Kinematic Theory Research Articles

Sports biomechanical analysis of knee joint injuries in table tennis players

Table tennis is a fast-paced, explosive sport that puts a lot of strain and stress on players’ lower limbs, particularly their knee joints. This work built a thorough mathematical model to investigate the dynamic and kinematic properties of the knee joint under various motion situations, with the goal of better understanding the biomechanical behavior of the knee joint in table tennis. A model of knee joint motion that takes into account the two degrees of freedom—flexion, extension, and rotation—is put forth based on the concepts of human biomechanics and kinematics theory. This model uses the Newton Euler equation to explain the mechanical behavior of the knee joint and integrates internal forces like muscle forces and external factors like ground reaction forces for torque balance analysis. This study offers a thorough examination of the force distribution and knee joint trajectory in table tennis using numerical simulation techniques. The findings show that the knee joint undergoes considerable compression and shear forces during intense activity, and that the joint’s stress properties vary significantly depending on the kind of movement. This finding is a valuable resource for table tennis players’ knee joint injury prevention and rehabilitation.

Stability analysis of micro-probe landings in complex terrain

Abstract Addressing the problem of landing stability of the micro-probes on the surface of extraterrestrial objects, combined with the geometric properties of the orthotetrahedron, this paper proposes a structural design method of the four-spine microprobe landing bracket that can adapt to the complex terrain and carries out the analysis of the landing stability of the four-spine bracket under the state of three-legged landing and the optimization of the structure for combined terrain of stones and slopes. Referring to the ZMP theory, the harsh working conditions of the four-spine bracket when landing are sorted out and determined. Based on the kinematics theory, the collision mechanism between the four-spine bracket and the ground is analyzed, and a landing model suitable for the micro-probes is established, which provides the basis for determining the landing stability of the micro-probe. Around the collision mechanism and landing model, the dimension optimization of the four-spine bracket is carried out, and the results of Adams dynamics simulation analysis and prototype test show that the landing stability of the four-spine bracket is improved, which verifies the validity of the optimization idea.

Efficient layerwise multiphysics spectral element model for delaminated composite strips with PWAS transducers

Efficient structural element-based models are essential for fast simulations of wave propagation in composite structures for model-based and physics-informed data-driven structural health monitoring. This article introduces the first efficient multiphysics time-domain spectral structural element for wave propagation analysis of beam and panel-type composite structures with piezoelectric transducers (patch or full layers) containing delaminations. A general framework is presented to model multiple delaminations and transducer patches located arbitrarily. The intact host and patch transducer-bonded laminates and sub-laminates between delaminations are modelled separately using an electromechanically coupled efficient layerwise zigzag theory (ZIGT) for kinematics and a piecewise quadratic variation for the electric potential across piezoelectric layers. The high-order spectral element (SE) features a virtual electric node to model equipotential surfaces of piezoelectric transducers apart from the usual physical nodes having mechanical and internal electric degrees of freedom. A hybrid point-least squares continuity approach is employed to maintain continuity at the intersections of delaminated sub-laminates or the patch-bonded laminate with the host laminate. The model’s performance in capturing electroelastic waves’ interaction with delamination is examined with reference to the conventional finite element (FE) solution based on the ZIGT, continuum-based FE solutions, and the SE solution based on a non-layerwise version of the laminate theory. Finally, the model is used to examine the impact of interfacial location and size of delaminations on wave propagation behaviour.

Analyze the moment of inertia of an object in uniformly accelerated linear motion and angular motion

Abstract. In studying particle kinematics, calculus plays an important role in analyzing and solving motion problems as a key mathematical tool. This paper mainly discusses the application of calculus in uniformly accelerated linear motion (LM) and angular motion (AM), focusing on the relationship between position, velocity, and acceleration and the analysis of the rate of change of motion. Through the study of uniformly accelerated LM, this paper guides researchers to use calculus to establish the mathematical relationship between position, velocity, and acceleration and verifies the accuracy of these formulas through practical cases. Similarly, in AM, this paper provides an in-depth understanding of the dynamic behavior of an object rotating around a fixed axis through calculus and calculates and applies important parameters in AM to solve practical problems by analyzing angular velocity and acceleration. In addition, this paper demonstrates the potential of calculus for a wide range of applications in dealing with variable speed motion and rate of change analysis. By integrating the rate of change of displacement and acceleration, it provides a precise tool for the optimization and resolution of engineering problems. In conclusion, calculus not only enriches the theory of kinematics but also demonstrates its important value in practical applications.

Trajectory error compensation method for grinding robots based on kinematic calibration and joint variable prediction

Trajectory accuracy, a crucial metric in assessing the dynamic performance of grinding robots, is influenced by the uncertain movement of the tool center point, directly impacting the surface quality of processed workpieces. This article introduces an innovative method for compensating trajectory errors. Initially, a strategy for error compensation is derived using differential kinematics theory. Subsequently, a robot kinematic calibration method utilizing ring particle swarm optimization (RPSO) is proposed to address static errors in the grinding robot. Simultaneously, a method for predicting robot joint variables based on a dual-channel feedforward neural network (DCFNN) is designed to mitigate dynamic errors. Finally, a simulation platform is developed to validate the proposed method. Simulation analysis using extensive data demonstrates an 89.3% improvement in absolute position accuracy and a 74.2% reduction in error fluctuation range, outperforming sparrow search algorithm (SSA), improved mayfly algorithm (IMA), multi-representation integrated predictive neural network (MRIPNN), etc. Algorithmic comparison reveals that kinematic calibration significantly reduces the average trajectory error, while joint variable prediction notably minimizes error fluctuation. Validation through trajectory straightness testing and a 3D printing propeller grinding experiment achieves a trajectory straightness of 0.2425 mm. Implementing this method enables achieving 86.1% surface machining allowance within tolerance, making it an optimal solution for grinding robots.

Mathematical principles of mechanical movements

The article proves that kinematic and dynamic theories in classical mechanics by I. Newton, considered a mathematical model of body displacement, are based on the laws of arithmetic progression (or linear function), trigonometry and quadratic function (equation). It is shown that formulas, equations of motion and graphs of dependencies in these theories are mathematical mechanisms that implement the relationship between uniformly varying mechanical quantities and quantities that implement (modify) changes. It is shown that the transition of a uniform change of one value to an accelerated (progressive) change occurs according to the scheme of transition of a linear function into a quadratic equation. It is shown that the formula of an arithmetic progression (linear function) is created by moving from variables in a quadratic equation to a time variable, and from changing and changing parameters to the coordinate, velocity and acceleration of the progression. In order for the content of the article to correspond to the topic, priority was given to mathematical initiatives (prerequisites, originals) of all the problems under consideration.

An alternative method to the Takagi-Taupin equations for studying dark-field X-ray microscopy of deformed crystals.

This study introduces an alternative method to the Takagi-Taupin equations for investigating the dark-field X-ray microscopy (DFXM) of deformed crystals. In scenarios where dynamical diffraction cannot be disregarded, it is essential to assess the potential inaccuracies of data interpretation based on the kinematic diffraction theory. Unlike the Takagi-Taupin equations, this new method utilizes an exact dispersion relation, and a previously developed finite difference scheme with minor modifications is used for the numerical implementation. The numerical implementation has been validated by calculating the diffraction of a diamond crystal with three components, wherein dynamical diffraction is applicable to the first component and kinematic diffraction pertains to the remaining two. The numerical convergence is tested using diffraction intensities. In addition, the DFXM image of a diamond crystal containing a stacking fault is calculated using the new method and compared with the experimental result. The new method is also applied to calculate the DFXM image of a twisted diamond crystal, which clearly shows a result different from those obtained using the Takagi-Taupin equations.

Ground Strength Test Technique of Variable-Camber Wing Leading Edge.

Morphing wing technology is crucial for enhancing the flight performance of aircraft. To address the monitoring challenges of full-scale variable-camber leading edges under flight conditions, this study introduces a ground-based strength testing technique aimed at precisely evaluating the deformation patterns and structural strength during actual operation. Firstly, the motion characteristics of the variable-camber leading edge were analyzed using numerical simulation based on kinematic theory. Secondly, a tracking loading test rig was designed and constructed to simulate the actuated deformation and aerodynamic loads of the leading edge. Next, mechanical boundary numerical simulation was then utilized to predict the motion trajectories of loading points on the upper and lower wing surfaces, and a multi-point coordinated control system was developed to achieve accurate experimental control. Finally, a multi-sensor iterative method was employed to ensure loading precision throughout the testing process. A case study was conducted using a leading edge test piece from a specific commercial aircraft. The results indicated that in the motion test of the variable-camber leading edge, the average error of the deflection angle was 4.59%; in the strength test, the average errors in the magnitude and direction of the applied load were 0.54% and 0.24%, respectively. These findings validate the effectiveness of the proposed technique in simulating the flight conditions of deforming wings and accurately obtaining the leading edge shape change curve, deformation accuracy curve, and strain curves of the upper and lower wing surfaces under deflection angles. Furthermore, this paper compares the deformation accuracy of different testing methods under test conditions, providing scientific evidence and technical support for the testing and evaluation of variable-camber leading edges.

The importance and use of vertical crack displacements for the assessment of existing reinforced concrete deep beams

The accurate assessment of cracked reinforced concrete structures is becoming increasingly more important as the world’s infrastructure ages and resources for retrofit and replacement remain limited. While existing approaches can be used to predict crack information for comparisons with on-site observations, there remains a need to establish methods that use crack measurements as a direct input to assess residual structural capacity. Critical wide cracks have been observed in lightly reinforced deep beams leading to questions about the safety of concrete bridges. To assess such deep members, this paper answers three important questions: 1) which critical crack displacements should be measured?; 2) where should the critical crack displacements be measured?; and 3) what is the residual shear capacity of the member, given the measured critical crack displacements? To answer these questions, detailed data from large-scale experiments is examined and interpreted with the two-parameter kinematic theory (2PKT). The results illustrate the importance of vertical crack displacements for conducting assessments of lightly reinforced deep beams. The paper shows that when the measured crack shape is incorporated into the 2PKT, the residual capacity of deep beams can be determined from measured critical crack displacements.

Influence of multisource errors of oil film contact surface on motion accuracy of hydrostatic guideway

PurposeThis study aims to explore the impact of multisource deformation errors on the oil film contact surface, which arise from manufacturing, assembly, oil pressure and thermal influences, on the motion accuracy of hydrostatic guideway.Design/methodology/approachUsing thermal-structural coupling simulations, this research investigates the effects of assembly, oil pressure and thermal factors on deformation errors of the oil film contact surface. By integrating these with manufacturing errors, a profile error model for the oil film contact surface is developed, characterizing the cumulative effect of these errors. Using kinematic theory and progressive Mengen flow controller characteristics, the motion error at any position of the hydrostatic guideway is quantified, examining how surface error traits impact motion accuracy.FindingsThe error averaging effect is affected by the profile error of oil film contact surface. Meanwhile, the motion accuracy of hydrostatic guideway is highly sensitive to the oil film contact surface error amplitude.Originality/valueThis approach allows for precise prediction and analysis of motion accuracy in hydrostatic guideways during the design and manufacturing stages. It also provides guidance for planning process tolerances.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-03-2024-0063/

Use of parametric X-ray radiation of electrons in crystals to determine the parameters of imaging-plates

Good agreement between experimental data and the results of calculations of the yield and angular distributions of parametric X-ray radiation of electrons in crystals within the framework of kinematic theory enables us to use the measurement results to determine the photon energy dependence of the sensitivity of X-ray plates. The results of measurements of the angular distributions of parametric X-ray radiation of electrons with an energy of 255 MeV in a Si crystal using imaging plates of several types were compared with the results of calculations that take into account all currently known experimental factors that influence the measurement results. The spectral dependence of the sensitivity of the studied X-ray plates was determined for photon energies of two orders of reflection and for the (111), (1̅1̅1), and (110) reflection planes.

A Lagrangian approach for variable speed limit implementation in C-ITS framework

With the development of Cooperative-Intelligent Transport System (C-ITS) technologies, new strategies based on embedded technologies have emerged to manage road networks. This paper focuses on adapting to this connectivity context a Variable Speed Limit (VSL) system to detect shockwaves and anticipate their propagation based on the kinematic wave theory to dampen them. We provide an alternative framework to adapt the VSL strategy, well-suited for Eulerian approaches, into a Lagrangian context. While the Eulerian approach is based on Loop Detector (LD) and macroscopic traffic indicators (e.g. flow, density), our Lagrangian approach relies on Road Side Units (RSUs) that record the GPS traces shared by Connected Vehicles (CVs). Based on the combination of CV trajectories, Fundamental and Space-Time Diagrams theory, shockwave estimation and prediction processes directly operate on congestion waves, which release the estimation issue for traffic density. The simulation-based analysis reveals that the performance of the Lagrangian approach is comparable to the Eulerian configurations.

A Static Security Region Analysis of New Power Systems Based on Improved Stochastic–Batch Gradient Pile Descent

The uncertainty in the new power system has increased, leading to limitations in traditional stability analysis methods. Therefore, considering the perspective of the three-dimensional static security region (SSR), we propose a novel approach for system static stability analysis. To address the slow training speed of traditional deep learning algorithms using batch gradient descent (BGD), we introduce an improved stochastic–batch gradient descent (S-BGD) search method that combines the advantages of stochastic gradient descent (SGD) in fast training. This method ensures both speed and precision in parameter training. Moreover, to tackle the problem of getting trapped in local optima and saddle points during parameter training, we draw inspiration from kinematic theory and propose a gradient pile (GP) training method. By utilizing accumulated gradients as parameter corrections, this method effectively avoids getting stuck in local optima and saddle points, thereby enhancing precision. Finally, we apply the proposed methods to construct the static security region for the IEEE-118 new power system using its data as samples, demonstrating the effectiveness of our approach.

A framework for formal verification of robot kinematics

As robotic applications continue to expand and task complexity increases, the adoption of more advanced and sophisticated control algorithms and models becomes critical. Traditional methods, relying on manual abstraction and modeling to verify these algorithms and models, may not fully encompass all potential design paths, leading to incomplete models, design defects, and increased vulnerability to security risks. The verification of control systems using formal methods is crucial for ensuring the safety of robots. This paper introduces a formal verification framework for robot kinematics implemented in Coq. It constructs a formal proof for the theory of robot motion and control algorithms, specifically focusing on the theory of robot kinematics, which includes the homogeneous representation of robot coordinates and the transformation relations between different coordinate systems. Subsequently, we provide formal definitions and verification for several commonly used structural robots, along with their coordinate transformation algorithms. Finally, we extract the Coq code, convert the functional algorithms into OCaml code, and perform data validation using various examples. It is worth emphasizing that the framework we have built possesses a high level of reusability, providing a solid technological foundation for the development of kinematics theorem libraries.

On the free and forced vibrations of porous GPL reinforced composite conical panels using a Legendre-Ritz method

An analysis is conducted in the present investigation to study the free and forced vibration characteristics of composite laminated conical panels. It is assumed that composite panel is reinforced with graphene platelets (GPLs) where the amount of GPLs may be different between the layers which results in a piecewise functionally graded media. In addition, the effect of uniform and non-uniform porosities is also included into the formulation. The elasticity modulus of the media is estimated following the Halpin-Tsai rule while the simple rule of mixtures approach is applied to obtain the mass density and Poisson's ratio on the panel. With the aid of the first order shear deformation theory of shells and Donnell kinematics, definition of strain, kinetic and potential energy of applied loads is given. After that with the general idea of Ritz method suitable for arbitrary types of boundary conditions and Legendre polynomials as the basic functions, the energies are discreted which results in the general form of the equations of motion. While standard eigenvalue solution is applied to obtain the natural frequencies, a Newmark time marching method is implemented to obtain the temporal evolution of displacement of the panel. Results of this study are well-compared with the available data in the open literature and after that novel results on the present study are provided in the form of figures and tables. It is highlighted that type of porosity and graded pattern of GPLs are both important on the frequencies and dynamic deflection of the panel.

Nonlinear Deflection Characteristics of Weakly Bonded Curved Composite Structure Under Hygro-Thermo-Mechanical Loadings

A customized MATLAB algorithm is developed for internally separated laminated composite panels experiencing large geometric deformations. The algorithm is designed to calculate nonlinear deflection responses under the effect of combined hygro-thermo-mechanical (HTM) loading. The hygrothermal (HT) load on the panel is in-plane, whereas the mechanical load acts upon the structure transversely. The analysis has adopted various kinematic theories and finite element (FE) techniques to determine the deformations computationally. The deflection behavior of the composite is characterized through a macro mechanical model considering the nonlinearity in geometry with and without accounting for the stretching effects across the panel thickness. Additionally, the changes in composite properties due to the environment and/or loadings are adopted to achieve a realistic response, preserving continuity assumptions between the individual layers of the weakly bonded structure. Moreover, various numerical examples are examined through different models to illustrate the influences of environmental factors and design-specific parameters on the flexural strength of weakly bonded structures. The findings strongly emphasize the necessity of employing diverse kinematic models when examining laminated structures, both with and without HT loading, while also acknowledging the potential for debonding.

Evaluation of Spatiotemporal Characteristics of Lane-Changing at the Freeway Weaving Area from Trajectory Data

Intensive lane-changing (LC) events are one of the great causes that make freeway weaving areas become bottlenecks. This study proposes an approach using vehicle trajectory data to investigate the spatiotemporal distributions of the number of LC events, void occupancies, and throughput variations at the freeway weaving area. Firstly, all LC events are extracted from the cleaned dataset and classified into four types according to the LC vehicles’ origin–destination lanes and LC directions. Secondly, the time and space void occupancies are calculated using the kinematic theory. Thirdly, the throughput variations are identified with the oblique N-curve method. Finally, the spatial and temporal distributions of the LC events, void occupancies, and throughput variations are plotted to analyze their characteristics and relationships. The spatial distributions of different types of LC events indicate that most LC events occur at the surrounding area of the on-ramp entrance. Spatial distributions of time void occupancies show that the time void in the original lanes is quite small while that in the target lanes is much larger. Furthermore, the time void occupancies amplify downstream when considering vehicles traveling on the road. By comparing the temporal distributions of LC events, void occupancies, and throughput variations, there is a lag effect between the large value occurrences of space void occupancy and throughput reduction and that of the LC events, which can conclude a causal relationship between LC events and the occurrences of the space void occupancies and throughput reductions.

Surface roughness prediction and roughness reliability evaluation of CNC milling based on surface topography simulation

Surface roughness is influenced by various factors with uncertainty characteristics, and roughness reliability can be used for the assessment of the surface quality of CNC milling. The paper develops a method for the assessment of surface quality by considering the coupling effect and uncertainty characteristic of various factors. According to the milling kinematics theory, the milling surface topography simulation was conducted by discretizing the cutting edge, machining time, and workpiece. Considering the coupling effect of various factors, a roughness prediction model is established by the SSA-LSSVM, and its prediction accuracy reaches more than 95%. Then, the roughness reliability model was developed by applying the response surface methodology to achieve the assessment of surface quality. The proposed method is verified by the milling experiments. The maximum values of the relative errors between the simulation and experimental results of the surface roughness and roughness reliability are 9% and 1.5% respectively, indicating the correctness of the method proposed in the paper.

Extended kinematical 3D gravity theories

In this work, we classify all extended and generalized kinematical Lie algebras that can be obtained by expanding the so\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathfrak{so} $$\\end{document} (2, 2) algebra. We show that the Lie algebra expansion method based on semigroups reproduces not only the original kinematical algebras but also a family of non- and ultra-relativistic algebras. Remarkably, the extended kinematical algebras obtained as sequential expansions of the AdS algebra are characterized by a non-degenerate bilinear invariant form, ensuring the construction of a well-defined Chern-Simons gravity action in three spacetime dimensions. Contrary to the contraction process, the degeneracy of the non-Lorentzian theories is avoided without extending the relativistic algebra but considering a bigger semigroup. Using the properties of the expansion procedure, we show that our construction also applies at the level of the Chern-Simons action.

Kinematic Analysis of Six-Legged Robot

Nowadays, robots are applied in many fields which means flexibility in robot movement is always in high demand. A walking robot is a form of a mobile robot that is gentle to the environment, and it is possible to move through various settings while selecting landing points. In this study, a systematic approach for dealing with a controlling algorithm is proposed for the six-legged walking robot. A mathematical model is applied for studying the kinematics and gaits of the six-legged robots based on parallel and serial kinematic mechanism theory. The kinematic analysis is based on classical kinematic theory, which uses a formulation that is helpful in computer algorithms. The experiment results show that the effectiveness of robot design and control algorithms are responsive to different movements.