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.

Kinematics ofmandibular advancement devices(MADs):Why do some MADs move the lower jaw backward duringmouth opening?

Mandibular advancement devices(MADs)are widely used treatments for obstructive sleep apnea.MADs function by advancing the lower jaw to open the upper airway.To increase patient comfort,most patients allow the mouth to be opened.However,not all systems maintain the lower jaw in a forward position during mouth opening,which results in the production of a retrusion that favors the collapse of the upper airway.Furthermore,the kinematic behavior of the mechanism formed by the mandible-device assembly depends on jaw morphology.This means that,during mouth opening,some devices cause lower jaw protrusion in some patients,but cause its retraction in others.In this study,we report the behavior of well-known devices currently on themarket.To do so,we developed a kinematic model of the lower jawdevice assembly.Thismodelwas validated for all devices analyzed using a high-resolution camera system.Our results show that some of the devices analyzed here did not produce the correct behavior during patient mouth opening.

Novel thick-target inverse kinematics method for the astrophysical ^(12)C+^(12)C fusion reaction

The ^(12)C+^(12)C fusion is one of the most important reactions in modern nuclear astrophysics.The trend and magnitude of the reaction rate within the Gamow window strongly influence various astrophysical processes.However,direct measurement of this reaction is extremely difficult,which makes it necessary to develop indirect methods.In this study,the ^(23)Na+p reaction system was used to study the compound nucleus ^(24)Mg.We employed a thick-target inverse kinematics method combined with the-charged-particle coincidence technique to measure the proton andexit channels of ^(24)Mg.Technical details of the ^(23)Na+p thick-target inverse kinematics experiment and analysis are presented herein.

Configuration and Kinematics of a 3-DOF Generalized Spherical Parallel Mechanism for Ankle Rehabilitation

The kinematic equivalent model of an existing ankle-rehabilitation robot is inconsistent with the anatomical structure of the human ankle,which influences the rehabilitation effect.Therefore,this study equates the human ankle to the UR model and proposes a novel three degrees of freedom(3-DOF)generalized spherical parallel mechanism for ankle rehabilitation.The parallel mechanism has two spherical centers corresponding to the rotation centers of tibiotalar and subtalar joints.Using screw theory,the mobility of the parallel mechanism,which meets the requirements of the human ankle,is analyzed.The inverse kinematics are presented,and singularities are identified based on the Jacobian matrix.The workspaces of the parallel mechanism are obtained through the search method and compared with the motion range of the human ankle,which shows that the parallel mechanism can meet the motion demand of ankle rehabilitation.Additionally,based on the motion-force transmissibility,the performance atlases are plotted in the parameter optimal design space,and the optimum parameter is obtained according to the demands of practical applications.The results show that the parallel mechanism can meet the motion requirements of ankle rehabilitation and has excellent kinematic performance in its rehabilitation range,which provides a theoretical basis for the prototype design and experimental verification.

3D Kinematics of Classical Cepheids According to Gaia EDR3 Catalog

The kinematics of about 2000 classical Cepheids of the Milky Way with data from Gaia EDR3 catalog has been studied.For some of these stars,there are line-of-sight velocities.On the basis of the nonlinear rotation model,the parameters of the rotation curve of the Galaxy were determined.The circular linear rotation velocity of the near-solar neighborhood around the Galaxy center was V0=236±3 km s^(−1) for the assumed Sun's galactocentric distance R0=8.1±0.1 kpc.Analysis of residual velocities of Cepheids based on the linear Ogorodnikov–Milne model showed the presence of the following significantly different from zero gradients:∂U/∂x,∂U/∂z,∂V/∂x,∂V/∂z and∂W/∂x,which behave differently depending on the selection radius.The most interesting is the gradient∂W/∂x∼−0.5±0.1 km s^(−1) kpc^(−1)(positive rotation of this star system around the Galactic axis y,Ωy)since the velocities W are free of Galactic rotation.Here we have an indirect influence of various effects leading to a perturbation of the vertical velocities of the Galactic disk stars.Based on a simpler model,a more accurate estimate of this rotation is obtained,Ωy=0.51±0.07 km s^(−1) kpc^(−1).

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.

Machine-learning-based head impact subtyping based on the spectral densities of the measurable head kinematics

Background:Traumatic brain injury can be caused by head impacts,but many brain injury risk estimation models are not equally accurate across the variety of impacts that patients may undergo,and the characteristics of different types of impacts are not well studied.We investigated the spectral characteristics of different head impact types with kinematics classification.Methods:Data were analyzed from 3262 head impacts from lab reconstruction,American football,mixed martial arts,and publicly available car crash data.A random forest classifier with spectral densities of linear acceleration and angular velocity was built to classify head impact types(e.g.,football,car crash,mixed martial arts).To test the classifier robustness,another 271 lab-reconstructed impacts were obtained from 5 other instrumented mouthguards.Finally,with the classifier,type-specific,nearest-neighbor regression models were built for brain strain.Results:The classifier reached a median accuracy of 96% over 1000 random partitions of training and test sets.The most important features in the classification included both low-and high-frequency features,both linear acceleration features and angular velocity features.Different head impact types had different distributions of spectral densities in low-and high-frequency ranges(e.g.,the spectral densities of mixed martial arts impacts were higher in the high-frequency range than in the low-frequency range).The type-specific regression showed a generally higher R2value than baseline models without classification.Conclusion:The machine-learning-based classifier enables a better understanding of the impact kinematics spectral density in different sports,and it can be applied to evaluate the quality of impact-simulation systems and on-field data augmentation.

Kinematics simulation and application for machine tool based on multi-body system theory

Based on the multi-body kinematics principle, the topological structure and restriction relation among parts of machine tool and 3D multi-body model are constructed, the kinematics simulation system of machine tool is developed. The designer can observe the movement and machining course of the whole machine tool and understand accurately the kinematics parameters of components such as position, velocity and acceleration. Also the designer can estimate the pose of components in the virtual circumstance and forecast accurately and correct problems which may appear during the design before the prototype is manufactured to assure the feasibility of design scheme, shorten period of product design and reduce product cost. The simulation system is used during the design of CK1416 high speed and precision numerical control lathe. The curves of ball screw angular velocity and carriage displacement agree well with the results of theoretical calculation and the constructed model is correct.

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.

A simplified model for extreme-wave kinematics in deep sea

Based on the fifth-order Stokes regular wave theory, a simplified model for extreme-wave kinematics in deep sea was developed. In this model, from the wave records the average of two neighboring wave periods for the extreme crest or trough was defined as the period of the Stokes wave by the up and down zero-crossing methods. Then the input wave amplitude was deduced by substituting the wave period and extreme crest or trough into the expression for the fifth-order Stokes wave elevation. Thus the corresponding formula for the wave velocity can be used to describe kinematics beneath the extreme wave. By comparison with the published numerical models and experimental data, the proposed model is validated to be able to calculate the extreme wave velocity rather easily and accurately.

INVERSE KINEMATICS FOR A 6 DOF MANIPULATOR BASED ON NEURAL NETWORK

A methodology is presented whereby a neural network is used to learn the inverse kinematic relationships of the position and orientation of a six joint manipulator. The arm solution for the orientation of a manipulator using a self organizing neural net is studied in this paper. A new training model of the self organizing neural network is proposed by thoroughly studying Martinetz, Ritter and Schulten′s self organizing neural network based on Kohonen′s self organizing mapping algorithm using a Widrow Hoff type error correction rule and closely combining the characters of the inverse kinematic relationship for a robot arm. The computer simulation results for a PUMA 560 robot show that the proposed method has a significant improvement over other methods documented in the references in self organizing capability and precision by training process.

Paleozoic Accretion-Collision Events and Kinematics of Ductile Deformation in the Eastern Part of the Southern-Central Tianshan Belt, China

The Tianshan range could have been built by both late Early Paleozoicaccretion and Late Paleozoic collision events. The late Early Paleozoic Aqqikkudug-Weiya suture ismarked by Ordovician ophiolitic melange and a Silurian flysch sequence, high-pressure metamorphicrelics, and mylonitized rocks. The Central Tianshan belt could principally be an Ordovician volcanicarc; whereas the South Tianshan belt, a back-arc basin. Macro- and microstructures, along withunconformities, provide some kinematic and chronological constraints on 2-phase ductile deformation.The earlier ductile deformation occurring at ca. 400 Ma was marked by north-verging ductileshearing, yielding granulite-bearing ophiolitic melange blocks and garnet-pyroxene-facies ductiledeformation, and the later deformation, a dextral strike-slip tectonic process, occurred during theLate Carboniferous-Early Permian. Early Carboniferous molasses were deposited unconformably onpre-Carboniferous metamorphic and ductilely sheared rocks, implying the end of the early orogeny.The large-scale ductile strike-slip along the Aqqikkudug-Weiya zone was possibly caused by thesecond tectonic event, the Hercynian collision between the northern Tarim block and the southernSiberian block. Late Paleozoic granitic magmatism and superimposed structures overprinted this EarlyPaleozoic deformation belt. Results of geometric and kinematic studies suggest that the primaryframework of the Southern-Central Tianshan belt, at least the eastern part of the Tianshan belt, wasbuilt by these two phases of accretion events.

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 FEATURE ANALYSIS OF A 3-DOF COMPLIANT MECHANISM FOR MICRO MANIPULATION

Kinematics and its related issues of a 3-DOF in-parallel compliant mechanismare focused on. The micro manipulation application that requires high accuracy is developed. Designof the developed micromanipulator is based on the modified Delta mechanism. The main advantages ofthis manipulator are the use of only revolute flexure hinges and the capability to produce puretranslation theoretically. The aim is to develop an efficient kinematic model used for positioningcontrol. For this purpose, the Jacobian matrix relating the end effector position with the actuatordisplacements is obtained by both theoretical derivation and experiment. Aiming at the abnormalityin the motion capabilities of the micromanipulator found in calibration experiment, the mobility ofthe compliant mechanism on a theoretical level is analyzed by using the matrix method and screwtheory. Both the experimental and theoretical results have verified that the compliant mechanismdoes have rotational motion.

Three Dimensional Kinematics Analysis of the Independent Suspension Multibody System

Based on the theory of multibody system dynamics, the spatial kinematics analysis of the Mcpherson independent suspension widely used in the car was carried out. A practical and simpler method was provided to reduce the number of the generalized coordinates and constraint functions. By solving the nonlinear equations, the motion of any points in the whole suspension and wheel system can be predicted, including the spatial changes of the wheel alignment parameters which are of great importance to the car performances.

Forward kinematics analysis of parallel manipulator using modified global Newton-Raphson method

In order to obtain direct solutions of parallel manipulator without divergence in real time,a modified global Newton-Raphson(MGNR) algorithm was proposed for forward kinematics analysis of six-degree-of-freedom(DOF) parallel manipulator.Based on geometrical frame of parallel manipulator,the highly nonlinear equations of kinematics were derived using analytical approach.The MGNR algorithm was developed for the nonlinear equations based on Tailor expansion and Newton-Raphson iteration.The procedure of MGNR algorithm was programmed in Matlab/Simulink and compiled to a real-time computer with Microsoft visual studio.NET for implementation.The performance of the MGNR algorithms for 6-DOF parallel manipulator was analyzed and confirmed.Applying the MGNR algorithm,the real generalized pose of moving platform is solved by using the set of given positions of actuators.The theoretical analysis and numerical results indicate that the presented method can achieve the numerical convergent solution in less than 1 ms with high accuracy(1×10-9 m in linear motion and 1×10-9 rad in angular motion),even the initial guess value is far from the root.

Bionic Mechanism and Kinematics Analysis of Hopping Robot Inspired by Locust Jumping

A flexible-rigid hopping mechanism which is inspired by the locust jumping was proposed, and its kinematic characteris- tics were analyzed. A series of experiments were conducted to observe locust morphology and jumping process. According to classic mechanics, the jumping process analysis was conducted to build the relationship of the locust jumping parameters. The take-offphase was divided into four stages in detail. Based on the biological observation and kinematics analysis, a mechanical model was proposed to simulate locust jumping. The forces of the flexible-rigid hopping mechanism at each stage were ana- lyzed. The kinematic analysis using pseudo-rigid-body model was described by D-H method. It is confirmed that the proposed bionic mechanism has the similar performance as the locust hind leg in hopping. Moreover, the jumping angle which decides the jumping process was discussed, and its relation with other parameters was established. A calculation case analysis corroborated the method. The results of this paper show that the proposed bionic mechanism which is inspired by the locust hind limb has an excellent kinematics performance, which can provide a foundation for design and motion planning of the hopping robot.

Global kinematics of tectonic plates and subduction zones since the late Paleozoic Era

Detailed global plate motion models that provide a continuous description of plate boundaries through time are an effective tool for exploring processes both at and below the Earth's surface. A new generation of numerical models of mantle dynamics pre-and post-Pangea timeframes requires global kinematic descriptions with full plate reconstructions extending into the Paleozoic(410 Ma). Current plate models that cover Paleozoic times are characterised by large plate speeds and trench migration rates because they assume that lowermost mantle structures are rigid and fixed through time. When used as a surface boundary constraint in geodynamic models, these plate reconstructions do not accurately reproduce the present-day structure of the lowermost mantle. Building upon previous work, we present a global plate motion model with continuously closing plate boundaries ranging from the early Devonian at 410 Ma to present day.We analyse the model in terms of surface kinematics and predicted lower mantle structure. The magnitude of global plate speeds has been greatly reduced in our reconstruction by modifying the evolution of the synthetic Panthalassa oceanic plates, implementing a Paleozoic reference frame independent of any geodynamic assumptions, and implementing revised models for the Paleozoic evolution of North and South China and the closure of the Rheic Ocean. Paleozoic(410-250 Ma) RMS plate speeds are on average ～8 cm/yr, which is comparable to Mesozoic-Cenozoic rates of ～6 cm/yr on average.Paleozoic global median values of trench migration trend from higher speeds(～2.5 cm/yr) in the late Devonian to rates closer to 0 cm/yr at the end of the Permian(～250 Ma), and during the Mesozoic-Cenozoic(250-0 Ma) generally cluster tightly around ～1.1 cm/yr. Plate motions are best constrained over the past 130 Myr and calculations of global trench convergence rates over this period indicate median rates range between 3.2 cm/yr and 12.4 cm/yr with a present day median rate estimated at～5 cm/yr. For Paleozoic times(410-251 Ma) our model results in median convergence rates largely～5 cm/yr. Globally,～90% of subduction zones modelled in our reconstruction are determined to be in a convergent regime for the period of 120-0 Ma. Over the full span of the model, from 410 Ma to 0 Ma,～93% of subduction zones are calculated to be convergent, and at least 85% of subduction zones are converging for 97% of modelled times. Our changes improve global plate and trench kinematics since the late Paleozoic and our reconstructions of the lowermost mantle structure challenge the proposed fixity of lower mantle structures, suggesting that the eastern margin of the African LLSVP margin has moved by as much as ～1450 km since late Permian times(260 Ma). The model of the plate-mantle system we present suggests that during the Permian Period, South China was proximal to the eastern margin of the African LLSVP and not the western margin of the Pacific LLSVP as previous thought.

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.