasing v, increasing m, decreasing n or decreasing γ. And the deformation of the gear becomes more homogeneous with increasing v, decreasing n or decreasing γ. Finally, a corresponding experiment is conducted, which verifies the accuracy of FE simulation conclusions.

Exact Solution of Klein-Gordon Equation for Charged Particle in Magnetic Field with Shape Invariant Method

Based on the shape invariance property we obtain exact solutions of the three-dimensional relativistic Klein Gordon equation for a charged particle moving in the presence of a certain varying magnetic field, and we also show its non-relativistic limit.

Form Invariance and Conserved Quantity for Non-holonomic Systems with Variable Mass and Unilateral Constraints

The paper studies the form invariance and a type of non-Noether conserved quantity called Mei conserved quantity for non-holonomic systems with variable mass and unilateral constraints. Acoording to the invariance of the form of differential equations of motion under infinitesimal transformations, this paper gives the definition and criterion of the form invariance for non-holonomic systems with variable mass and unilateral constraints. The condition under which a form invariance can lead to Mei conservation quantity and the form of the conservation quantity are deduced. An example is given to illustrate the application of the results.

Deformation behaviors of 21-6-9 stainless steel tube numerical control bending under different friction conditions

For contact dominated numerical control(NC) bending process of tube, the effect of friction on bending deformation behaviors should be focused on to achieve precision bending forming. A three dimensional(3D) elastic-plastic finite element(FE) model of NC bending process was established under ABAQUS/Explicit platform, and its reliability was validated by the experiment. Then, numerical study on bending deformation behaviors under different frictions between tube and various dies was explored from multiple aspects such as wrinkling, wall thickness change and cross section deformation. The results show that the large friction of wiper die-tube reduces the wrinkling wave ratio η and cross section deformation degree ΔD and increases the wall thinning degree Δt. The large friction of mandrel-tube causes large η, Δt and ΔD, and the onset of wrinkling near clamp die. The large friction of pressure die-tube reduces Δt and ΔD, and the friction on this interface has little effect on η. The large friction of bending die-tube reduces η and ΔD, and the friction on this interface has little effect on Δt. The reasonable friction coefficients on wiper die-tube, mandrel-tube, pressure die-tube and bending die-tube of 21-6-9(0Cr21Ni6Mn9N) stainless steel tube in NC bending are 0.05-0.15, 0.05-0.15, 0.25-0.35 and 0.25-0.35, respectively. The results can provide a guideline for applying the friction conditions to establish the robust bending environment for stable and precise bending deformation of tube bending.

Conformal Invariance and a New Type of Conserved Quantities of Mechanical Systems with Variable Mass in Phase Space

Conformal invariance and a new type of conserved quantities of mechanical systems with variable mass in phase space are studied. Firstly, the definition and determining equation of conformal invariance are presented. The relationship between the conformal invariance and the Lie symmetry is given, and the necessary and sufficient condition that the conformal invarianee would be the Lie symmetry under the infinitesimal transformations is provided. Secondly, a new type of conserved quantities of the conformal invariance are obtained by using the Lie symmetry of the system. Lastly, an example is given to illustrate the application of the results.

Continuous Spectrum of Trigonometric Rosen-Morse and Eckart Potentials from Free Particle Spectrum

The shape invariant symmetry of the Trigonometric Rosen-Morse and Eckart potentials has been studied through realization of so（3） and so（2, 1） Lie algebras respectively. In this work, by using the free particle eigenfunction, we obtain continuous spectrum of these potentials by means of their shape invariance symmetry in an algebraic method.

Boundedness of Solutions for Elliptic Variational Inequalities

The boundedness is proved under more general structural conditions to solutions of elliptic variational inequalities and a priori estimates are obtained to maximum modulus of solutions for some special cases.

On Relative Stability in 4-Dimensional Duck Solution

This paper gives the existence of a relatively stable duck solution in a slow-fast system in R2＋2 with an invariant manifold. The slow-fast system in R2＋： has a 2-dimensional slow vector field and a 2-dimensional fast vector field. The fast vector field restricts a feasible region of the slow vector field strictly. In the case of the slow-fast system in R2＋1 , that is, the fast vector field is l-dimension, it is classified according to its sign, because it gives only negative（-）, positive（＋） or zero sign. Then it is attractive, repulsive or stationary. On the other hand, in R2~2 , the fast vector field has combinatorial cases. It causes a complex state to analyze the system. First, we introduce a local model near the pseudo singular point on which we classify the fast vector field attractive（-,-）, attractive-repulsive（-,＋） or repulsive（＋,＋）, simply as possible. We prove the existence of a 4-dimensional duck solution in the local model. Secondarily, we assume that the slow-fast system has an invariant manifold near the pseudo singular point. When the invariant manifold has a homoclinic point near the pseudo singular point, we show that the slow-fast sytem has a 4-dimensional duck solution having a relatively stable region.

Stress-Induced Phase Transformation in Incompressible Materials and Stability of Multi-Phase Deformation

The stress-induced phase transformation in incompressible materials and the interfacial stability of multi-phase deformation were studied. The existence of multi-phase deformation was determined through exploring whether the material would lose the strong ellipticity at some deformation gradient. Then, according to the stability criterion which is based on a quasi-static approach, the stability of the multi-phase deformation in incompressible materials was investigated by studying the growth/decay behaviour of the interface in the undeformed configuration when it is perturbed. At last, the way to define multi-phase deformation in incompressible materials was concluded and testified by a corresponding numerical example.

The Third Invariant Form of Hydrodynamic Equations and Application for Definition of Water Hammer Characteristics in Pipe

There were for a long time two invariant forms of hydrodynamic equations： one was related to coordinate system of references, and the other was versus to measure units of characteristics. These both invariant forms had important roles in the development of theoretical and practical applications of hydro-aerodynamics and related industries. The third invariant form of hydrodynamic equations is one for the dimensions of spaces. For this goal, the hyper quantities （space and physics） are introduced. Then these are created we can easily cover all problems in arbitrary dimensions （3D, 2D, 1D, separate space for liquids or constituent matters）. In particularly, when they are applied to water hammer problem, which is an especially problem, we can receive immediately celerity and pressure of the event.

Comparative Study of Self-Compacting Concrete with Manufactured and Dune Sand

Sand is an inert element essential in the composition of concrete; its use ensures granular continuity between the cement and gravel for better cohesion of concrete. This paper presents the results of a study that investigated the influence of sand quality on the properties of fresh and hardened SCC （self-compacting concrete）. The dune sands are very fine materials characterized by a high intergranular porosity, high surface area and low fineness modulus; on the other hand crushed （manufactured） sand has a high rate into thin and irregular shapes which influence the workability of concrete. The amount of dune sand varies from （0%, 50% to 100%） by weight of fine aggregates. The results show that the rheological properties favour the use of dune sands; however the mechanical properties support the use of crushed sand.

Octupole Deformations of Even-Even Rn, Th, and U Nuclei in Relativistic Mean Field Theory

The octupole deformations and other ground state properties of even-even Rn, Th and U isotopes are investigated systematically within the framework of the reflection asymmetric relativistic mean field （RAS-RMF） model. The calculation results reproduce the binding energies and the quadrupole deformations well. The calculation results indicate these nuclei at ground states evolve from neaxly-spherical （N = 130） shape to quadrupole deformation shape with the increase of the neutron number. It is also found that among the Rn isotopes, only^222,224 Rn axe oetupole deformed and the octupole deformations for them are small. However, more nuclei （N ≌ 134 148） in Th and U isotopes are octupole deformed and the octupole deformations for some of them are significant （｜β3｜- 0.1 or even larger）.

ON FORMABILITY OF LINEAR CONTINUOUS-TIME MULTI-AGENT SYSTEMS

This paper is focused on formability of multi-agent systems （MASs）. The problem is concerned with the existence of a protocol that has the ability to drive the MAS involved to the desired formation, and thus, is of essential importance in designing formation protocols. Formability of an MAS depends on several key factors： agents＇ dynamic structures, connectivity topology, properties of the desired formation and the admissible control set. Agents of the MASs considered here are described by a general continuous linear time-invariant （LTI） model. By using the matrix analysis and algebraic graph theory, some necessary and sufficient conditions on formability of LTI-MASs are obtained. These conditions characterize in some sense the relationship of formability, connectivity topology, formation properties and agent dynamics with respect to some typical and widely used admissible protocol sets.