Kinematics and dynamics analysis of a 3-7R parallel decoupling mechanism

One kind of movable-pair analysis method is adopted to analyze the configuration of a 3-7R （revolute-pair） parallel decoupling mechanism, and the mechanism＇s characteristics are summarized. The mechanism has three orthogonal distributional branch-chains, and all movable pairs are rotational joints. The movable platform of the mechanism has x, y, z translational decoupling directions. Furthermore, in order to verify the mechanism＇s decoupling characteristics, the mechanism＇s kinematics analysis is solved, and the mechanism＇s direct/inverse kinematics model, input/output velocities and accelerations are deduced, which confirm its decoupling movement characteristics. Finally, one kind of mechanism link decomposed-integrated approach is adopted, and the mechanism＇s dynamics model is completed with the Lagrange method, which also proves its decoupling force characteristics. All of these works provide significant theory for the further study of the mechanism＇s control strategy, design, path planning etc.

Kinematics and Dynamics Hessian Matrices of Manipulators Based on Screw Theory

The complexity of the kinematics and dynamics of a manipulator makes it necessary to simplify the modeling process.However,the traditional representations cannot achieve this because of the absence of coordinate invariance.Therefore,the coordinate invariant method is an important research issue.First,the rigid-body acceleration,the time derivative of the twist,is proved to be a screw,and its physical meaning is explained.Based on the twist and the rigid-body acceleration,the acceleration of the end-effector is expressed as a linear-bilinear form,and the kinematics Hessian matrix of the manipulator（represented by Lie bracket）is deduced.Further,Newton-Euler＇s equation is rewritten as a linear-bilinear form,from which the dynamics Hessian matrix of a rigid body is obtained.The formulae and the dynamics Hessian matrix are proved to be coordinate invariant.Referring to the principle of virtual work,the dynamics Hessian matrix of the parallel manipulator is gotten and the detailed dynamic model is derived.An index of dynamical coupling based on dynamics Hessian matrix is presented.In the end,a foldable parallel manipulator is taken as an example to validate the deduced kinematics and dynamics formulae.The screw theory based method can simplify the kinematics and dynamics of a manipulator,also the corresponding dynamics Hessian matrix can be used to evaluate the dynamical coupling of a manipulator.

Kinematics and Dynamics of Deployable Structures with Scissor-Like-Elements Based on Screw Theory

Because the deployable structures are complex multi-loop structures and methods of derivation which lead to simpler kinematic and dynamic equations of motion are the subject of research effort, the kinematics and dynamics of deployable structures with scissor-like-elements are presented based on screw theory and the principle of virtual work respectively. According to the geometric characteristic of the deployable structure examined, the basic structural unit is the common scissor-like-element（SLE）. First, a spatial deployable structure, comprised of three SLEs, is defined, and the constraint topology graph is obtained. The equations of motion are then derived based on screw theory and the geometric nature of scissor elements. Second, to develop the dynamics of the whole deployable structure, the local coordinates of the SLEs and the Jacobian matrices of the center of mass of the deployable structure are derived. Then, the equivalent forces are assembled and added in the equations of motion based on the principle of virtual work. Finally, dynamic behavior and unfolded process of the deployable structure are simulated. Its figures of velocity, acceleration and input torque are obtained based on the simulate results. Screw theory not only provides an efficient solution formulation and theory guidance for complex multi-closed loop deployable structures, but also extends the method to solve dynamics of deployable structures. As an efficient mathematical tool, the simper equations of motion are derived based on screw theory.

Kinematics and Dynamics Analysis of a Quadruped Walking Robot with Parallel Leg Mechanism

It is desired to require a walking robot for the elderly and the disabled to have large capacity,high stiffness,stability,etc.However,the existing walking robots cannot achieve these requirements because of the weight-payload ratio and simple function.Therefore,Improvement of enhancing capacity and functions of the walking robot is an important research issue.According to walking requirements and combining modularization and reconfigurable ideas,a quadruped/biped reconfigurable walking robot with parallel leg mechanism is proposed.The proposed robot can be used for both a biped and a quadruped walking robot.The kinematics and performance analysis of a 3-UPU parallel mechanism which is the basic leg mechanism of a quadruped walking robot are conducted and the structural parameters are optimized.The results show that performance of the walking robot is optimal when the circumradius R,r of the upper and lower platform of leg mechanism are 161.7 mm,57.7 mm,respectively.Based on the optimal results,the kinematics and dynamics of the quadruped walking robot in the static walking mode are derived with the application of parallel mechanism and influence coefficient theory,and the optimal coordination distribution of the dynamic load for the quadruped walking robot with over-determinate inputs is analyzed,which solves dynamic load coupling caused by the branches’ constraint of the robot in the walk process.Besides laying a theoretical foundation for development of the prototype,the kinematics and dynamics studies on the quadruped walking robot also boost the theoretical research of the quadruped walking and the practical applications of parallel mechanism.

Kinematics and dynamics analysis of a three-degree-of-freedom parallel manipulator

Kinematics and dynamics analyses were performed for a spatial 3-revolute joint-revolute joint-clylindric pair(3-RRC) parallel manipulator.This 3-RRC parallel manipulator is composed of a moving platform,a base platform,and three revolute joint-revolute joint-column pair chains which connect the moving platform and the base platform.Firstly,kinematics analysis for 3-RRC parallel manipulator was conducted.Next,on the basis of Lagrange formula,a simply-structured dynamic model of 3-RRC parallel manipulator was derived.Finally,through a calculation example,the variation of motorial parameters of this 3-RRC parallel manipulator,equivalent moment of inertia,driving force/torque and energy consumption was discussed.The research findings have important significance for research and engineering projects such as analyzing dynamic features,mechanism optimization design and control of 3-RRC parallel manipulator.

Velocity Dispersion σ_(aper)Aperture Corrections as a Function of Galaxy Properties from Integral-field Stellar Kinematics of 10,000 MaNGA Galaxies

The second moment of the stellar velocity within the effective radius,denoted by σ^(2)_(e),is a crucial quantity in galaxy studies,as it provides insight into galaxy properties and their mass distributions.However,large spectroscopic surveys typically do not measure σ_(e) directly,instead providing σ_(aper),the second moment of the stellar velocity within a fixed fiber aperture.In this paper,we derive an empirical aperture correction formula,given byσ_(aper)/σ_(e)=(R_(aper)/R_(e))^(α),using spatially resolved stellar kinematics extracted from approximately 10,000 Sloan Digital Sky Survey-Mapping Nearby Galaxies at Apache Point Observatory integral field unit observations.Our analysis reveals a strong dependence ofαon the r-band absolute magnitude M_(r),g-i color,and Sérsic index nSer,whereαvalues are lower for brighter,redder galaxies with higher Sérsic indices.Our results demonstrate that the aperture correction derived from previous literature on early-type galaxies cannot be applied to predict the aperture corrections for galaxies with intermediate Sérsic indices.We provide a lookup table ofαvalues for different galaxy types,with parameters in the ranges of-18>M_(r)>-24,0.4<g-i<1.6,and 0<n_(Ser)<8.A Python script is provided to obtain the correction factors from the lookup table.

The Yukawa and Exponential Potentials for a Galaxy’s Spherical Central Bulge*

By adding an extra term to the Newtonian potential, matter outside the orbit of a star adds to the gravitational acceleration acting on that star. In this work, we solve the Poisson equation for non-Newtonian potentials of a spherically symmetric distribution of mass. We derive equations for calculating the centripetal acceleration and velocity of galactic disk stars that are due to the Newtonian and exponential potentials of the galaxy’s central bulge.

New HⅠObservations Toward the NGC 5055 Galaxy Group with FAST

We report a new high-sensitivity HⅠmapping observation of the NGC 5055 galaxy group over an area of 1°.5×0°.75 with the Five-hundred-meter Aperture Spherical radio Telescope(FAST).Our observation reveals that the warped HⅠdisk of NGC 5055 is more extended than what was previously observed by WSRT,out to239(61.7 kpc).The total HⅠmass of NGC 5055 is determined to be~1.1×10^(10)M_Θ.We identified three HⅠclouds with HⅠmasses of the order of~10^(7)M_Θat the southeastern edge of the HⅠdisk,as well as a candidate high-velocity cloud with an HⅠmass of(1.2±0.5)×10^(6)M_Θto the north of NGC 5055.The HⅠcontent of UGCA337 is robustly detected for the first time by the FAST observations.It has a narrow HⅠlinewidth of W_(50)=17.4±3.8 km s^(-1)with a total HⅠmass of(3.5±0.3)×10^(6)M_Θ.Comparing the gas content and g-r color of UGCA 337 with typical low-mass dwarf galaxies,UGCA 337 appears relatively gas-poor despite its blue color.This suggests that UGCA 337 may have undergone gas stripping in the past.We also analyzed the possible origin of the diffuse HⅠclouds located at the outskirts of NGC 5055,and speculate that they might be the remnant features of a merger event in the past.

Evaluation of slope stability through rock mass classification and kinematic analysis of some major slopes along NH-1A from Ramban to Banihal, North Western Himalayas

The network of Himalayan roadways and highways connects some remote regions of valleys or hill slopes,which is vital for India’s socio-economic growth.Due to natural and artificial factors,frequency of slope instabilities along the networks has been increasing over last few decades.Assessment of stability of natural and artificial slopes due to construction of these connecting road networks is significant in safely executing these roads throughout the year.Several rock mass classification methods are generally used to assess the strength and deformability of rock mass.This study assesses slope stability along the NH-1A of Ramban district of North Western Himalayas.Various structurally and non-structurally controlled rock mass classification systems have been applied to assess the stability conditions of 14 slopes.For evaluating the stability of these slopes,kinematic analysis was performed along with geological strength index(GSI),rock mass rating(RMR),continuous slope mass rating(CoSMR),slope mass rating(SMR),and Q-slope in the present study.The SMR gives three slopes as completely unstable while CoSMR suggests four slopes as completely unstable.The stability of all slopes was also analyzed using a design chart under dynamic and static conditions by slope stability rating(SSR)for the factor of safety(FoS)of 1.2 and 1 respectively.Q-slope with probability of failure(PoF)1%gives two slopes as stable slopes.Stable slope angle has been determined based on the Q-slope safe angle equation and SSR design chart based on the FoS.The value ranges given by different empirical classifications were RMR(37-74),GSI(27.3-58.5),SMR(11-59),and CoSMR(3.39-74.56).Good relationship was found among RMR&SSR and RMR&GSI with correlation coefficient(R 2)value of 0.815 and 0.6866,respectively.Lastly,a comparative stability of all these slopes based on the above classification has been performed to identify the most critical slope along this road.

What is the Role of Gravity,Turbulence and Magnetic Fields in High-mass Star Formation Clouds?

To explore the potential role of gravity,turbulence and magnetic fields in high-mass star formation in molecular clouds,this study revisits the velocity dispersion–size(σ–L)and density–size(ρ–L)scalings and the associated turbulent energy spectrum using an extensive data sample.The sample includes various hierarchical density structures in high-mass star formation clouds,across scales of 0.01–100 pc.We observeσ∝L^(0.26)andρ∝L^(-1.54)scalings,converging toward a virial equilibrium state.A nearly flat virial parameter–mass(α_(vir)-M)distribution is seen across all density scales,withα_(vir)values centered around unity,suggesting a global equilibrium maintained by the interplay between gravity and turbulence across multiple scales.Our turbulent energy spectrum(E(k))analysis,based on theσ–L andρ–L scalings,yields a characteristic E(k)∝k^(-1.52).These findings indicate the potential significance of gravity,turbulence,and possibly magnetic fields in regulating dynamics of molecular clouds and high-mass star formation therein.

The ALMA-QUARKS Survey.Ⅱ.The ACA 1.3 mm Continuum Source Catalog and the Assembly of Dense Gas in Massive Star-Forming Clumps

Leveraging the high resolution,sensitivity,and wide frequency coverage of the Atacama Large Millimeter/submillimeter Array(ALMA),the QUARKS survey,standing for“Querying Underlying mechanisms of massive star formation with ALMA-Resolved gas Kinematics and Structures”,is observing 139 massive starforming clumps at ALMA Band 6(λ~1.3 mm).This paper introduces the Atacama Compact Array(ACA)7 m data of the QUARKS survey,describing the ACA observations and data reduction.Combining multiwavelength data,we provide the first edition of QUARKS atlas,offering insights into the multiscale and multiphase interstellar medium in high-mass star formation.The ACA 1.3 mm catalog includes 207 continuum sources that are called ACA sources.Their gas kinetic temperatures are estimated using three formaldehyde transitions with a non-LTE radiation transfer model,and the mass and density are derived from a dust emission model.The ACA sources are massive(16–84 percentile values of 6–160 M_(⊙)),gravity-dominated(M∝R^(1.1))fragments within massive clumps,with supersonic turbulence(M>1)and embedded star-forming protoclusters.We find a linear correlation between the masses of the fragments and the massive clumps,with a ratio of 6%between the two.When considering fragments as representative of dense gas,the ratio indicates a dense gas fraction(DGF)of 6%,although with a wide scatter ranging from 1%to 10%.If we consider the QUARKS massive clumps to be what is observed at various scales,then the size-independent DGF indicates a self-similar fragmentation or collapsing mode in protocluster formation.With the ACA data over four orders of magnitude of luminosity-to-mass ratio(L/M),we find that the DGF increases significantly with L/M,which indicates clump evolutionary stage.We observed a limited fragmentation at the subclump scale,which can be explained by a dynamic global collapse process.

Study of Complex Nitrogen and Oxygen-bearing Molecules toward the High-mass Protostar IRAS 18089–1732

The observation of oxygen(O)-and nitrogen(N)-bearing molecules gives an idea about the complex prebiotic chemistry in the interstellar medium.Recent millimeter and submillimeter wavelength observations have shown the presence of complex O-and N-bearing molecules in the star formation regions.So,the investigation of those molecules is crucial to understanding the chemical complexity in the star-forming regions.In this article,we present the identification of the rotational emission lines of N-bearing molecules ethyl cyanide(C_(2)H_(5)CN)and cyanoacetylene(HC_(3)N),and O-bearing molecule methyl formate(CH_(3)OCHO)toward high-mass protostar IRAS18089–1732 using the Atacama Compact Array.We also detected the emission lines of both the N-and O-bearing molecule formamide(NH_(2)CHO)in the envelope of IRAS 18089–1732.We have detected the v=0 and 1 state rotational emission lines of CH_(3)OCHO.We also detected the two vibrationally excited states of HC_(3)N(v7=1 and v7=2).The estimated fractional abundances of C_(2)H_(5)CN,HC_(3)N(v7=1),HC_(3)N(v7=2),and NH_(2)CHO toward IRAS 18089–1732 are(1.40±0.5)×10^(-10),(7.5±0.7)×10^(-11),(3.1±0.4)×10^(-11),and(6.25±0.82)×10^(-11)respectively.Similarly,the estimated fractional abundances of CH_(3)OCHO(v=0)and CH_(3)OCHO(v=1)are(1.90±0.9)×10^(-9)and(8.90±0.8)×10^(-10),respectively.We also created the integrated emission maps of the detected molecules,and the observed molecules may have originated from the extended envelope of the protostar.We show that C_(2)H_(5)CNand HC_(3)N are most probably formed via the subsequential hydrogenation of the CH_(2)CHCNand the reaction between C_(2)H_(2)and CN on the grain surface of IRAS 18089–1732.We found that NH_(2)CHO is probably produced due to the reaction between NH_(2)and H_(2)CO in the gas phase.Similarly,CH_(3)OCHO is possibly created via the reaction between radical CH_(3)O and radical HCO on the grain surface of IRAS 18089–1732.

Merger Dynamics of the Pair of Galaxy Clusters-A399 and A401

Convincing evidence for a past interaction between the two rich clusters A399 and A401 was recently found in the X-ray imaging observations. We examine the structure and dynamics of this pair of galaxy clusters. A mixture-modeling algorithm was applied to obtain a robust partition into two clusters, which allowed us to discuss the virial mass and velocity distribution of each cluster. Assuming that these two clusters follow a linear orbit and they have once experienced a close encounter, we model the binary cluster as a two-body system. As a result, four gravitationally bound solutions are obtained. The recent X-ray observations seem to favor a scenario in which the two clusters with a true separation of 5.4h-1 Mpc are currently expanding at 583 km s-1 along a direction with a projection angle of 67.5°, and they will reach a maximum extent of 5.65 h-1 Mpc in about 1.0 h-1 Gyr.

Stellar kinematics and populations out to 1.5 effective radii in the elliptical galaxy NGC 4636

We present high quality long slit spectra along the major and minor axes out to 1.5 effective radii of the massive galaxy NGC 4636 taken by the Hobby-Eberly Telescope. Using the Fourier Correlation Quotient method, we measured the stellar line-of-sight velocity distribution along the axes. Furthermore, six Lick/IDS indices （Hβ, Mgb, Fe5015, Fe5270, Fe5335, Fe5406） are derived from the clean spectrum. By comparing the measured absorption line strengths with the predictions of Simple Stellar Population （SSP） models, we derived ages, total metallicity and a abundance profiles of the galaxy. This galaxy presents old and [α/Fe] overabundant stellar populations. Indeed, using the SSP model, we obtained the broadband color profiles. The theoretical colors match well with the measured colors and present red sharp peaks at the galaxy center. The sharp peaks of the colors are mainly shaped by the high metallicity in the galaxy＇s center. Interestingly, the galaxy has steep negative metaUicity gradients, but the trend flattens outwards. This result likely suggests that the center and outer regions of the galaxy formed through different formation processes.

Kinematics Analysis and Optimization of the Fast Shearing-extrusion Joining Mechanism for Solid-state Metal

Dynamical Joining of the solid-state metal is the key technology to realize endless hot rolling. The heating and laser welding method both require long joining time. Based on super deformation method, a 7-bar and 2-slider mechanism was developed in Japan, and the joining time is less than 0.5 s, however the length of each bar are not reported and this mechanism is complex. A relatively simple 6-bar and 1-slider mechanism is put forward, which can realize the shearing and extrusion motion of the top and bottom blades with a speed approximately equal to the speed of the metal plates. In order to study the kinematics property of the double blades, based on complex vector method, the multi-rigid-body model is built, and the displacement and speed functions of the double blades, the joining time and joining thickness are deduced, the kinematics analysis shows that the initial parameters can＇t satisfy the joining process. Hence, optimization of this mechanism is employed using genetic algorithm（GA） and the optimization parameters of this mechanism are obtained, the kinematics analysis show that the joining time is less than 0.1 s, the joining thickness is more than 80% of the thickness of the solid-state metal, and the horizontal speeds of the blades are improved. A new mechanism is provided for the joining of the solid-state metal and a foundation is laid for the design of the device.

VECTRIX AND SOME OF ITS PROPERTIES SUITED TO FLIGHT DYNAMICS

A vectrix cross-product operator identity is presented which shows thesymmetrical relationship between a column matrix and a vectrix. The kinematics ofvectrices and other commonly used relations are then easily obtained with it. The timederivative of the transformation matrix is extended to a more general form ofexpression. The results can be used conveniently in the modeling of flight dynamics inwhich many reference frames must be used.

Mapping the emission line strengths and kinematics of supernova remnant S147 with extensive LAMOST spectroscopic observations

We present extensive spectroscopic observations of supernova remnant （SNR） S 147 collected with the Large sky Area Multi-Object fiber Spectroscopic Telescope （LAMOST）. The spectra were care- fully sky-subtracted taking into account the complex filamentary structure of S 147. We have utilized all available LAMOST spectra toward S 147, including sky and stellar spectra. By measuring the prominent optical emission lines including Ha, [NII] ）λ 6584 and [S n] λλ6717, 6731, we present maps of radial velocity and line intensity ratio covering the whole nebula of S 147 with unprecedented detail. The maps spatially correlate well with the complex filamentary structure of S147. For the central 2° of S147, the radial velocity varies from - 100 to 100 krn s^-1 and has peaks between - 0 and 10 km s^-1. The intensity ratios of Hα/[S n）λλ6717,6731, [Sn] λ 6717/λ 6731 and Ha/IN Hα/λ 6584 peak at about 0.77, 1.35 and 1.48, respectively, with a scatter of 0.17, 0.19 and 0.37, respectively. The intensity ratios are consistent with the literature values. However, the range of variations of line intensity ratios estimated here, which are representative of the whole nebula, is larger than previously estimated.

The nature of orbits in a prolate elliptical galaxy model with a bulge and a dense nucleus

We study the transition from regular to chaotic motion in a prolate elliptical galaxy dynamical model with a bulge and a dense nucleus. Our numerical investigation shows that stars with angular momentum Lz less than or equal to a critical value Lzc, moving near the galactic plane, are scattered to higher z, when reaching the central region of the galaxy, thus displaying chaotic motion. An inverse square law relationship was found to exist between the radius of the bulge and the critical value Lzc of the angular momentum. On the other hand, a linear relationship exists between the mass of the nucleus and Lzc. The numerically obtained results are explained using theoretical arguments. Our study shows that there are connections between regular or chaotic motion and the physical parameters of the system, such as the star＇s angular momentum and mass, the scale length of the nucleus and the radius of the bulge. The results are compared with the outcomes of previous work.

Theory of Gravitons in Spiral and Dwarf Galaxy Rotation Curves

We hypothesize that gravitons contribute significantly to the process that flattens galaxy rotation curves. Gravitons travelling against a gravitational field experience an energy loss due to gravitational redshift identical to the effect on light. This energy loss requires an increased rotational velocity to stabilize a galaxy. We will show that this approach successfully explains the rotational properties of spiral and dwarf galaxies.

Hawking radiation and thermodynamics of a Vaidya-Bonner black hole

Using Parikh＇s tunneling method, the Hawking radiation on the apparent horizon of a Vaidya-Bonner black hole is calculated. When the back-reaction of particles is neglected, the thermal spectrum can be precisely obtained. Then, the black hole thermodynamics can be calculated successfully on the apparent horizon. When a relativistic perturbation is applied to the apparent horizon, a similar calculation can also lead to a purely thermal spectrum. The first law of thermodynamics can also be derived successfully at the new supersurface near the apparent horizon. When the event horizon is thought of as a deviation from the apparent horizon, the expressions of the characteristic position and temperature are consistent with the previous viewpoint which asserts that the thermodynamics should be based on the event horizon. It is concluded that the thermodynamics should be constructed exactly on the apparent horizon while the event horizon thermodynamics is just one of the perturbations near the apparent horizon.