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 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 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 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.

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.

INVERSE KINEMATIC AND DYNAMIC ANALYSIS OF A 3-DOF PARALLEL MECHANISM

According to the structure character of the passive sub-chain of the 3TPS-TPparallel mechanism, the kinematic constraint equations of the movable platform are established,based on which the closed-form inverse kinematics formula of the parallel mechanism are presented.Through parting the spherical joints of the active sub-chains and using the force and momentequilibrium of both the active sub-chains and passive sub-chain, the constraint forces acting on theparted joints are determined. Subsequently, the analytic expressions of the actuator driving forcesare derived by means of the force equilibrium of the upper links of active sub-chains.

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.

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.

Design and dynamic analysis of a scissors hoop-rib truss deployable antenna mechanism

As the support mechanism of space-borne antennas,space deployable antenna mechanism belongs to complex multi-closed-loop coupling mechanism,configuration design and dynamic analysis are more difficult than general parallel mechanism.In this paper,an unequal-length scissors mechanism(ULSM)is proposed by changing the position of the internal rotational joint through a basic scissors mechanism.A scissors hoop-rib truss deployable antenna mechanism(SHRTDAM)is constructed by replacing the parabolic rib with the ULSM.Kinematic analysis of SHRTDAM is conducted,and the degree of freedom(DOF)of the whole antenna mechanism is analyzed based on screw theory,the result showed that it has only one DOF.Velocity and acceleration characteristics of SHRTDAM are obtained by the screw derivative and rotation transformation.Based on Lagrange equation,dynamic model of this mechanism is established,the torque required to drive the mechanism is simulated and verified by Adams and MATLAB software.In addition,a ground experiment prototype of 1.5-m diameter was fabricated and a deployment test is conducted,which demonstrated the mobility and deployment performance of the whole mechanism.The mechanism proposed in this paper can provide a good reference for the design and analysis of large aperture space deployable antennas.

KINEMATIC WAVE PROPERTIES OF ANISOTROPIC DYNAMICS MODEL FOR TRAFFIC FLOW

The analyses of kinematic wave properties of a new dynamics model for traffic flow are carried out. The model does not exhibit the problem that one characteristic speed is always greater than macroscopic traffic speed, and therefore satisfies the requirement that traffic flow is anisotropic. Linear stability analysis shows that the model is stable under certain condition and the condition is obtained. The analyses also indicate that the model has a hierarchy of first- and second-order waves and allows the existence of both smooth traveling wave and shock wave. However, the model has a distinctive criterion of shock wave compared with other dynamics models, and the distinction makes the model more realistic in dealing with some traffic problems such as wrong-way travel analysis.

Dynamics Analysis of Close-coupling Multiple Helicopters System

The particularity and practicality of harmony operations of close-coupling multiple helicopters indicate that the researches on it are urgent and necessary, Using the model that describes two hovering helicopters carrying one heavy load, an inertia coordinate system and body coordinate systems of each sub-system are established. A nonlinear force model is established too. The equilibrium computation results can be regarded as the reference control inputs of the flight control system under hovering or low-speed flight condition. After the establishment of a translation kinematics model and a posture kinematics model, a coupling dynamics model of the multiple helicopter system is set up. The results can also be regarded as the base to analyze stabilization and design a controller for a close-coupling multiple helicopters harmony operation system.

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.

Kinematic and Dynamic Characteristics Analysis of Bennett's Linkage

Bennett's linkage is a spatial fourlink linkage,and has an extensive application prospect in the deployable linkages.Its kinematic and dynamic characteristics analysis has a great significance in its synthesis and application. According to the geometrical conditions of Bennett 's linkage,the motion equations are established,and the expressions of angular displacement,angular velocity and angular acceleration of the followers and the displacement,velocity and acceleration of mass center of link are shown. Based on Lagrange's equation,the multi-rigid-body dynamic model of Bennett's linkage is established. In order to solve the reaction forces and moments of joint,screw theory and reciprocal screw method are combined to establish the computing method.The number of equations and unknown reaction forces and moments of joint are equal through adding link deformation equations. The influence of the included angle of adjacent axes on Bennett 's linkage 's kinematic characteristics,the dynamic characteristics and the reaction forces and moments of joint are analyzed.Results show that the included angle of adjacent axes has a great effect on velocity,acceleration,the reaction forces and moments of Bennett's linkage. The change of reaction forces and moments of joint are apparent near the singularity configuration.

Pseudo-static/dynamic solutions of required reinforcement force for steep slopes using discretization-based kinematic analysis

This paper presents a procedure for assessing the reinforcement force of geosynthetics required for maintaining dynamic stability of a steep soil slope. Such a procedure is achieved with the use of the discretization technique and kinematic analysis of plasticity theory, i.e. discretization-based kinematic analysis. The discretization technique allows discretization of the analyzed slope into various components and generation of a kinematically admissible failure mechanism based on an associated flow rule.Accordingly, variations in soil properties including soil cohesion, internal friction angle and unit weight are accounted for with ease, while the conventional kinematic analysis fails to consider the changes in soil properties. The spatialetemporal effects of dynamic accelerations represented by primary and shear seismic waves are considered using the pseudo-dynamic approach. In the presence of geosynthetic reinforcement, tensile failure is discussed providing that the geosynthetics are installed with sufficient length. Equating the total rates of work done by external forces to the internal rates of work yields the upper bound solution of required reinforcement force, below which slopes fail. The reinforcement force is sought by optimizing the objective function with regard to independent variables, and presented in a normalized form. Pseudo-static analysis is a special case and hence readily transformed from pseudodynamic analysis. Comparisons of the pseudo-static/dynamic solutions calculated in this study are highlighted. Although the pseudo-static approach yields a conservative solution, its ability to give a reasonable result is substantiated for steep slopes. In order to provide a more meaningful solution to a stability analysis, the pseudo-dynamic approach is recommended due to considerations of spatial etemporal effect of earthquake input.

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.

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.

Modeling the Newtonian dynamics for rotation curve analysis of thin-disk galaxies

We present an efficient, robust computational method for modeling the Newtonian dynamics for rotation curve analysis of thin-disk galaxies. With appropriate mathematical treatments, the apparent numerical difficulties associated with singularities in computing elliptic integrals are completely removed. Using a boundary element discretization procedure, the governing equations are transformed into a linear algebra matrix equation that can be solved by straightforward Gauss elimination in one step without further iterations. The numerical code implemented according to our algorithm can accurately determine the surface mass density distribution in a disk galaxy from a measured rotation curve （or vice versa）. For a disk galaxy with a typical flat rotation curve, our modeling results show that the surface mass density monotonically decreases from the galactic center toward the periphery, according to Newtonian dynamics. In a large portion of the galaxy, the surface mass density follows an approximately exponential law of decay with respect to the galactic radial coordinate. Yet the radial scale length for the surface mass density seems to be generally larger than that of the measured brightness distribution, suggesting an increasing mass-tolight ratio with the radial distance in a disk galaxy. In a nondimensionalized form, our mathematical system contains a dimensionless parameter which we call the ＂galactic rotation number＂ that represents the gross ratio of centrifugal force and gravitational force. The value of this galactic rotation number is determined as part of the numerial solution. Through a systematic computational analysis, we have illustrated that the galactic rotation number remains within 4-10% of 1.70 for a wide variety of rotation curves. This implies that the total mass in a disk galaxy is proportional to V02 Rg, with V0 denoting the characteristic rotation velocity （such as the ＂flat＂ value in a typical ro- tation curve） and Rg the radius of the galactic disk. The predicted total galactic mass of the Milky Way is in good agreement with the star-count data.

Gas emission and dynamics in the infrared dark cloud G31.23＋0.05

We performed a multiwavelength study towards the infrared dark cloud （IRDC） G31.23＋0.05 with new CO observations from Purple Mountain Observatory and archival data （the GLIMPSE, MIPSGAL, HERSCHEL, ATLASGAL, BGPS and NVSS surveys）. From these observations, we iden- tified three IRDCs with systemic velocities of 108.36 ± 0.06 （cloud A）, 104.22 ± 0.11 （cloud B） and 75.73 ± 0.07 km s-1 （cloud C） in the line of sight towards IRDC G31.23. Analyses of the molecular and dust emission suggest that cloud A is a filamentary structure containing a young stellar object; clouds B and C both include a starless core. Clouds A and B are gravitationally bound and have a chance to form stars. In addition, the velocity information and the position-velocity diagram suggest that clouds A and B are adjacent in space and provide a clue hinting at a possible cloud-cloud collision. Additionally, the distribution of dust temperature shows a temperature bubble. The compact core in cloud A is associated with an UCHII region, an IRAS source, H20 masers, CH3OH masers and OH masers, suggesting that massive star formation is active there. We estimate the age of the HII region to be （0.03-0.09）Myr, indicating that the star inside is young.

A Tentative Study on Dynamics of a New Parallel NC Machine Tool with Long Travel, Large Rotating Angle and High Moving Speed

In view of the structure of traditional five-coord in ate machine tool, the work-piece and machine tool often move along their respec tive guides simultaneously on the whole. In this kind of machine structure, the total mass of moving parts including work-pieces, fixtures, rotating table, wor king table and so on is often very large. Besides, the elastic reform of transmi ssion and the viscous friction force of the guide can not be ignored. As a resul t, the machine tool can not move with high velocity and acceleration, and can no t meet the needs of modern fast and efficient production. The emergence of virtual-axis machine tool has provided a new approach for the solution of the above problems. The kernel of the virtual-axis machine tool is the parallel mechanism. So far, research of parallel mechanism in the world has achieved many results and various applied equipments based on parallel mecha nism have been worked out, but the research generally focuses on the working spa ce and kinematics analysis, dynamics are rarely considered. To meet the requirements of the modern fast and efficient production, reduce the cost and promote the machine tool’s acceleration character, not only should we analyze the kinematics of machine tool, but also we should study its dynamics a nd optimize the structure on the basis of analysis. In this paper, the kinem atics and dynamics of a 5-DOF (degrees of freedom) machine tool with novel para llel mechanism that has three moving DOF and one rotating DOF are studied by Rob ot-Wittenberg method. The dynamics character of the parallel robotic machine is analyzed and used to guide the structure design of machine tool. At last, the c orrectness is verified through a numerical simulation of 5-DOF. Hence, the dyna mics model can generally solve the problems existing in the parallel and hybrid machine tools. The dynamics character of the parallel robotic machine is studied and analyzed in quantity. The dynamics equation of the system can be written as This is a set of differential equations of four DOF system. Theoretically, the c losed solution of the forward and inverse problems can be gained by solving the above equations. The system equations quite suit to program at the computer. Whe n the forces are given, the state variables’ numerical solution can be gain ed through integral; and when the dynamics parameters are given, the forces can also be solved. But the multiple valued phenomena can not be avoided. We have developed simulation software based on the dynamics model presented by t his paper. The different effects of the structure parameters can be given by numerical simulation.