Kinematic Theory Research Articles

Design of a 2T1R-Type Parallel Mechanism: Performance Analysis and Size Optimization

The planar three-degree-of-freedom (DoF) parallel mechanism plays a significant role in the fields of automobiles and electronics due to its advantages such as high stiffness, large carrying capability, and stable operation. In this paper, a planar 3-DoF (2T1R) parallel mechanism is derived by structural evolution from the parallelogram by means of Grassmann line geometry and the Atlas method. First, the position equation of the mechanism is established and the inverse kinematics and Jacobian matrix are investigated. The maximum deviation between the theory and simulation results of the inverse kinematics and Jacobian matrix is 0.48%, which verifies the accuracy of the theoretical model. Then, the constraint conditions of the mechanism are defined. Based on the inverse position solution, the numerical method is used to solve the workspace of the mechanism. It is concluded that the ratio of the workspace to the entire triangular space is about 15% higher than that of the 3-PRR parallel mechanism. Next, based on the Jacobian matrix, the performance indexes are established to evaluate stiffness and dexterity. Finally, the size of the mechanism is optimized by means of the genetic algorithm to improve the comprehensive performance.

Detailed crack‐based assessment of a 4‐m deep beam test specimen

AbstractWhen shear cracking occurs in existing reinforced concrete deep members, engineers are faced with the challenge of determining the safety of the members. This paper presents a crack‐based assessment approach that utilizes the Two‐Parameter Kinematic Theory (2PKT) as a framework for the assessment of lightly reinforced concrete deep beams. The paper presents three assessment approaches with progressively increasing levels of approximation (LoAs). The first level of approximation (LoA I) involves using the 2PKT in a predictive manner for situations where the crack shapes are unknown, LoA II improves upon LoA I by incorporating more detailed modeling of the strain in the transverse reinforcement at the location of the critical cracks, and LoA III includes the details of LoA II but also uses the detailed crack geometry as an input in the assessment. Each of the LoAs is presented and compared with experimental data from a 4‐m deep beam test in the literature. The shear carrying mechanisms determined from the kinematic model are evaluated and compared across LoAs. Finally, the paper utilizes LoA III to study the size effect in shear for deep beams. The results quantify the influence of aggregate interlock on the size effect in shear critical deep beams.

Vibrations of graphene platelet reinforced composite doubly curved shells subjected to thermal shock

An investigation is performed in this research to study the response of doubly curved shells subjected to rapid surface heating. Doubly curved shell is made from a composite laminated media where each layer is reinforced with graphene platelets (GPLs). Also each layer may have different amount of GPLs which results in a piecewise functionally graded graphene platelet reinforced composite (FG-GPLRC) shell. The elasticity modulus of the shell is estimated by means of the Halpin-Tsai rule where the size of the reinforcements is also included. It should be noted that mass density, thermal expansion coefficient, Poisson’s ratio and specific heat are evaluated using the simple rule of mixture approach. The one-dimension transient heat conduction equation is established and solved for each layer of the composite media. The continuity of the temperature change and heat flux are also considered between the layers. After that, time dependent thermal moment and thermal force are evaluated and inserted into the equations of motion of the structure. First order shear deformation theory of shells and Donnell kinematics are applied to establish the basic equations of the shell. With the aid of the Ritz method and Chebyshev polynomials as the basic functions, the matrix representation of the motion equations of the doubly curved shallow shells subjected to rapid surface heating are established. These equations are traced in time using the Newmark time marching scheme. Results of this study are compared with the available data in the open literature. After that novel results are provided for vibrations induced by rapid surface heating in FG-GPLRC doubly curved shells.

STABILITY ANALYSIS OF ROCK BLOCKS WITH ENTIRE SPHERE STEREOGRAPHIC PROJECTION BASED ON THE BLOCK THEORY: A CASE STUDY FOR A TUNNEL ENTRANCE PROJECT

This paper presents a static equilibrium kinematic analysis of rock performed in the tunnel entrance project using entire sphere stereographic projection under block theory. The objective of this study is to improve the predictive analysis of rock masses in terms of stability in rock masses area. Different key blocks with failure modes are determined. The conventional upper hemisphere stereographic projection is also employed for comparative analysis. Based on the findings, it was concluded that the planar failure is not probable in the case of the kinematic and block theory method in the tunnel entrance area. However, the wedge failure is more probable in both cases of analysis and the number of possible slide blocks in the case of kinematic analysis was found to be less than in the case of block theory; In these conditions, the support system should be provided for the reasons of safety. The comparative analysis shows that the results of block theory analysis are close to reality and provide more precision on the stable and unstable block than the results of kinematic analysis; Moreover, the block theory method using the entire sphere stereographic projection provides more precision on the sliding angle than the use of one sphere stereographic projection. Based on this study, the tunnel entrance is more stable for the dip slope face equal to 45 and not probable for slope face 60˚ and 85˚; but these results were limited in the case of stability analysis under gravitational loading.

Parametric X-ray radiation from nanopowders

The first observation of Parametric X-ray Radiation (PXR) produced in a crystalline powder constituted of crystallites whose largest dimensions are of the order of some nanometers is reported. PXR was registered during the interaction of a 7 MeV electron beam with a platinum powder. The experimental results were compared with the kinematical theory showing a good agreement concerning the position, form, and intensity of all observed PXR spectral peaks. Finally, an analysis of the influence of crystallite dimensions on the PXR peak full width hall maximum (FWHM) and PXR peak intensity was performed.

A Real-Time Prediction Model for Individual Vehicle Travel Time on an Undersaturated Signalized Arterial Roadway

Predicting the segment travel time of a vehicle, which includes its travel time on a road segment and the delay for passing the downstream intersection, can greatly help the drivers to better control a vehicle’s speed to reduce signal delay and gasoline consumption. However, so far, few effective methods have been developed that can accurately characterize an individual vehicle’s segment travel time. To address this problem, this article seeks to develop an analytical model to predict each vehicle’s travel time on a signalized arterial roadway under nonsaturated traffic conditions. The proposed model is developed based on the following three situations a vehicle can experience when passing through a signalized intersection: 1) passing directly in the green time phase, 2) decelerating until coming to a complete stop in the red intervals, and 3) decelerating initially, but passing through without a stop. The situation that a vehicle will encounter is predicted by analyzing the correlation between a vehicle’s entry time to the segment and the signal-phase timing using the kinematic wave theory. Then, the intersection delay of each vehicle is predicted based on the queue shockwave speed and the discharge shockwave speed. A vehicle’s travel time on a road segment is predicted by summing the intersection delay and the segment free-flow travel time. The numerical application shows that the proposed model can accurately characterize a vehicle’s travel time. Thereby, it can be applied in a connected environment to predict the segment travel time to improve the mobility of the traffic.

Realistic simulation of reflection high-energy electron diffraction patterns for two-dimensional lattices using Ewald construction

Reflection high-energy electron diffraction (RHEED) is a powerful tool for characterizing crystal surface structures. However, the setup geometry leads to distorted and complicated patterns, which are not straightforward to link to the real-space structures. A program with a graphical user interface is provided here to simulate the RHEED patterns. Following the Ewald construction in the kinematic theory, we find out the exact geometric transformation in this model that determines the positions of diffraction spots. The program can deal with many forms of surface structures, including surface reconstructions or domains. The simulations exhibit great agreement with the experimental results in various cases. This program will benefit the structure analysis in thin-film growth and surface science studies.

Effect of steel fibers on the shear behavior of Self-Compacting reinforced concrete deep Beams: An experimental investigation and analytical model

The shear behavior of reinforced concrete deep beams made of self-compacting concrete with different volume fractions of discrete macro steel fibers (0.5%,1.0%, and 1.5%) is studied. All the beams are tested at shear span to depth ratio of 1.0, and the effect of loading plate width on shear carrying capacity is also studied. Similarly, the effectiveness of steel fibers in improving the shear behavior is compared with the beams made of plain concrete and the beams with 0.3% web reinforcement in both horizontal and vertical directions. Test results revealed that the addition of macro steel fibers significantly improved the performance of deep beams, particularly first cracking load, ultimate shear capacity, ultimate deformation, and ductility. However, the addition of steel fiber more than 1.0% volume fraction did not increase the ultimate shear capacity. A simplified analytical model is proposed to predict the ultimate shear capacity of steel fiber reinforced concrete deep beams. The existing cracking strut and tie method (CSTM) is extended to include the effect of fibers, and a simplified fiber-reinforced cracking strut and tie method (FR-CSTM) is proposed. Predictions of FR-CSTM are compared with CSTM and two-parameter kinematic theory (2PKT). The comparisons of predictions with test results and existing models show that the proposed method can capture the ultimate shear capacity of deep beams with reasonable accuracy.

Simplified Three-Parameter Kinematic Theory for Shear Strength of Short Reinforced Concrete Walls

Simplified Three-Parameter Kinematic Theory for Shear Strength of Short Reinforced Concrete Walls

Static, free vibrational and buckling analysis of laminated composite beams using isogeometric collocation method

Isogeometric collocation (IGA-C) method is a computational approach to solve boundary value problems. In this method (IGA-C), the differential equations are solved in strong form instead of the weak form approach adopted by Galerkin based formulations. IGA-C method is computationally efficient in comparison to conventional finite element method and Galerkin-Isogeometric approaches. IGA-C method does not involve the process of assembling global stiffness matrix from element stiffness matrix. Another advantage of IGA-C is that it requires a single integration point per element irrespective of the order of Non-Uniform Rational B-Spline functions (NURBS) adopted. Isogeometric collocation has also been demonstrated as a stable, efficient and accurate higher order computational method for explicit problems. For a wider adoption of isogeometric collocation method, beam/plate/shell finite elements within the framework of IGA-C method need to be formulated. Owing to the extensive adoption of laminated composites in structural components, development of beam finite elements for laminated composite beams based on isogeometric collocation method will prove useful during analysis of composite structures. IGA-C method is proposed in this study for the static bending, free vibration and buckling analysis of laminated composite beams. Classical laminated plate theory (CLPT), first order shear deformation theory (FSDT) and higher order shear deformation theory (HSDT) are considered for all the three analyses. The computational approach proposed for laminated beam based on HSDT contains two Degrees of Freedom (DOF) per node. Computational approach for analysing laminated composite beams based on each of these kinematic theories and using IGA-C method is presented. Accuracy of the proposed computational approaches is checked by solving different numerical examples. Values of normalized transverse displacement, normalized stresses, normalized natural frequencies and normalized critical buckling loads are compared with results from the literature and are found to be accurate.

Ex vivo experimental characterizations for understanding the interrelationship between tissue mechanics and collagen microstructure of porcine mitral valve leaflets

Unidirectional blood flow in the left side of the heart is regulated by the mitral valve. To better understand the mitral valve function, researchers have examined the structural and mechanical properties of the mitral valve leaflets; however, limitations of the previous studies include the use of mechanics- and structure-altering tissue modifications (e.g., optical clearing) that limit the ability to quantify the unique load-dependent reorientation and realignment of the collagen fibers as well as their interrelation with the valve tissue mechanics. Herein, we aimed to circumvent these limitations by utilizing an integrated polarized-light imaging and biaxial testing system for understanding the mechanics–microstructure interrelationship for porcine mitral valve leaflets. We further performed constitutive modeling and evaluated the accuracy of the affine fiber kinematics theory. From the tissue mechanics perspective, the posterior leaflet was more extensible in the radial direction than the anterior leaflet (14.2% difference in radial tissue stretch), while exhibiting smaller collagen and elastin moduli based on the determined constitutive model parameters. From the collagen microstructure’s standpoint, the posterior leaflet had smaller increases in optical anisotropy (closely related to the degree of fiber alignment) than the anterior leaflet (32.8±7.7% vs. 50.0±19.7%). Further, the leaflets were found to possess two distinct fiber families – one family oriented along the circumferential tissue direction, and another more disperse family with a 30°–40° offset from the first fiber family. Finally, affine fiber kinematics consistently underpredicted the collagen fiber reorientations Overall, this study improved our understanding of the mitral valve leaflets that is essential for facilitating tissue-emulated valve replacement and cardiac valve modeling frameworks.

An Overview of Cable-Driven Parallel Robots: Workspace, Tension Distribution, and Cable Sagging

The researching, designing, calculating, and controlling cable-driven parallel robots (CDPRs) are being promoted in recent years. The researches focus on optimizing the design of CDPRs configuration, computing workspace, calculating cable tension distribution, designing the mechanical structure, and developing controller. However, due to the complexity of the structure and unidirectional characteristic of cable, many computational methods have been applied to solve the above problems. To facilitate the performance of theoretical studies on important issues in the design and control of the CDPRs, a summary of computational methods is needed for important issues related to the functionality and accuracy of CDPRs such as defining the workspace, distributing the cable tensions, and calculating the sagging of the cable. This paper summarizes published studies on CDPRs and focuses on classifying and analyzing methods used to calculate important issues in the process of calculating and designing CDPRs. The efficiency of these calculation methods is also analyzed and evaluated based on the mathematical theories of kinematics and dynamics of CDPRs. The content of this study is an effective reference for studies on important problems in the process of designing and implementing CDPRs, helping researchers shorten the time to review related topics.

Ship’s Wake on a Finite Water Depth in the Presence of a Shear Flow

The ship’s wake in the presence of a shear flow of constant vorticity at a finite water depth is investigated by expanding the Whitham-Lighthill kinematic theory. It has been established that the structure of a wave ship wake radically depends on Froude number Fr (in terms of water depth) and especially on the critical Froude number Frcr, which depends on the magnitude and direction of the shear flow. At its subcritical values Fr<Frcr two types of waves are presented: long transverse and short divergent waves inside the wedge area with an angle depending on Fr For the supercritical range Fr>Frcr only divergent waves are presented inside the wake region. Critical Froude number Frcr is variable and mostly depends on collinear with the ship path component of the shear flow: it decreases with the unidirectional shear flow and increases on the counter shear current. The wedge angle of the ship wake expands with an increase in the unidirectional shear flow and narrows in the oncoming flow in the subcritical mode of the ship’s motion Fr<Frcr. Wake angle decreased with Froude number for Fr>Frcr and only divergent waves with the crests almost collinear with ship path are finally presented in the narrow ship wake. For a critical value of the Froude number Fr=Frcr, the ship’s wake has a total wedge angle of 180° with waves directed parallel to the ship’s motion. The presence of a shear flow crossing the path of the ship gives a strong asymmetry to the wake. An increase in the perpendicular shear flow leads to an increase in the difference between the angles of the wake arms.

Numerical hygrothermal frequency of pre-damage shallow shell panel: A nonlinear FE approach

ABSTRACT In this work, the nonlinear eigenvalues of the debonded composite panel (flat, single and doubly curve) are evaluated under unlike humidity and temperature conditions. To obtain the said modal responses a macro mechanical isoparametric finite element-based numerical model of pre-damage laminated composite is developed. The structural panel deformations are counted through two different kinematic theories with small deviations (related to the drilling degrees of freedom). The geometrical distortions of the panel component are expressed using the common Green’s strain relation in Lagrangian scope. The governing differential equation (converted to nonlinear eigenvalue equations) is derived from a dynamic version of the variational principle. The direct iterative approach has been adopted to compute the nonlinear frequencies in association with the finite element steps. Also, the element sensitivity behavior of the obtained numerical solution is verified and extended further to check the efficacy (comparing the results from the published domain). In continuation, the nonlinear modal values are computed through a series of examples considering the role of debonding with the structural parameters in detail.

Explanation of What Time in Kinematics Is and Dispelling Myths Allegedly Stemming from the Special Theory of Relativity

One of the biggest unsolved problems in physics is explaining what time is. The paper explains what time is in kinematics theories. It has been proved that in the kinematics of Special Theory of Relativity (STR) and Special Theory of Ether (STE) time is measured by the light clock. Therefore, all properties of time in kinematics result from the properties of a signal clock. The paper explains the time dilation phenomenon on the basis of STE. The presented explanation is not only a classic description of time dilation but is based on the construction of an innovative technical model of this phenomenon. Time dilation is due to the properties of the light clock. It is a natural property of this clock. The article shows that the claim that the speed of light in a vacuum is the maximum speed in the real world has no theoretical basis. In modern physics, such a doctrine has been adopted as a result of an overinterpretation of the mathematics on which the Special Theory of Relativity is based. The presented model shows how, using atomic clocks, it may be possible to determine the movement in relation to the universal frame of reference in which electromagnetic signals propagate. This article contains only original research.

Capability of Intermittent Bus Lane Utilization for Regular Vehicles

Intermittent bus lanes (IBLs) can improve road capacity by allowing other regular vehicles to drive in the idle space of a dedicated bus lane. However, excessive vehicles in the IBL will cause additional bus delays. To avoid such problems, this study proposes a method to determine the capability of IBL permitted for regular vehicles first, and then use it as the total amount restriction of lane-borrowing vehicles to implement a bus lane control strategy that will improve road capacity and avoid additional bus delays. A model for calculating the capability of IBL is also provided. Vehicles between two buses are designated as potentially lane-borrowing vehicles that could follow the buses to leave the road section. The evolution process of these vehicles in the unit is analyzed using kinematic wave theory to obtain the formed traffic queue length. Using the rear bus trajectory to set the length limit on the traffic queue, the estimated total amount of lane-borrowing vehicles is corrected to establish the final capability of the IBL. The applicability of the method was evaluated from three perspectives: bus departure interval, road traffic saturation, and near-side bus stop. The simulation results showed that the proposed method can guarantee no additional bus delay compared to the situation of a dedicated bus lane. It can also improve road capacity more than traditional IBL under any degree of saturation and bus departure interval. Compared with traditional IBL, the average travel time of regular vehicles is shorter, except when the degree of saturation is high and the bus departure interval is large.

Positive Torque Modulation Method and Key Technology of Conventional Beam Pumping Unit

The large fluctuation of net torque and the existence of negative torque on the crank output shaft of the beam pumping unit are the decisive factors leading to its low efficiency and high energy consumption. The conventional pumping unit CYJ10-4.2-53HF was selected as the study object on the basis of the fixed shaft secondary balance principle and the positive torque modulation scheme was first proposed according to the following secondary balance principle based on the linkage. The kinematics analysis of the suspension point and the secondary incremental velocity mechanism were carried out using the theory of rigid body plane kinematics. The force analysis of each moving part of the pumping unit was carried out, the net torque expression of the crank output shaft was obtained, and an example calculation was performed. The positive torque beam pumping unit was developed and tested in a field test. The tests showed that the positive torque beam pumping unit was able to fully realize positive torque operation under field well conditions, with a power saving rate of 23.73% and a 14.5% increase in system efficiency, and that the reliability of the pumping unit meets the requirements for field application.

Design of a DSP-Based Motion-Cueing Algorithm Using the Kinematic Solution for the 6-DoF Motion Platform

A motion-cueing algorithm is a motion simulation system that makes the pilot feel the flight motion by calculating the attitude of the platform. This paper presents the design a kinematics model and two motion-cueing algorithms for a multi-axis motion platform. Firstly, the relationship between each axis is derived from the kinematics theory and motion platform transformation. Next, two motion-cueing algorithms are designed providing the pilot with the bodily sensations of the 6-DoF motion platform. By using a hardware-in-the-loop (HIL) approach simulated in a real-time digital simulator, the control operations are performed in a digital signal processor (DSP). All of the motion-cueing algorithms, including the classical washout algorithm and the optimal control algorithm, are realized through a DSP, TMS-320F-28377D. The simulation results verify the theoretical analysis and illustrate the correctness and practicability of the proposed method.

On some properties of Hassani transforms

In the present paper, based on the ideas of Algerian physicist M.E. Hassani, the generalizedHassani spatial-temporal transformations in real Hilbert space are introduced. The originaltransformations, introduced by M.E. Hassani, are the particular cases of the transformations,introduced in this paper. It is proven that the classes of generalized Hassani transforms donot form a group of operators in the general case. Further, using these generalized Hassanitransformations as well as the theory of changeable sets and universal kinematics, the mathematicallystrict models of Hassani kinematics are constructed and the performance of the relativityprinciple in these models is discussed.

A Symmetry-Based Kinematic Theory for Nanocrystal Morphology Design.

The growth of crystalline nanoparticles (NPs) generally involves three processes: nucleation, growth, and shape evolution. Among them, the shape evolution is less understood, despite the importance of morphology for NP properties. Here, we propose a symmetry‐based kinematic theory (SBKT) based on classical growth theories to illustrate the process. Based on the crystal lattice, nucleus (or seed) symmetry, and the preferential growth directions under the experimental conditions, the SBKT can illustrate the growth trajectories. The theory accommodates the conventional criteria of the major existing theories for crystal growth and provides tools to better understand the symmetry‐breaking process during the growth of anisotropic structures. Furthermore, complex dendritic growth is theoretically and experimentally demonstrated. Thus, it provides a framework to explain the shape evolution, and extends the morphogenesis prediction to cases, which cannot be treated by other theories.