Rigid Body Research Articles

How might a planet between mars and jupiter influence the inner solar system? effects on orbital motion, obliquity, and eccentricity

The Kepler Space Telescope and the Transiting Exoplanet Satellite Survey have discovered a wide diversity of exoplanetary system architectures. In comparison to exoplanet systems, one peculiarity in the solar system is the distinct lack of a super-Earth analog, a planet archetype prevalent in the exoplanet population. Models suggest however, that the formation of an Earth-to-Super-Earth mass planet could have readily occurred in the inner regions of the solar system (<3 AU) without the migration of the Jovian worlds. In this study, we test the consequences of such a hypothesis using a three-dimensional (3D) N-Rigid-Body integrator. Previous work employed numerical models that assumed planets and interacting bodies as point-mass particles and neglected changes in spin evolution and obliquity. These neglects of one-dimensional models may be problematic when attempting to accurately track the orbital motion of a planet. With a 3D model in which the planet is modeled as a rigid body to account for its finite size and rotation, we investigate three inner terrestrial planets over 2 Myr periods and found that an additional super-Earth sized planet between 2 and 3.5 AU would have (i) destabilized Earth’s orbit over timescales of 1 Myr, (ii) increased Mars’s obliquity by ∼55°, and (iii) perturbed the eccentricity of Venus by up to e∼0.4. Our study explores an “alternate fate” of the terrestrial planets and our results suggest that if a super-Earth had formed in the inner solar system, orbital evolution histories of many terrestrial worlds would have looked very different.

An Enriched Polyhedral-based Simulation for the Contact Modeling with Form Defects and Mechanical Loads

Contact modeling is an important activity in the geometrical and tolerancing management. The research on contact modeling using methods based on sets of constraints has focused on the stack-up functions or graph reductions for the accumulation of geometric variations. Even when the Skin Model paradigm is used to simulate form defects on mating surfaces, the impact of disregarding those defects has not been formally discriminated. In this paper, an enriched polyhedral-based approach for the contact modeling of mechanisms is proposed. The contact is simulated through a rigid body model with no frictional forces based on the screw theory. In this method, the external loadings on the mechanism are translated into an additional half-space in the polyhedron that imposes an additional restriction to the polyhedron operand. By explicitly including the external mechanical loadings, the impact of the form defects on a functional condition can be discriminated precisely. In this paper, a case study of a sliding contact between two mating parts of a spectrometer is presented to further illustrate the method advantages.

Theoretical characteristics of a three-point Roberts linkage.

The Roberts linkage is recognized for enabling long-period pendulum motion in a compact format. Utilizing this characteristic, we are developing a three-point Roberts linkage for vibration isolation systems, with an eye toward its potential contribution to the development of next-generation interferometric gravitational wave antennas. In this article, we derived the equations to determine the essential parameters when using this linkage as a vibration isolation system, namely, the equivalent pendulum length and the relationship between translational motion of the center of mass and rigid body rotation, from size parameters. In addition, we analyzed the behavior in response to various errors.

CME Velocity Field Calculation Model Based on an Unsupervised Transformer Optical Flow Network

The optical flow algorithm (OF) is one the main methods for calculating image velocity field and has many applications in space weather. Most OF calculations are applied to the motion of labeled rigid objects and are not suitable for velocity detection of high-energy particles, such as in a coronal mass ejection (CME). Fluctuations in exposure time and the influence of space weather will lead to inconsistent brightness of the same feature point at different times. To address this problem, we propose an unsupervised multiscale optical flow network based on Vision Transformer, named UTFlowNet. The network comprises a multiscale feature extraction module and a coarse-to-fine global optical flow calculation module. The movement of high-energy particles emitted during a CME eruption follows certain physical rules. Therefore, we apply fluid motion–based loss functions to analyze the motion of high-energy particles more effectively, addressing the problem of CME motion field extraction. Our method can be applied to the real-time automatic extraction of a CME’s velocity field and performs well with inconsistent brightness, large-scale motion, and strong CME noise. Additionally, we can estimate subpixel level fine-grained velocity. Our model may be affected by overfitting during cross–data set inference, so we encourage performing a small amount of transfer learning on new data sets to mitigate this issue. In order to verify the accuracy of our method, we conducted experiments and verification on the Solar and Heliospheric Observatory LASCO C2 data and the High Altitude Observatory MLSO data. We constructed a large-scale displacement simulation data set based on LASCO C2 data and tested on it, achieving the best results.

Investigation of higher-order springing of a ship in regular waves by experimental analysis and two-way CFD-FEA coupled method

In this paper, the higher-order springing phenomenon is addressed for a segmented barge ship model through experimental and numerical measures. An efficient in-house two-way coupled numerical solver between Computational Fluid Dynamics (CFD) and Finite Element Analysis (FEA) is developed and validated against experimental results. The coupling method is based on a domain-separated approach and necessitates the resolution of individual boundary value problems in distinct domains. To ensure convergence within these individual domains, an implicit numerical scheme is employed and further facilitated exchange of variables for coupling. The current approach emphasizes the overall convergence between two solvers, maintaining a strongly coupled setup to comprehensively address fluid-structure interaction phenomena, including added mass and damping effects. A series of tank tests were conducted first to measure the wave-induced sectional loads and motions, during which the springing responses to very high-order harmonics of wave load were observed. By comparing the numerical prediction with the tank test results for rigid body motion and flexible vertical bending moment (VBM), the proposed numerical method demonstrated agreement with experimental results, affirming its validity and robustness. Finally, the springing response up to 14th order harmonics is discussed and investigated.

Numerical Analysis of the Cell Droplet Loading Process in Cell Printing

Cell printing is a promising technology in tissue engineering, with which the complex three-dimensional tissue constructs can be formed by sequentially printing the cells layer by layer. Though some cell printing experiments with commercial inkjet printers show the possibility of this idea, there are some problems, such as cell damage due the mechanical impact during cell direct writing, which include two processes of cell ejection and cell landing. Cell damage observed during the bioprinting process is often simply attributed to interactions between cells and substrate. However, in reality, cell damage can also arise from complex mechanical effects caused by collisions between cell droplets during continuous printing processes. The objective of this research is to numerically simulate the collision effects between continuously printed cell droplets within the bioprinting process, with a particular focus on analyzing the consequent cell droplet deformation and stress distribution. The influence of gravity force was ignored, cell droplet landing was divided into four phases, the first phase is cell droplet free falling at a certain velocity; the second phase is the collision between the descending cell droplet and the pre-existing cell droplets that have been previously printed onto the substrate. This collision results in significant deformation of the cell membranes of both cell droplets in contact; the third phase is the cell droplet hitting a rigid body substrate; the fourth phase is the cell droplet being bounced. We conducted a qualitative analysis of the stress and strain of cell droplets during the cell printing process to evaluate the influence of different parameters on the printing effect. The results indicate that an increase in jet velocity leads to an increase in stress on cell droplets, thereby increasing the probability of cell damage. Adding cell droplet layers on the substrate can effectively reduce the impact force caused by collisions. Smaller droplets are more susceptible to rupture at higher velocities. These findings provide a scientific basis for optimizing cell printing parameters.

An unresolved SPH-DEM model for simulation of ductile and brittle surface erosion by abrasive water-jet (AWJ) impact

The abrasive water-jet (AWJ) erosion process involves the complex interaction between fluid medium, abrasive particles and solid material, which brings great challenges to the establishment of numerical model. Because traditional grid-based methods are not suitable for the problems of local deformation and material removal, the meshfree method smoothed particle hydrodynamics (SPH), based on the unresolved coupling and the discrete element method (DEM), is adopted to establish the model for AWJ study. The fluid medium is treated as a weakly compressible viscous liquid, the solid material is treated as an elastic-plastic material, and the abrasives are treated as rigid bodies. The fluid and solid phases are discretized with SPH particles, and the abrasives are described with DEM particles. The Johnson-Cook (J-C) and Johnson-Holmquist-II (JH-2) constitutive models are used to describe the stress-strain behavior of ductile and brittle materials, respectively. The effectiveness of the numerical model is further verified by AWJ impact experiments. The plastic deformation and cumulative failure characteristics of ductile materials, and the crack formation and propagation characteristics of brittle materials are systematically analyzed. The results provide insight for the AWJ research and lay a foundation for investigation of other complex fluid-particle flow in a numerical way.

On delivering polar solvation free energy of proteins from energy minimized structures using a regularized super-Gaussian Poisson-Boltzmann model.

The biomolecules interact with their partners in an aqueous media; thus, their solvation energy is an important thermodynamics quantity. In previous works (J. Chem. Theory Comput. 14(2): 1020-1032), we demonstrated that the Poisson-Boltzmann (PB) approach reproduces solvation energy calculated via thermodynamic integration (TI) protocol if the structures of proteins are kept rigid. However, proteins are not rigid bodies and computing their solvation energy must account for their flexibility. Typically, in the framework of PB calculations, this is done by collecting snapshots from molecular dynamics (MD) simulations, computing their solvation energies, and averaging to obtain the ensemble-averaged solvation energy, which is computationally demanding. To reduce the computational cost, we have proposed Gaussian/super-Gaussian-based methods for the dielectric function that use the atomic packing to deliver smooth dielectric function for the entire computational space, the protein and water phase, which allows the ensemble-averaged solvation energy to be computed from a single structure. One of the technical difficulties associated with the smooth dielectric function presentation with respect to polar solvation energy is the absence of a dielectric border between the protein and water where induced charges should be positioned. This motivated the present work, where we report a super-Gaussian regularized Poisson-Boltzmann method and use it for computing the polar solvation energy from single energy minimized structures and assess its ability to reproduce the ensemble-averaged polar solvation on a dataset of 74 high-resolution monomeric proteins.

In-situ synchrotron high energy X-ray diffraction study on the deformation mechanisms of D019-α2 phase during high-temperature compression in a TiAl alloy

The α2 phase with an ordered hexagonal structure has a strong mechanical anisotropy. The limited plasticity interacting with crystallographic texture formation undoubtedly complicate the deformation mechanisms of the α2 phase. Taking advantage of in-situ synchrotron high energy X-ray diffraction (HEXRD), this study unveils the origin of the α2 texture and its correlation with plastic deformation. Upon loading at 800 °C, the dislocation glide in the γ phase initiates at a stress of 370 MPa and that in the α2 phase at a stress of 670 MPa. Nevertheless, the texture evolution of the α2 phase sets in in parallel with that of the γ phase, and these textures are preliminarily established at a stress of 650 MPa. A main <11 2‾ 0> fiber texture with the c axis of the α2 unit cell aligned vertically to the compression axis has been unexpectedly evolved. This texture forms primarily via rigid body rotation and is correlated with glide and twin activation in the neighboring γ phase. The preferential orientation primarily favors double prismatic glide in α2 and in addition triggers the tensile twin activation. The grain rotation caused by the tensile twin slightly affects the α2 transverse texture evolution. The results unveil a complex interaction between the α2 phase deformability, texture evolution and the combined elastic-plastic deformation of the phases γ and α2 in TiAl alloys.

Elastodynamic analysis of rotating solids by novel nodal position finite element method

This study develops a novel 8-node isoparametric hexahedral element using the Nodal Position Finite Element Method (NPFEM) for elastodynamic analysis of rotating solids. The element also incorporates the flexural modes directly into its element shape function to alleviate the shear locking when modeling the bending deformation of solids. Unlike conventional displacement-based finite element methods, which require the decoupling of elastic deformation from rigid-body motions, the NPFEM eliminates this process by directly representing strain and kinetic energies through nodal position coordinates, which avoids potential approximation errors in the decoupling process. To validate the accuracy and efficacy of this new NPFEM solid element, numerical simulations of a beam under static and dynamic loads are conducted and benchmarked against the theoretical solutions. Then, dynamic analysis of a rotating blade demonstrates that the NPFEM element can directly account for the centrifugal stiffening effect and superharmonic resonance of rotating blades without resorting to conventional methods. The successful implementation of this NPFEM element in complex simulations highlights its potential to provide significant advancements in computational mechanics.

Physics-informed neutral network with physically consistent and residual learning for excavator precision operation control

The data-driven methodologies can establish accurate Inverse Dynamics Model (IDM) of the excavator thus improving control precisions. However, the inherent black-box nature of these models often results in overfitting to the dataset, leading to predictions that deviate from the constraints of physical system. Consequently, this can lead to controller failures, introducing unpredictable behavior that threatens operation precision. In addition, the uncertainty of the external disturbance poses great challenge to the precision of controller. This study presents a physics-informed neural network to build accurate IDM with physical consistency. The Rigid Body Dynamics (RBD) of the excavator are coupled within a Deep Lagrangian Network (DeLaN), while a Convolutional Neural Network (CNN) and a Long Short-Term Memory Network (LSTM) are employed to assimilate the residual nonlinear characteristics, such as hydraulic flexibilities and stick–slip friction. To the uncertainty of the external disturbance, the Prescribed Performance Inverse Dynamics Controller combination with the DeLaN-CNN-LSTM model (PPIDC-DCL) is constructed for precise control by constraining the control error within a finite region. The experimental results demonstrate that the model captures the underlying structure of the dynamic and builds the IDM with high accuracy and robustness. Moreover, the PPIDC-DCL controller effectively constrains the control error and realizes precision control. The proposed method has potential applications and provides novel insights for achieving precise operation control of excavators.

“Symptoms” of Chinese Women’s Appearance Anxiety

The pervasive issue of “appearance anxiety” among young females has emerged as a significant psychosocial concern in contemporary society. This study employs qualitative research methods to investigate the social mechanisms underlying the development of “appearance anxiety” among young women, adopting a sociological standpoint on body-related matters. The findings of this study reveal that social factors contribute to the development of “appearance anxiety” in young women, as they strive to establish intimate relationships and attain societal validation. Consequently, young women are compelled to conform to societal gender norms, subjecting themselves to the scrutiny of aesthetic standards, while simultaneously resisting the detrimental effects of “appearance anxiety” through various forms of body consumption practices. Although the proliferation of information network media has provided women with expanded platforms for self-presentation, it has concurrently reinforced both societal aesthetic ideals and consumerist culture. Moreover, the media’s perpetuation of rigid body image standards, coupled with the propagation of misconceptions about body consumption, further entangles young women in a cyclic social framework characterized by “societal aesthetics - appearance anxiety - body consumption.”

Investigation of the influence of the support structure on violin components in experimental modal analysis

AbstractVarious support structures are utilized in the investigation of the vibration characteristics of violins. Common mountings include rigid ropes, rubber ropes, and foam blocks arranged in different configurations. The impact of the support structure on the outcomes of experimental modal analysis on musical instruments has yet to be explored. This study aims to determine the most suitable support structure for experimental modal analysis of violin components by comparing results from various experimental modal analyses conducted on a violin top and back using different mounting configurations. Results were evaluated using criteria such as vibration characteristics, rigid body frequencies, number of modes, modal damping, amplitude, and mode shapes. In summary, the support structures using rubber ropes and foam blocks yielded the best results. The recommended configurations for rubber ropes are X‐shaped or orthogonal to the longitudinal axis of the violin plates. When using foam blocks, it is essential to select foam with appropriate material parameters, as differences in density and stiffness resulted in significant variations of the measurement results.

Inverse dynamics analysis of 4-DOF stacking robot with closed chain structure

A four-degree-of-freedom PR1300 stacking robot with two parallel quadrilateral structures connected in series at the shoulder was designed. The hybrid robot with local closed chains has the characteristics of compact structure, high stiffness, and high modularity. To solve the dynamic problem of the hybrid robot. Firstly, by analyzing the induced relationship between joints, the stacking robot with a local closed chain structure is transformed into two branch chain mechanisms, and the kinematic model of the robot is established using the D-H parameter method. Secondly, the Kane method is applied to model the dynamics of the two branch chains separately, and the rigid body dynamics Kane equation of the entire 4-DOF stacking robot with a closed chain structure is obtained through the augmented matrix. Finally, the SolidWorks Motion mechanical simulation platform and MATLAB software were used to program dynamic simulations and numerical calculations, and the results were compared to verify the correctness of the dynamic theory derivation. This theory provides a necessary theoretical basis for the subsequent synthesis of robot dynamic scales.

Non-Inertial Dynamic Analysis of 3-SPS/U Parallel Platform by Screw Theory and Kane’s Method

This paper presents an improved method for the non-inertial dynamic analysis of the 3-SPS/U parallel platform (3-SPS/U PM), employing the screw theory and Kane’s method, where S, P, and U denote spherical, prismatic, and universal joints, respectively. The proposed method extends the traditional inertial dynamic analysis to non-inertial systems. First, the generalized screw method is introduced, followed by the derivation of a transformation formula that adapts the screw method to various co-ordinate systems. Subsequently, the velocities and accelerations of each rigid body within the platform under non-inertial conditions are examined by combining the extended screw method with the system’s inverse kinematics model. The extended screw method is not only conceptually simple, but also adaptable to other non-inertial systems. Finally, the standard non-inertial dynamic model of the 3-SPS/U PM is derived through the Kane’s method and validated by the co-simulations with RecurDyn (V9R5) and MATLAB/Simulation (2019b).

Active constrained motion control for a robot-assisted endoscope manipulator in pediatric minimal access surgery.

Robot-assisted laparoscopic surgery has three main system requirements: safety, simplicity, and intuitiveness. However, accidental movement of the endoscope due to body fatigue and misunderstanding of the verbal orders between the surgeon and assistant will contribute to highly unexpected tool-tissue interactions, particularly in pediatric minimal access surgery with restricted working space. This study introduces a compact, lightweight endoscope manipulator with a mechanical remote-center-motion function. Using a custom-designed human-machine interface, the surgeon can intuitively control the movement of the endoscope manipulator over their view. In addition, an active constrained motion control algorithm is proposed to generate a forbidden-region constraint for avoiding collisions between the endoscope tip and surrounding organs in a pediatric abdominal cavity with restricted space. Simulations and experiments demonstrate the performance of the proposed compact endoscope manipulator and the active constrained surface tracking control scheme.

A novel approach to solving Euler’s nonlinear equations for a 3DOF dynamical motion of a rigid body under gyrostatic and constant torques

This research focuses on approaching a new technique to solve the rotary movement of a three degrees-of-freedom (DOF) semi-symmetric rigid body (RB) affected by a gyrostatic torque (GT) and under the influence of the RB’s constant-fixed torques (RBCFTs). The governing nonlinear differential equations (NDEs) for the RB are derived from the famous Euler’s equations, along with another system to calculate Euler’s angles, which gives an accurate solution for the RB’s position during its motion. In the case of a semi-symmetric body about its minor axis, novel analytical solutions for the RB’s angular velocities are presented in addition to the solutions of Euler’s angles. Our procedure to obtain these solutions arises through decoupling the governing NDEs into two coupled DEs, and the averaged time parameter is used. General solutions of the later DEs are presented in view of series expansions. The impact of the internal and external torques on the body’s motion is graphically simulated, which gives an overview of the periodicity of the derived solution and the effect of various values of these torques on the solution. Moreover, these simulations present other prospects for the body’s stability by analyzing them using the famous Lyapunov function. The importance of this study arises from its wide applications in our lives in many fields, such as mathematics and physics. It also holds immense potential for enhancing mechanical systems, elucidating celestial motion, and enhancing spacecraft efficiency.

Extended influence coefficient method for meshing stiffness evaluation of spur gears considering rotor flexibility

Rotor-supported gears are applied in transmission systems, and the rotor flexiblility leads to the misalignment of the gear pair with multiple degrees of freedom, which ultimately leads to the decrease of meshing stiffness. To evaluate the meshing stiffness of rotor-supported gears, the extended influence coefficient method (EICM) is proposed in this paper. Firstly, the gear contact position adjustment under misalignment condition is carried out. Then, the extended influence coefficients of bending, shearing, axial compression, Hertzian contact and fillet foundation deformation of gears are derived to obtain the extended influence coefficient matrix. Afterward, the load-deformation equations under different contact states are obtained, and the meshing stiffness is calculated. Subsequently, a cantilever rotor-gear coupling dynamic model is established by the rigid body element-extended influence coefficient method (RBE-EICM), and the dynamic meshing stiffness considering rotor flexibility is obtained. The accuracy of EICM and RBE-EICM is verified by comparison with finite element method, literature methods and experimental data, respectively. Finally, the effects of supporting layout, input torque and rotor diameter on the dynamic characteristics of cantilever rotor-supported gears are discussed.

Static and free vibration response of FGM plates using higher order shear deformation theory and strain-based finite element formulation

The primary objective and novelty of this work lie in the development of a new four-node quadrilateral finite element based on strain-based high-order shear deformation theory (HSDT). This is the first study to apply this innovative approach to analyze both the static and free vibration behaviors of functionally graded (FG) plates. Another key novelty is the reduction in the number of unknowns to five, unlike other high-order shear deformation theories that employ a larger number of unknowns. This reduction is achieved by applying the condition of zero transverse shear stress at the top and bottom free surfaces of the FG plate and by assuming that the transverse shear strains are sinusoidally distributed through the thickness. The material properties of FG plates are modeled to vary according to a simple power law based on the volume fractions of their constituents. The developed finite element possesses five degrees of freedom (DOFs) per node, resulting from the combination of two strain-based elements: the first is a membrane with two DOFs, and the second is a bending plate with three DOFs. The displacement fields of the proposed element are expressed using high-order terms based on the strain approach, which satisfy compatibility equations and rigid body modes. Furthermore, the concept of the neutral surface is introduced to eliminate membrane-bending coupling. The elementary stiffness and mass matrices are derived using both the total potential energy principle and Hamilton’s principle. The performance and convergence of the proposed element are validated through examples from the literature.

Gust load alleviation of a flexible flying wing with linear parameter-varying modeling and model predictive control

This paper presents a practical model predictive control (MPC) framework for gust load alleviation of a flexible flying wing. Both the controller solving and state estimation are based on a reduced-order model, which features a linear parameter-varying (LPV) form, avoiding online linearization and reducing the scale of the corresponding quadratic programming problem. An improved modeling and model reduction process is used to enhance modeling efficiency and ensure that the reduced-order model can accurately capture the rigid-flexible coupled characteristics of the flexible flying wing under arbitrary gusts. By reconstructing the output of the control-oriented model to include both rigid-body motion and flexible vibrations, the rigid-flexible coupled multi-objective control is established as an MPC problem for reference tracking. The online optimization is formulated in a sparse fashion and combined with an iterative algorithm based on predicted trajectories, describing the variation of model dynamics within the prediction horizon more accurately. With a time-varying Kalman estimator for state updating, the closed-loop simulations are performed for gust alleviation performance validation. Additionally, the real-time potential of the proposed MPC framework is demonstrated through Monte Carlo simulations.