Force Diagram Research Articles

Kinematics and kinetics of a knee assistance exoskeleton for sit-to-stand and stand-to-sit motions with energy storage and regeneration: A bond graph approach

A bond graph model for the kinematics and kinetics of a knee assistance exoskeleton for sit-to-stand (SiTSt) or stand-to-sit (StTSi) motions is presented. The exoskeleton is actuated by a wire rope connected to a lead screw and slider nut assembly driven by an electric motor. An energy storage spring (ESS) is used for energy storage and regeneration. The ESS and wire rope apply opposite forces on the slider nut resulting in switching of contact surfaces. The kinematics of the lead screw and slider nut assembly is discussed and a bond graph model for the same is developed considering switching of contact surfaces and friction. Kinetics equations are derived from the model and verified by free body diagram (FBD) analysis. The efficacy of the developed model is demonstrated through simulations, where the switching and effects of friction are captured elegantly. Further, mechanics of wrapping is discussed considering the friction between the wire rope and the pulley. Finally, the bond graph model of the proposed exoskeleton is developed. Simulations are carried out by varying the stiffness of ESS and friction coefficients. A reduction in the assistance motor torque, power and energy requirements due to ESS and wrapping is demonstrated.

Wind as a context for Newton’s first and second law and force diagrams

Wind as a context for Newton’s first and second law and force diagrams

Mechanical Behaviour Assessment and Optimization of Construction Sequence for an HSS Vierendeel Truss

Long-span Vierendeel trusses in construction are challenged by smooth force transfer and critical stress control concerns. In this article, construction sequences characterized by loading/unloading due to various assemblies of the branches and/or temporary lattice column supports are focused on to reproduce their related mechanical behaviours in finite element modelling. Typical bending moment and shear force diagrams for hollow structure section (HSS) chords are analysed first, and then combined with a corrected assessment index in the development of an optimized construction scheme through effective discussion. It is observed that the branch assembly sequence has significant but reversed influences on either the bending moments or the shear forces of the interior support and the midspan of the HSS chords. The influence of the branch assembly sequence on the bending moment and shear force are compromised with the introduction of a temporary support. The corrected assessment index superimposed by the internal force and the deflection is demonstrated properly to represent the strength and the serviceability requirements, especially for characterizing the removal of a temporary support after the completed construction of a twelve-panel Vierendeel truss for the roof of an assembly hall.

A Comprehensive Investigation of the Geometric Functionally Graded Auxetic Double Arrowhead Composite Lattice Structures: Exploring Tailored Longitudinal and Lateral Young’s Modulus

Lattice structures with negative Poisson’s ratios (NPR) can integrate advanced functionalities in various engineering applications, including biomedical, aerospace and protective systems. This study explores the mechanical properties of auxetic double arrowhead honeycomb composites, a novel geometric functionally graded auxetic double arrowhead composite with NPR. Analytical expressions for Young’s modulus in both longitudinal and lateral directions are derived and validated using finite element simulations. To this aim, the Euler–Bernoulli beam theory and the free body diagram were used to investigate the elastic response on two different types of arrowhead composite structures. Two types of structures are investigated: uniform (constant forming angle) and geometrically functionally graded (varying forming angle with height). For experimental validation, chopped carbon fiber-reinforced polylactic acid (PLA) composite lattice structures were fabricated via fused filament fabrication. Results indicate that increasing the forming angle enhances lateral stiffness (Young’s modulus) while decreasing longitudinal stiffness. The rate of change of Young’s modulus in the lateral direction is higher than that in the longitudinal direction based on the variations of the forming angles. It was concluded that geometric functionally graded structures could simultaneously have a better elastic response with a more significant Young’s modulus for both longitudinal and lateral directions.

Magnetic Mineral Dissolution in Heqing Core Lacustrine Sediments and Its Paleoenvironment Significance

The magnetic parameters within lacustrine sediments serve as invaluable proxies for deciphering the paleoenvironmental and paleoclimatic conditions. However, the dissolution of magnetic minerals can significantly alter detrital magnetic mineral assemblages, thereby complicating their interpretation in paleoenvironmental reconstructions. In an effort to clarify the impact of this dissolution on the grain size of magnetic minerals in lacustrine sediments, we undertook a thorough analysis of the rock magnetic properties on samples from the interval characterized by low ARM (anhysteretic remanent magnetization)/SIRM (saturation isothermal remanent magnetization) values between 140 and 320 ka in the Heqing (HQ) lacustrine drill core, located in Southwest China. Temperature-dependent magnetic susceptibility and FORC diagrams revealed a predominance of single-vortex and pseudo-single domain (PSD) magnetite and maghemite within the sample. When compared to samples from both the glacial and interglacial periods, the high SIRM, elevated magnetic susceptibility, and low ARM/SIRM ratio intervals from 140 to 320 ka suggested a high concentration of magnetic minerals coupled with a relatively low concentration of fine-grained particles in the sediments. The reductive dissolution of the fine-grained magnetic oxides is responsible for the reduction in the fine-grained magnetic particles in this interval. Our findings indicate that pedogenic fine-grained magnetite and maghemite are the first to dissolve, followed by the dissolution of coarser-grained iron oxides into finer particles. This process underscores the complex interplay between magnetic mineral dissolution and grain size distribution in lacustrine sediments, with significant implications for the reliability of paleoenvironmental interpretations derived from magnetic parameters.

A personalized clinical assessment: multi-sensor approach for understanding musculoskeletal health in the frail population

BackgroundSarcopenia is a muscle disorder causing a progressive reduction of muscle mass and strength, but the mechanism of its manifestation is still partially unknown. The three main parameters to assess are: muscle strength, muscle volume or quality and low physical performance. There is not a definitive approach to assess the musculoskeletal condition of frail population and often the available tests to be performed in those clinical bedridden patients is reduced because of physical impairments. In this paper, we propose a novel instrumental multi-domain and non-invasive approach during a well-defined protocol of measurements for overcoming these limitations. A group of 28 bedridden elder people, subjected to surgery after hip fracture, was asked to perform voluntary isometric contractions at the 80% of their maximum voluntary contraction with the non-injured leg. The sensor employed before and/or during the exercise were: ultrasound to determine the muscle architecture (vastus lateralis); force acquisition with a load cell placed on the chair, giving an indication of the muscle strength; surface electromyography (EMG) for monitoring muscular electrical activity; time-domain (TD) near-infrared spectroscopy (NIRS) for evaluating muscle oxidative metabolism.ResultsA personalized “report card” for each subject was created. It includes: the force diagram (both instantaneous and cumulative, expected and measured); the EMG–force diagram for a comparison between EMG derived median frequency and measured force; two graphs related to the hemodynamic parameters for muscle oxidative metabolism evaluation, i.e., oxy-, deoxy-, total-hemoglobin and tissue oxygen saturation for the whole exercise period. A table with the absolute values of the previous hemodynamic parameters during the rest and the ultrasound related parameters are also included.ConclusionsIn this work, we present the union of protocols, multi-domain sensors and parameters for the evaluation of the musculoskeletal condition. The novelties are the use of sensors of different nature, i.e., force, electrical and optical, together with a new way to visualize and combine the results, by means of a concise, exhaustive and personalized medical report card for each patient. This assessment, totally non-invasive, is focused on a bedridden population, but can be extended to the monitoring of rehabilitation progresses or of the training of athletes.

Research on the Control Method of a 2DOF Parallel Platform Based on Electromagnetic Drive

In this paper, a spatial two-degree-of-freedom (2DOF) parallel platform based on electromagnetic redundant drive and its control method are investigated. The platform is redundantly driven by three electromagnetic-spring conforming branched chains, and the design provides better flexibility and responsiveness than conventional parallel structures. The introduction of the electromagnetic drive alleviates the stresses within the conventional rigid redundant drive structure and reduces the detrimental effects associated with rigid redundancy. In this paper, the structure and equivalent SPU model of the platform are first introduced, with S referring to the kinematic sub, P to the spherical sub, and U to the universal joint. The degrees of freedom of the platform are analyzed, and the inverse kinematic model and velocity Jacobi matrix are derived, so as to derive the relationship between the pitch, roll angles, and length of the gimbal chain, and the relational equation between the angle and the current is further established to realize the electromagnetic control of the parallel redundant platform. The control part is realized as follows. Firstly, the angle information of the platform is obtained from the gyroscope to the microcontroller, the filtered angle is derived through the Untraceable Kalman Filter (UKF), and the angle value can be fused with data by both the mathematical model and PID algorithm to introduce the current value required to achieve the balance and realize the balance. In the simulation part, this paper uses Simulink and Simscape in MATLAB for joint simulation, and by giving the simulated trajectory and the desired trajectory of the joints, the driving force diagrams of the three branched chains based on the Least-Second Paradigm method are derived, and the trajectory error and driving force error are given to validate the reliability of the method of this paper.

Theory of Time – 2024 R (Universal Theory for Everything)

“Theory of Time” is a research and analysis report on ‘All kind of Transformation processes’ to find out the reason for changes, this is a Universal Theory & applicable for all natural phenomena. I had found some systematic/ logical/ relational imbalance among the principles of AC Transformer, Ohm’s law, series parallel circuits and law of conservation of energy. I did systematic analysis and research on above said combination principles and identified / formulated/ organized a common transformation mechanism for all and is called ‘Universal Transformation System’(UTS). Here, relative components of all kind of transformation systems are determined, organized systematically for better understanding on relations and also all physical phenomena mechanisms are interpreted through the lens of UTS & found the reformed results are meeting with the general/ natural principles of all kind of transformation systems. I did deeper and wider analysis on electro-magnetic circuits to understand the structure/ mechanism of the transformation system. Law of conservation of energy, AC Transformer’s principles, Newton’s laws and Ohm’s law are base for this theory. By doing relational analysis I could derive Equivalent mechanical transformation principles from Electricity Transformation principles and Mechanical Resistance () to Transformation (RMech.) equation has been successfully formulated. Finally Obtained / reformed results are compared with our practical science and found that the derived principles are meeting with the natural principles of system and its transformation processes. Further, explaining about “how the time is running?”; “what are all the relative components of the time?”; Whether is it possible to stop the time running process? etc. This ©2024 is going to be the final/ completed report on ‘Theory of Time’… in the name of ‘Theory of Nature’. I have finished my research and analysis on all kind of transformation systems. This is updated one, here, I have added some new analysis on secret behind the Black Hole, exact mechanism of Gyroscopic Effects, Donut formation of matter, about human beings, ‘Relation between Centripetal and Centrifugal controls’, importance of Newton’s Absolute time, galactic control on solar system, gravity generator, fusion generator, mechanism of Lagrange Points, there are two differences only in all, review on General Relativity & Special Relativity, constancy of light speed under UTS, optimized free body diagrams, Thermodynamics, ‘𝒎𝒗𝒓’ under UTS, atomic formation structures under gravity & electromagnetism, soul, Law & Justice, tug of war, all mechanisms, you &me

The effects of setup parameters on the measured kinetic output of cervical disc prostheses

Mechanical testing machines are used to evaluate kinematics, kinetics, wear, and efficacy of spinal implants. The simulation of "physiological" spinal loading conditions necessitates the simultaneous use of multiple actuators. The challenge in achieving a desired loading profile lies in achieving close synchronization of these actuators. Errors in load application can be attributed to both the control system and the intrinsic sample response. Moreover, the presence of friction in the setup can have an impact on the measured outcome. The optimization of setup parameters can substantially improve the ability to simulate spinal loading conditions and obtain reliable data on implant performance. In this study, a reproducible kinematic test protocol was developed to evaluate the sensitivity of the kinetic response (i.e., measured loads, moments, and stiffnesses) of a cervical disc prosthesis to several testing parameters. In this context, five ceramic ball and socket sample implants were mounted in a 6 DOF material testing machine and tested with a constant axial compressive force of 100 N in two motion modes: 1) flexion-extension (±7.5°) and 2) lateral bending (±6°). Parameters including rotation rate, slider friction, friction between the samples' articulating surfaces, and moment arm were considered to determine their effects on measured kinetic parameters. The sensitivity analysis indicated that all setup parameters except friction between the samples' articulating surfaces had a substantial effect on the results. The findings were then compared to predictions from a free body diagram to determine the optimal setup parameters. Consequently, the setup with the lowest rotation rate and employing passive sliders yielded results that were consistent with the free body diagram. This study demonstrated the significance of a comprehensive setup evaluation for reliable and reproducible testing of spinal implants, also for comparison between labs.

Analogy use in textbook introductions to isostasy: Presentations, perceptions and physics

In teaching, analogies can be used to support the introduction of a new concept or idea with reference to a more familiar one. This relies on the learner’s correct understanding of the (supposedly) familiar situation, their identification of the relevant similarities (structural relations) between the two situations, and of the limits of the similarities. Without these, analogies may reinforce or introduce misconceptions. Through content analysis of 14 introductory textbooks, semi-structured interviews with four students, and analysis of two analogies, we explore how analogies are used as part of introductions to isostasy in introductory geoscience textbooks. Analogies were ubiquitous, but prior knowledge of the source domain was typically assumed and the majority were not elaborated (explained to the learner). Interviews indicate that, in the absence of sufficient elaboration, students turn to superficial similarities for clues on how to apply the analogies. Many textbooks used analogies amenable to this approach, indicating an alignment between textbook strategy and student reactions. However, giving precedence to superficial similarities over explicit elaboration of structural relations may favor a novice approach to learning. Analyzing an analogy using free-body diagrams demonstrates how an apparently relevant analogy can introduce misconceptions, both in terms of the underlying physics (introducing a fictitious force) and the Earth application (unnatural behavior of the lithosphere) when not sufficiently, or correctly, elaborated. We conclude that the introductory textbooks place much of the responsibility for appropriate use of their analogies, and for avoiding misconceptions, on the learners and their teachers.

Nonlinear Dynamics and Meshing State Transition Analysis of Spalling Defect Gears with Multi-Lubrication Conditions

The purpose of this paper is to analyze the dynamic characteristics and the meshing state transition characteristics of spalling defect gears under various lubrication conditions. The time-varying geometric parameters, motion parameters and load distribution of the gears in the state of positive meshing and reverse impact are analyzed. The time-varying meshing stiffness considering the time-varying friction coefficient under elastohydrodynamic lubrication (EHL), mixed lubrication and boundary lubrication are calculated, and the spalling defect is introduced in the stiffness calculation process. The equivalent lubrication model of the gear is established, the switching condition of the lubrication state is derived, and the distribution of the lubrication state in the torque-speed plane is discussed. The multimeshing state dynamic model of the spalling defect gear is established, and the evolution characteristics of the coexistence response and the transition of the meshing state under different lubrication conditions are simulated by using the attraction domain, phase trajectory, meshing force and bifurcation diagram. The results show that the phase trajectory of the gear with the spalling defect is deformed compared with that of the healthy gear. The change of lubrication state has little effect on the phase trajectory and attraction domain of the gear with spalling defect, but has a great influence on the meshing force. At the spalling boundary, the meshing force is changed abruptly, and the worse the lubrication state, the more obvious the mutation. Due to the influence of spalling on tooth stiffness, it will also affect the meshing force in the nonspalling area.

Discovery of delayed gas production after implantation of a continuous-flow left ventricular assist device and a preliminary exploration of the mechanisms of its occurrence.

To characterize the gas production phenomenon in the animal model of left ventricular assist device (LVAD), and study its mechanism. An in vitro bubble precipitation experiment was conducted, and the blood samples of Parma spp. animals were divided into ordinary group and oxygen-enriched group according to whether they were oxygenated or not at the time of blood collection, and a static control group was set up respectively. Blood gases were drawn and analyzed before and after the experiment. Activate the pump, and the number of air bubbles in the loop was measured by ultrasound at different rotational speeds; CFD was applied to simulate the flow field in the blood pump, and pressure, fluid velocity vector and shear force diagrams were plotted, and a thrombus model was constructed and the flow field was simulated and plotted as a cloud diagram. There was a statistical difference in the number of bubbles in the inflow and outflow tubes of the blood pump (P values of 0.04 and 0.023, respectively), and the number of bubbles in the outflow tubes of both groups was significantly higher than the number of bubbles in the inflow tubes. The number of bubbles in the tubes of both the oxygen-enriched and normal groups was significantly higher than that in the inflow group. In both the normal and oxygen-enriched groups, more gas was produced at higher speeds than at lower speeds. Blood gas analysis showed that the reduced gas composition in the blood was mainly oxygen. Flow field simulation results: the high rotation speed group had lower central pressure and greater scalar shear. The thrombus simulation group was more prone to turbulence, sudden pressure changes, and greater shear than the normal group. Blood gas production is associated with higher partial pressures of blood oxygen, higher rotation speed, and intrapump thrombosis, and the mechanism of pump gas production is degassing of dissolved gases rather than cavitation of water, and the gas released is most likely to have oxygen. The degassing phenomenon is an warning factor for pump thrombosis.

Insight into the Intra and Inter-wire Magnetic Interactions of Co Nanowire Arrays by FORC Diagrams

Insight into the Intra and Inter-wire Magnetic Interactions of Co Nanowire Arrays by FORC Diagrams

Analisis Korelasi Kualitas Free-Body Diagram dan Penguasaan Konsep Siswa Pada Materi Dinamika

The goal of learning physics is not to memorize the formulas or equations, but to increase conceptual understanding. For increase conceptual understanding about motion, force analysis skill is the most fundamental skills needed by students. Free-body diagram will help students to analyze force. So this study aims to determine and analyze the correlation between quality of free-body diagrams and mastery of dynamics concepts. The research was conducted at SMAN 2 Sungai Penuh. The population is students of XI MIA. Using whole population sampling, 50 students. The learning process and tests on dynamics were to gather the data about quality of free-body diagram and concept understanding. Both data was normally distributed and linearly related with a positive correlation shown by a scatterplot. The Pearson correlation test conducted to show the relationship between variables. There was high correlation between the quality of free-body diagrams and conceptual understanding as indicated by the Pearson correlation coefficient . The correlation was highly positive, which means that students who draw high quality free-body diagram tend to have high conceptual understanding.

CИЛОВОЙ АНАЛИЗ ПЛОСКИХ РЫЧАЖНЫХ МЕХАНИЗМОВ ВЕКТОРНЫМ МЕТОДОМ

An analytical method is presented for force analysis of plain lever mechanisms with one degree of freedom, based on the vector method. Using the example of a two-drive structural group, a method is outlined for finding reaction vectors in all its kinematic pairs, while maintaining the clarity and consistency of the solution inherent in the graphic-analytical method of diagrams of component forces. An original analytical description is given for finding the vectors of tangential and normal components of reactions in kinematic pairs. Application of the proposed method of force analysis makes it possisble to find reaction vectors in kinematic pairs without compiling and solving complex systems of equilibrium equations or graphical construction. Adaptation of the proposed force analysis in modern mathematical packages allows for the study of plain lever mechanisms with one degree of freedom in a short time and with high accuracy.

The driven unicycle

The free-body diagram of a unicycle pedalled across level ground is analysed, showing that riders must tilt their bodies into the direction of the acceleration. A comparison is made with an unpowered round object rolling without slipping up or down an inclined plane. A Newtonian analysis predicts an acceleration of the unicycle as a function of the tilt angle that is in good agreement with measurements of an actual unicycle using a smartphone.

Construction of complex high order subharmonic vibrations in a nonlinear rotor system I: Eigenvalue dynamics and prediction

In real turbomachinery testing, we always confront strange high order vibrations which scatter a few points or draw some local lines in the experimental bifurcation diagrams. Such vibrations maybe ignored due to the lack of experiences and knowledge while they can be important in design and operation due to the nonsmooth jumping and instability. This paper proposes a new method for predicting the complex high order subharmonic vibrations for a nonlinear rotor system with light rub. The nonlinearity is induced by the contact of the bristles and the rotor. A continuous nonlinear rotor system is established based on the geometric and bending force diagrams. We discretize the complex orbits and built implicit mappings between the adjacent nodes. A directional eigenfunctional matrix is constructed which maps each nodes and passes the perturbation along the orbits for semi-analytical prediction of the high order subharmonic vibrations. Stability criterion is defined. Numerical bifurcation diagrams and harmonic contours are presented for quick glance of the global subahrmonic vibrations. Two local subharmonic vibrations of odd orders are succesfuly predicted. Local high order subharmonic vibrations of “full tree” and “half tree” are predicted and achieved accurately. An experimental platform is established to compare the semi-analytical predictions with experimental results. The research delivers a new perspective for predicting and computing the high order subharmonic vibrations in nonlinear rotor system.

A computational implementation of Vector-based 3D Graphic Statics (VGS) for interactive and real-time structural design

This article presents a computational implementation for the Vector-based Graphic Statics (VGS) framework making it an effective CAD tool for the design of spatial structures in static equilibrium (VGS-tool). The paper introduces several key features that convert a purely theoretical graph and geometry based framework into a fully automated computational procedure, including the following new contributions: a general algorithm for constructing 3-dimensional interdependent force and force diagrams; the implementation of a procedure that allows the interdependent transformation of both diagrams; an approach to apply specific constraints to the computationally generated diagrams; the integration of the algorithms as a plug-in for a CAD environment (Grasshopper3D of Rhino3D). The main features of the proposed framework are highlighted with a design case study developed using the newly introduced CAD plug-in (namely the VGS-tool). This plugin uses synthetic-oriented and intuitive graphical representation to allow the user to design spatial structures in equilibrium as three-dimensional trusses. The goal is to facilitate collaboration between structural engineers and architects during the conceptual phase of the design process.

Bifurcation Analysis and Sticking Phenomenon for Unmanned Rotor-Nacelle Systems with the Presence of Multi-Segmented Structural Nonlinearity

Whirl flutter is a phenomenon caused by an aeroelastic instability, causing oscillations to propagate in manned or unmanned rotor-nacelle type aircraft. Under the conditions where multi-segmented freeplay are present, complex behaviors can dominate these oscillations and can lead to disastrous consequences. This study investigates a rotor-nacelle system with multi-segmented stiffnesses with a freeplay gap to encompass the real-world influences of aircraft. The mathematical aerodynamics model considers a quasi-steady application of strip theory along each blade to outline the external forces being applied. A free-body diagram is then used to incorporate the structural stiffness and damping terms with multi-segmented freeplay considered in the structural stiffness matrix. Multiple structural responses of the defined system are investigated and characterized to determine the influence of varying symmetric and asymmetric multi-segmented stiffnesses with varying gap parameters, including a route to impact investigation. The findings are characterized using phase portraits, Poincaré maps, time histories, and basins of attraction. It is found that under these conditions, the structural influences can lead to aperiodic oscillations with the existence of grazing bifurcations. Furthermore, these results unveil that under certain conditions and high freestream velocities, the sticking phenomenon becomes apparent which is strongly dependent on the strength of the multi-segmented representation, its gap sizes, and its symmetry. Lastly, a route to impact study shows the strong coupled influence between pitch and yaw when asymmetric conditions are applied and the possible presence of grazing-sliding bifurcations. The numerical simulations performed in this study can form a basis for drone designers to create reliable rotor-nacelle systems resistant to whirl flutter caused by freeplay effects.

COMPLEX RESISTANCE OF A COMPRESSED-BENT ROD TAKINGINTO ACCOUNT ELASTIC COMPLIANCE OF ITS SUPPORT

This work deals with the urgent problem in the mechanics of a deformable solid: studying factors of the stress-strain state of a single-span statically indeterminate beam with complex boundary conditions that is under conditions of complex resistance (axial compression with plane transverse bending). To solve the problem, both analytical methods (the method of forces in the form of “five” support moments, the method of initial parameters) and the numerical finite difference method with a “linear” grid with density n=8 were used. The necessary resolving equations and matrices are given to take into account changes in the rigidity parameter of the right hinged support and variations in concentrated and uniformly distributed loads, both along the axis of the beam and across it. In the final form, diagrams of deflections, bending moments and shear forces were constructed for specific values of bending rigidity and the degree of elastic compliance of the right hinge-yielding support. Reliability of the theoretical principles and applied results obtained by the authors is confirmed on the basis of the given alternative calculation methods.