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.

Learning from Fish: Kinematics and Experimental Hydrodynamics for Roboticists

Over the past 20 years, experimental analyses of the biomechanics of locomotion in fishes have generated a number of key findings that are relevant to the construction of biomimetic fish robots. In this paper, we present 16 results from recent experimental research on the mechanics, kinematics, fluid dynamics, and control of fish locomotion that summarize recent work on fish biomechanics. The findings and principles that have emerged from biomechanical studies of fish locomotion provide important insights into the functional design of fishes and suggest specific design features relevant to construction of robotic fish-inspired vehicles that underlie the high locomotor performance exhibited by fishes.

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.

Unified Modeling Approach of Kinematics, Dynamics and Control of a Free-Flying Space Robot Interacting with a Target Satellite

In this paper a unified control-oriented modeling approach is proposed to deal with the kinematics, linear and angular momentum, contact constraints and dynamics of a free-flying space robot interacting with a target satellite. This developed approach combines the dynamics of both systems in one structure along with holonomic and nonholonomic constraints in a single framework. Furthermore, this modeling allows consid-ering the generalized contact forces between the space robot end-effecter and the target satellite as internal forces rather than external forces. As a result of this approach, linear and angular momentum will form holonomic and nonholonomic constraints, respectively. Meanwhile, restricting the motion of the space robot end-effector on the surface of the target satellite will impose geometric constraints. The proposed momentum of the combined system under consideration is a generalization of the momentum model of a free-flying space robot. Based on this unified model, three reduced models are developed. The first reduced dynamics can be considered as a generalization of a free-flying robot without contact with a target satellite. In this re-duced model it is found that the Jacobian and inertia matrices can be considered as an extension of those of a free-flying space robot. Since control of the base attitude rather than its translation is preferred in certain cases, a second reduced model is obtained by eliminating the base linear motion dynamics. For the purpose of the controller development, a third reduced-order dynamical model is then obtained by finding a common solution of all constraints using the concept of orthogonal projection matrices. The objective of this approach is to design a controller to track motion trajectory while regulating the force interaction between the space robot and the target satellite. Many space missions can benefit from such a modeling system, for example, autonomous docking of satellites, rescuing satellites, and satellite servicing, where it is vital to limit the con-tact force during the robotic operation. Moreover, Inverse dynamics and adaptive inverse dynamics control-lers are designed to achieve the control objectives. Both controllers are found to be effective to meet the specifications and to overcome the un-actuation of the target satellite. Finally, simulation is demonstrated by to verify the analytical results.

Inverse Dynamics of A 3-DOF Parallel Mechanism Based on Analytical Forward Kinematics

For the development of a parallel mechanism(PM),it is necessary to establish a dynamic model which can accurately meet the requirements of real-time control.Compared with the general dynamic analysis model based on the inverse kinematics,the dynamic analysis model based on the forward kinematics has the advantage of low-complexity.In this paper,a new type of 3-DOF PM with analytical forward displacement analysis is proposed.Different from the general dynamic analysis based on the inverse kinematics,the displacement,velocity and acceleration equations of the PM are established and solved by forward kinematics.The inverse dynamic equation of the PM is constructed and solved by analyzing the forces on each link and based on Newton-Euler method.Then the theoretical results of an example are compared with the simulation results,which shows that the simulation results are basically consistent with the theoretical results.And the maximum error of the driving force of each pair is 1.32%,5.8%and 5.2%,respectively,which verifies the correctness of the dynamic model.The PM has a potential application prospect in the grasping,spraying and picking of workpieces.The research results of this paper provide a theoretical basis for the design,manufacture and application of the PM.

Semiclassical approach to spin dynamics of a ferromagnetic S = 1 chain

Motivated by recent experimental progress on the quasi-one-dimensional quantum magnet Ni Nb2O6, we study the spin dynamics of an S = 1 ferromagnetic Heisenberg chain with single-ion anisotropy by using a semiclassical molecular dynamics approach. This system undergoes a quantum phase transition from a ferromagnetic to a paramagnetic state under a transverse magnetic field, and the magnetic response reflecting this transition is well described by our semiclassical method.We show that at low temperature the transverse component of the dynamical structure factor depicts clearly the magnon dispersion, and the longitudinal component exhibits two continua associated with single-and two-magnon excitations,respectively. These spin excitation spectra show interesting temperature dependence as effects of magnon interactions. Our findings shed light on the experimental detection of spin excitations in a large class of quasi-one-dimensional magnets.

Ultrafast magneto-optical dynamics in nickel(111)single crystal studied by the integration of ultrafast reflectivity and polarimetry probes

With the integration of ultrafast reflectivity and polarimetry probes,we observed carrier relaxation and spin dynamics induced by ultrafast laser excitation of Ni(111)single crystals.The carrier relaxation time within the linear excitation range reveals that electron-phonon coupling and dissipation of photon energy into the bulk of the crystal take tens of picoseconds.On the other hand,the observed spin dynamics indicate a longer time of about 120 ps.To further understand how the lattice degree of freedom is coupled with these dynamics may require the integration of an ultrafast diffraction probe.

Ab initio nonadiabatic molecular dynamics study on spin–orbit coupling induced spin dynamics in ferromagnetic metals

Understanding the photoexcitation induced spin dynamics in ferromagnetic metals is important for the design of photo-controlled ultrafast spintronic device.In this work,by the ab initio nonadiabatic molecular dynamics simulation,we have studied the spin dynamics induced by spin–orbit coupling(SOC)in Co and Fe using both spin-diabatic and spin-adiabatic representations.In Co system,it is found that the Fermi surface(E_(F))is predominantly contributed by the spin-minority states.The SOC induced spin flip will occur for the photo-excited spin-majority electrons as they relax to the E_(F),and the spin-minority electrons tend to relax to the EFwith the same spin through the electron–phonon coupling(EPC).The reduction of spin-majority electrons and the increase of spin-minority electrons lead to demagnetization of Co within100 fs.By contrast,in Fe system,the E_(F) is dominated by the spin-majority states.In this case,the SOC induced spin flip occurs for the photo-excited spin-minority electrons,which leads to a magnetization enhancement.If we move the E_(F) of Fe to higher energy by 0.6eV,the E_(F) will be contributed by the spin-minority states and the demagnetization will be observed again.This work provides a new perspective for understanding the SOC induced spin dynamics mechanism in magnetic metal systems.

Community structure and species diversity dynamics of a subtropical evergreen broad-leaved forest in China:2005 to 2020

Here,we characterize the temporal and spatial dynamics of forest community structure and species diversity in a subtropical evergreen broad-leaved forest in China.We found that community structure in this forest changed over a 15-year period.Specifically,renewal and death of common species was large,with the renewal of individuals mainly concentrated within a few populations,especially those of Aidia canthioides and Cryptocarya concinna.The numbers of individual deaths for common species were concentrated in the small and mid-diameter level.The spatial distribution of community species diversity fluctuated in each monitoring period,showing a more dispersed diversity after the 15-year study period,and the coefficient of variation on quadrats increased.In 2010,the death and renewal of the community and the spatial variation of species diversity were different compared to other survey years.Extreme weather may have affected species regeneration and community stability in our subtropical monsoon evergreen broad-leaved forests.Our findings suggest that strengthening the monitoring and management of the forest community will help better understand the long-and short-term causes of dynamic fluctuations of community structure and species diversity,and reveal the factors that drive changes in community structure.

The Effect of Lateral Offset Distance on the Aerodynamics and Fuel Economy of Vehicle Queues

The vehicle industry is always in search of breakthrough energy-saving and emission-reduction technologies.In recent years,vehicle intelligence has progressed considerably,and researchers are currently trying to take advantage of these developments.Here we consider the case of many vehicles forming a queue,i.e.,vehicles traveling at a predetermined speed and distance apart.While the majority of existing studies on this subject have focused on the influence of the longitudinal vehicle spacing,vehicle speed,and the number of vehicles on aerodynamic drag and fuel economy,this study considers the lateral offset distance of the vehicle queue.The group fuel consumption savings rate is calculated and analyzed.As also demonstrated by experimental results,some aerodynamic benefits exist.Moreover,the fuel consumption saving rate of the vehicle queue decreases as the lateral offset distance increases.

Prospect on Present-Day Crustal Kinematics and Dynamics Research in Sichuan-Yunnan Area with Geodetic Data

Combining the dense GPS and gravity observation data in Sichuan-Yunnan area, where there are the relatively complete active tectonic zones and seismic data, this paper applies the geodesy and geophysical inversion technique and the advanced numerical simulation to the synthesis study of geodesy inversion to find the dynamic process of tectonic movement and deformation in the area and finally to investigate the kinematics characteristic of the geological structure of different layer and different scale. This paper discusses the kinematics, dynamics model about the crustal movement of active blocks in Sichuan-Yunnan area and its adjacent areas.

The impact of demographic dynamics on food consumption and its environmental outcomes:Evidence from China

With increasing population and changing demographics,food consumption has experienced a significant transition in quantity and quality.However,a dearth of knowledge remains regarding its environmental impacts and how it responds to demographic dynamics,particularly in emerging economies like China.Using the two-stage Quadratic Almost Demand System(QUAIDS)model,this study empirically examines the impact of demographic dynamics on food consumption and its environmental outcomes based on the provincial data from 2000 to 2020 in China.Under various scenarios,according to changes in demographics,we extend our analysis to project the long-term trend of food consumption and its environmental impacts,including greenhouse gas(GHG)emissions,water footprint(WF),and land appropriation(LA).The results reveal that an increase in the proportion of senior people significantly decreases the consumption of grain and livestock meat and increases the consumption of poultry,egg,and aquatic products,particularly for urban residents.Moreover,an increase in the proportion of males in the population leads to higher consumption of poultry and aquatic products.Correspondingly,in the current scenario of an increased aging population and sex ratio,it is anticipated that GHG emissions,WF,and LA are likely to decrease by 1.37,2.52,and 3.56%,respectively.More importantly,in the scenario adhering to the standards of nutritional intake according to the Dietary Guidelines for Chinese Residents in 2022,GHG emissions,WF,and LA in urban areas would increase by 12.78,20.94,and 18.32%,respectively.Our findings suggest that changing demographics should be considered when designing policies to mitigate the diet-environment-health trilemma and achieve sustainable food consumption.

Finite Deformation, Finite Strain Nonlinear Dynamics and Dynamic Bifurcation in TVE Solids with Rheology

This paper presents a mathematical model consisting of conservation and balance laws (CBL) of classical continuum mechanics (CCM) and ordered rate constitutive theories in Lagrangian description derived using entropy inequality and the representation theorem for thermoviscoelastic solids (TVES) with rheology. The CBL and the constitutive theories take into account finite deformation and finite strain deformation physics and are based on contravariant deviatoric second Piola-Kirchhoff stress tensor and its work conjugate covariant Green’s strain tensor and their material derivatives of up to order m and n respectively. All published works on nonlinear dynamics of TVES with rheology are mostly based on phenomenological mathematical models. In rare instances, some aspects of CBL are used but are incorrectly altered to obtain mass, stiffness and damping matrices using space-time decoupled approaches. In the work presented in this paper, we show that this is not possible using CBL of CCM for TVES with rheology. Thus, the mathematical models used currently in the published works are not the correct description of the physics of nonlinear dynamics of TVES with rheology. The mathematical model used in the present work is strictly based on the CBL of CCM and is thermodynamically and mathematically consistent and the space-time coupled finite element methodology used in this work is unconditionally stable and provides solutions with desired accuracy and is ideally suited for nonlinear dynamics of TVES with memory. The work in this paper is the first presentation of a mathematical model strictly based on CBL of CCM and the solution of the mathematical model is obtained using unconditionally stable space-time coupled computational methodology that provides control over the errors in the evolution. Both space-time coupled and space-time decoupled finite element formulations are considered for obtaining solutions of the IVPs described by the mathematical model and are presented in the paper. Factors or the physics influencing dynamic response and dynamic bifurcation for TVES with rheology are identified and are also demonstrated through model problem studies. A simple model problem consisting of a rod (1D) of TVES material with memory fixed at one end and subjected to harmonic excitation at the other end is considered to study nonlinear dynamics of TVES with rheology, frequency response as well as dynamic bifurcation phenomenon.

Theoretical and experimental investigation of the resonance responses and chaotic dynamics of a bistable laminated composite shell in the dynamic snap-through mode

The dynamic model of a bistable laminated composite shell simply supported by four corners is further developed to investigate the resonance responses and chaotic behaviors.The existence of the 1:1 resonance relationship between two order vibration modes of the system is verified.The resonance response of this class of bistable structures in the dynamic snap-through mode is investigated,and the four-dimensional(4D)nonlinear modulation equations are derived based on the 1:1 internal resonance relationship by means of the multiple scales method.The Hopf bifurcation and instability interval of the amplitude frequency and force amplitude curves are analyzed.The discussion focuses on investigating the effects of key parameters,e.g.,excitation amplitude,damping coefficient,and detuning parameters,on the resonance responses.The numerical simulations show that the foundation excitation and the degree of coupling between the vibration modes exert a substantial effect on the chaotic dynamics of the system.Furthermore,the significant motions under particular excitation conditions are visualized by bifurcation diagrams,time histories,phase portraits,three-dimensional(3D)phase portraits,and Poincare maps.Finally,the vibration experiment is carried out to study the amplitude frequency responses and bifurcation characteristics for the bistable laminated composite shell,yielding results that are qualitatively consistent with the theoretical results.

Mitochondrial recruitment in myelin:an anchor for myelin dynamics and plasticity?

Optimal propagation of neuronal electrical impulses depends on the insulation of axons by myelin,produced in the central nervous system by oligodendrocytes.Myelin is an extension of the oligodendrocyte plasma membrane,which wraps around an axon to form a compact multi-layered sheath.Myelin is composed of a substantially higher proportion of lipids compared to other biological membranes and enriched in a small number of specialized proteins.

Acute effect of foot strike patterns on in vivo tibiotalar and subtalar joint kinematics during barefoot running

Background:Foot kinematics,such as excessive eversion and malalignment of the hindfoot,are believed to be associated with running-related injuries.The maj ority of studies to date show that different foot strike patterns influence these specific foot and ankle kinematics.However,technical deficiencies in traditional motion capture approaches limit knowledge of in vivo joint kinematics with respect to rearfoot and forefoot strike patterns(RFS and FFS,respectively).This study uses a high-speed dual fluoroscopic imaging system(DFIS)to determine the effects of different foot strike patterns on 3D in vivo tibiotalar and subtalar joints kinematics.Methods:Fifteen healthy male recreational runners underwent foot computed tomography scanning for the construction of 3-dimensional models.A high-speed DFIS(100 Hz)was used to collect 6 degrees of freedom kinematics for participants’tibiotalar and subtalar joints when they adopted RFS and FFS in barefoot condition.Results:Compared with RFS,FFS exhibited greater internal rotation at 0%-20%of the stance phase in the tibiotalar joint.The peak internal rotation angle of the tibiotalar joint under FFS was greater than under RFS(p<0.001,Cohen’s d=0.92).RFS showed more dorsiflexion at 0%-20%of the stance phase in the tibiotalar joint than FFS.RFS also presented a larger anterior translation(p<0.001,Cohen’s d=1.28)in the subtalar joint at i nitial contact than FFS.Conclusion:Running with acute barefoot FFS increases the internal rotation of the tibiotalar joint in the early stance.The use of high-speed DFIS to quantify the movement of the tibiotalar and subtalar joint was critical to revealing the effects of RF S and FFS during running.

Conformational dynamics as an intrinsic determinant of prion protein misfolding and neurotoxicity

The prion protein(PrP) is the key molecular and pathological mediator of prion diseases,a heterogeneous group of brain disorders with fatal outcomes.Prion diseases are rare but deserve special attention because of their unique familial,sporadic,and transmissible etiologies,all caused by a single agent:misfolded conformations of PrP.

Target layer state estimation in multi-layer complex dynamical networks considering nonlinear node dynamics

In many engineering networks, only a part of target state variables are required to be estimated.On the other hand,multi-layer complex network exists widely in practical situations.In this paper, the state estimation of target state variables in multi-layer complex dynamical networks with nonlinear node dynamics is studied.A suitable functional state observer is constructed with the limited measurement.The parameters of the designed functional observer are obtained from the algebraic method and the stability of the functional observer is proven by the Lyapunov theorem.Some necessary conditions that need to be satisfied for the design of the functional state observer are obtained.Different from previous studies, in the multi-layer complex dynamical network with nonlinear node dynamics, the proposed method can estimate the state of target variables on some layers directly instead of estimating all the individual states.Thus, it can greatly reduce the placement of observers and computational cost.Numerical simulations with the three-layer complex dynamical network composed of three-dimensional nonlinear dynamical nodes are developed to verify the effectiveness of the method.