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Keywords = rigid body motion

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12 pages, 229 KiB  
Article
Rehabilitation Treatment for Shoulder Pain in Parkinson’s Disease: A Pilot Study
by Emanuele Amadio, Luca Cimini, Ilaria Ruotolo, Alessandra Carlizza, Anna Berardi, Andrea Marini Padovani, Giovanni Sellitto, Giovanni Fabbrini and Giovanni Galeoto
J. Clin. Med. 2025, 14(4), 1127; https://doi.org/10.3390/jcm14041127 - 10 Feb 2025
Viewed by 206
Abstract
Background/Objectives: Due to rigidity, musculoskeletal pain is more common in people with Parkinson’s disease (PD) compared with age-matched older adults, and the shoulder is one of the body parts that is most involved. In the literature, there is no clear standard for the [...] Read more.
Background/Objectives: Due to rigidity, musculoskeletal pain is more common in people with Parkinson’s disease (PD) compared with age-matched older adults, and the shoulder is one of the body parts that is most involved. In the literature, there is no clear standard for the treatment of shoulder pain in people with PD. This clinical trial study aimed to evaluate the effectiveness of physiotherapy treatment for people with PD with painful shoulders. Methods: The main goals were improvements in pain intensity, balance, quality of life (QoL), and activities of daily living (ADL), evaluated with the Parkinson’s Disease Questionnaire 39 (PDQ-39), Berg Balance Scale (BBS), Community Integration Questionnaire (CIQ-R), 12-Item Short-Form Survey (SF-12), Disabilities of the Arm, Shoulder, and Hand (DASH) scale, and Numeric Pain Rating Scale (NPRS). Also, the evaluation comprised range of motion (ROM) evaluation with a goniometer and the Medical Research Council (MRC) scale. The inclusion criteria of this study were a diagnosis of PD associated with shoulder pain, and a stage of disease of 1–2 on the Hoehn and Yahr scale. Results: The sample comprised 16 participants; the mean age of the participants was 72. Through feedback collected from the individuals participating in this study, it emerged that the rehabilitation approach specifically designed for individuals suffering from shoulder pain associated with Parkinson’s disease produced remarkable results. Conclusions: These results were confirmed by a series of statistically significant data, which showed significant improvements in several areas: joint mobility, muscle strength, motor coordination, the ability to perform daily activities, emotional state, pain reduction, QoL improvement, and balance in both dynamic and static conditions. Full article
(This article belongs to the Section Clinical Rehabilitation)
12 pages, 1496 KiB  
Article
Center of Mass Estimation During Single-Leg Standing Using a Force Platform and Inertial Sensors
by Ryosuke Takahashi and Motomichi Sonobe
Sensors 2025, 25(3), 871; https://doi.org/10.3390/s25030871 - 31 Jan 2025
Viewed by 395
Abstract
Single-leg standing is a conventional balance evaluation method used in medicine. Although the center of mass (COM) displacement should be evaluated to determine balance quality, no practical COM estimation methods have been developed for single-leg standing. This study aimed to estimate the COM [...] Read more.
Single-leg standing is a conventional balance evaluation method used in medicine. Although the center of mass (COM) displacement should be evaluated to determine balance quality, no practical COM estimation methods have been developed for single-leg standing. This study aimed to estimate the COM displacement in the anteroposterior and mediolateral directions during single-leg standing using practical measurements. We used a force platform and three inertial measurement units to estimate the COM displacement based on rigid-link models in the sagittal and frontal planes. The rigid-link models were composed of the stance leg, upper body, and non-stance leg. Seven healthy male subjects participated in the experiment to validate the estimation accuracy. The COM estimation accuracy was verified by comparison with measurements obtained using an optical motion capture system. The root mean square error of this method was 1.18 mm in the sagittal plane and 1.26 mm in the frontal plane. This technique will contribute to the detailed evaluation of individual balance abilities in the medical and sports fields. Full article
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19 pages, 6136 KiB  
Article
Numerical Simulation Study of the Motion Characteristics of Autonomous Underwater Vehicles During Mooring Lurking Procedure
by Yuyang Hu, Zhaoyong Mao, Bo Cheng, Bo Li and Wenlong Tian
J. Mar. Sci. Eng. 2025, 13(2), 275; https://doi.org/10.3390/jmse13020275 - 31 Jan 2025
Viewed by 452
Abstract
A two-dimensional coupled dynamics model for a moored autonomous underwater vehicle (AUV) was developed using the lumped mass method for mooring cable dynamics and the Newton-Euler method for rigid body dynamics. This model enables the integrated simulation of AUV motion, flow field interactions, [...] Read more.
A two-dimensional coupled dynamics model for a moored autonomous underwater vehicle (AUV) was developed using the lumped mass method for mooring cable dynamics and the Newton-Euler method for rigid body dynamics. This model enables the integrated simulation of AUV motion, flow field interactions, and mooring cable behavior. The study investigates the effects of varying ocean current velocities and mooring cable lengths on AUV motion responses. The results indicate that under the influence of mooring forces, the AUV stabilizes near its equilibrium position after release and undergoes periodic oscillatory motion. Specifically, when the X-direction oscillation completes two cycles and the Y-direction oscillation completes four cycles, the AUV demonstrates an 8-shaped trajectory, with maximum motion amplitudes observed. These findings provide insights into the dynamic behavior of moored AUVs in ocean environments, contributing to the design and operation of long-term underwater monitoring systems. Full article
(This article belongs to the Section Ocean Engineering)
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24 pages, 6889 KiB  
Article
Development of a Simplified Human Body Model for Movement Simulations
by Michał Olinski and Przemysław Marciniak
Appl. Sci. 2025, 15(3), 1011; https://doi.org/10.3390/app15031011 - 21 Jan 2025
Viewed by 449
Abstract
The main goal of this paper is to develop a simplified model of the human body motion system that enables its application for movement simulations and the analysis of the kinematic and dynamic parameters occurring during the performance of activities. The model is [...] Read more.
The main goal of this paper is to develop a simplified model of the human body motion system that enables its application for movement simulations and the analysis of the kinematic and dynamic parameters occurring during the performance of activities. The model is established on the basis of the modified Hanavan model and consists of rigid solids with simple geometry that are connected mostly with spherical joints. Based on anthropometric data from the literature, a complete set of equations parameterizing the dimensions and mass of each segment was formulated. The equations depend on only two body measurements (height and mass). The model is built in the Adams system as a 3D numerical dynamic model and tested using data gathered with an IMU sensors system. A volunteer lifting an object with a bent spine from the ground with both hands is used for this purpose. Three angles (from the IMUs) are applied to each model’s joint to best simulate human movement and to analyze the angular displacements, velocities, and torques. These results are consistent with theoretical expectations and assumptions, thus proving that reproducing human movements with the developed model is possible and that it also allows various parameters of the human body to be obtained. Full article
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18 pages, 11030 KiB  
Proceeding Paper
Numerical Simulation Research on Separation Process of Jettisoned FDR from Civil Aircraft
by Feifan Zhang and Zhaoke Xu
Eng. Proc. 2024, 80(1), 25; https://doi.org/10.3390/engproc2024080025 - 2 Jan 2025
Viewed by 118
Abstract
The safety of Jettisoned FDRS in the process of separation from an aircraft is a key factor in designing Jettisoned FDRs and enabling them to pass airworthiness certification and be widely used in civil aircraft. The separation process of Jettisoned FDR installed on [...] Read more.
The safety of Jettisoned FDRS in the process of separation from an aircraft is a key factor in designing Jettisoned FDRs and enabling them to pass airworthiness certification and be widely used in civil aircraft. The separation process of Jettisoned FDR installed on NASA Common Research Model is studied by the simulation method based on anisotropic unstructured hybrid grid and overset grid technology coupled with the rigid body 6-DOF equation. First, the numerical simulation accuracy of software under same simulation method is verified by WPFS standard model. Then, according to the three main aerodynamic parameters, including incoming Mach number, angle of attack α and sideslip angle β, 10 conditions including standard condition are designed and the separation process of recorder is simulated numerically. The simulation obtained the movement of Jettisoned FDRs in 6 degrees of freedom relative to the body coordinate system in different operating conditions during the separation process and confirmed that Jettisoned FDRs can be safely separated under these operating conditions. Finally, combined with the standard operating condition, the impact of three parameters’ changes on recorder’s 6 degrees of freedom motion and the time required to complete separation are analyzed, and conditions to ensure the safe separation of Jettisoned FDRs are summarized according to the requirements of airworthiness terms. Full article
(This article belongs to the Proceedings of 2nd International Conference on Green Aviation (ICGA 2024))
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18 pages, 5268 KiB  
Article
Vibration Control of Flexible Launch Vehicles Using Fiber Bragg Grating Sensor Arrays
by Bartel van der Veek, Hector Gutierrez, Brian Wise, Daniel Kirk and Leon van Barschot
Sensors 2025, 25(1), 204; https://doi.org/10.3390/s25010204 - 2 Jan 2025
Viewed by 649
Abstract
The effects of mechanical vibrations on control system stability could be significant in control systems designed on the assumption of rigid-body dynamics, such as launch vehicles. Vibrational loads can also cause damage to launch vehicles due to fatigue or excitation of structural resonances. [...] Read more.
The effects of mechanical vibrations on control system stability could be significant in control systems designed on the assumption of rigid-body dynamics, such as launch vehicles. Vibrational loads can also cause damage to launch vehicles due to fatigue or excitation of structural resonances. This paper investigates a method to control structural vibrations in real time using a finite number of strain measurements from a fiber Bragg grating (FBG) sensor array. A scaled test article representative of the structural dynamics associated with an actual launch vehicle was designed and built. The main modal frequencies of the test specimen are extracted from finite element analysis. A model of the test article is developed, including frequency response, thruster dynamics, and sensor conversion matrices. A model-based robust controller is presented to minimize vibrations in the test article by using FBG measurements to calculate the required thrust in two cold gas actuators. Controller performance is validated both in simulation and on experiments with the proposed test article. The proposed controller achieves a 94% reduction in peak–peak vibration in the first mode, and 80% reduction in peak–peak vibration in the second mode, compared to the open loop response under continuously excited base motion. Full article
(This article belongs to the Special Issue Spacecraft Vibration Suppression and Measurement Sensor Technology)
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16 pages, 4012 KiB  
Article
Dynamic Response of a Single-Rotor Wind Turbine with Planetary Speed Increaser and Counter-Rotating Electric Generator in Starting Transient State
by Radu Saulescu and Mircea Neagoe
Appl. Sci. 2025, 15(1), 191; https://doi.org/10.3390/app15010191 - 29 Dec 2024
Viewed by 743
Abstract
The paper addresses the dynamic modeling and numerical simulation of a novel single-rotor wind system with a planetary speed increaser and counter-rotating direct current (DC) generator, patented by authors, during the transient stage from rest. The proposed analytical dynamic algorithm involves the decomposition [...] Read more.
The paper addresses the dynamic modeling and numerical simulation of a novel single-rotor wind system with a planetary speed increaser and counter-rotating direct current (DC) generator, patented by authors, during the transient stage from rest. The proposed analytical dynamic algorithm involves the decomposition of the wind system into its component rigid bodies, followed by the description of their dynamic equations using the Newton–Euler method. The linear mechanical characteristics of the DC generator and wind rotor are added to these dynamic equations. These equations allow for the establishment of the close-form equation of motion of the wind system and, implicitly, the time variation of the mechanical power parameters. Numerical simulations of the obtained analytical dynamic model were performed in MATLAB-Simulink in start-up mode from rest for the case study of a 100 kW wind turbine. These results allowed highlighting the time variation of angular velocities and accelerations, torques, and powers for all system shafts, both in the transient regime and steady-state. The implementation, in this case, of the counter-rotating generator indicates a 6.4% contribution of the mobile stator to the generator’s total power. The paper’s results are useful in the design, virtual prototyping, and optimization processes of modern wind energy conversion systems. Full article
(This article belongs to the Section Energy Science and Technology)
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18 pages, 3108 KiB  
Article
Seismic Response Analysis of Concrete Box-Type Subgrade in High-Speed Railways
by Ying-Ying Chen, Hong Xiao, Xu-Guo Song, Shuai-Jie Guo, Bei-Er Luo and Mahantesh M. Nadakatti
Appl. Sci. 2024, 14(24), 11899; https://doi.org/10.3390/app142411899 - 19 Dec 2024
Viewed by 531
Abstract
China is prone to frequent earthquakes, impacting both the construction and operation of high-speed railways. The seismic response analysis is essential for the promotion and structural optimization of novel box-type subgrade structures. This paper develops a nonlinear integrated spatial dynamic model of a [...] Read more.
China is prone to frequent earthquakes, impacting both the construction and operation of high-speed railways. The seismic response analysis is essential for the promotion and structural optimization of novel box-type subgrade structures. This paper develops a nonlinear integrated spatial dynamic model of a ballastless track and box-type subgrade, investigating structural vibrations under multi-dimensional seismic actions using the time–frequency domain method. A seismic performance analysis of the structure is conducted to examine the influence of seismic intensity on its seismic response. Results indicate that the box-type subgrades exhibit good integrity under seismic actions, primarily undergoing rigid body motion, with forces in all components well below design strength, meeting the Chinese seismic fortification requirements. Compared to traditional simply supported beams, box-type subgrades show better adaptability to earthquakes. As seismic intensity increases, vibrations and deformations of box-type subgrades change linearly, while vibrating forces increase nonlinearly. Full article
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21 pages, 9019 KiB  
Article
Efficient Locomotion for Space Robots Inspired by the Flying Snake
by Zhiyuan Yang, Sikai Zhao, Nanlin Zhou, Jian Qi, Ning Zhao, Jizhuang Fan, Jie Zhao and Yanhe Zhu
Aerospace 2024, 11(12), 1025; https://doi.org/10.3390/aerospace11121025 - 15 Dec 2024
Viewed by 776
Abstract
Robots are becoming an integral part of space facilities construction and maintenance, and may need to move to and from different work locations. Robotic arms that are widely employed, which are mounted on fixed bases, have difficulty coping with increasingly complex missions. The [...] Read more.
Robots are becoming an integral part of space facilities construction and maintenance, and may need to move to and from different work locations. Robotic arms that are widely employed, which are mounted on fixed bases, have difficulty coping with increasingly complex missions. The challenge discussed in this paper is the problem of the efficient locomotion of robotic systems. Inspired by the gliding motion of a flying snake launched from a tree and combined with the weightlessness of the space environment, we design similar motions for the robot, including the following three steps. First, the robot folds its body like a snake and initiates flight by accelerating the global center of mass (CM), focusing on the movement direction and generating suitable momentum. Then, during the flight (free-floating) phase, the joint motions are planned using a nonlinear optimization technique, considering the nonholonomic constraints introduced by the momentum conservation and the system states at the initial and final states of the floating. Meanwhile, the difficulties caused by long-distance flights are addressed to reduce the motion computational cost and energy consumption by introducing the phase plane analysis method. Finally, the landing motion is designed to avoid rigid collisions and rollover on the radial plane. The numerical simulations illustrate that the three phases of maneuvers are smooth and continuous, which can help the space robots efficiently traverse the environment. Full article
(This article belongs to the Section Astronautics & Space Science)
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21 pages, 19119 KiB  
Article
Caterpillar-Inspired Multi-Gait Generation Method for Series-Parallel Hybrid Segmented Robot
by Mingyuan Dou, Ning He, Jianhua Yang, Lile He, Jiaxuan Chen and Yaojiumin Zhang
Biomimetics 2024, 9(12), 754; https://doi.org/10.3390/biomimetics9120754 - 11 Dec 2024
Viewed by 752
Abstract
The body structures and motion stability of worm-like and snake-like robots have garnered significant research interest. Recently, innovative serial–parallel hybrid segmented robots have emerged as a fundamental platform for a wide range of motion modes. To address the hyper-redundancy characteristics of these hybrid [...] Read more.
The body structures and motion stability of worm-like and snake-like robots have garnered significant research interest. Recently, innovative serial–parallel hybrid segmented robots have emerged as a fundamental platform for a wide range of motion modes. To address the hyper-redundancy characteristics of these hybrid structures, we propose a novel caterpillar-inspired Stable Segment Update (SSU) gait generation approach, establishing a unified framework for multi-segment robot gait generation. Drawing inspiration from the locomotion of natural caterpillars, the segments are modeled as rigid bodies with six degrees of freedom (DOF). The SSU gait generation method is specifically designed to parameterize caterpillar-like gaits. An inverse kinematics solution is derived by analyzing the forward kinematics and identifying the minimum lifting segment, framing the problem as a single-segment end-effector tracking task. Three distinct parameter sets are introduced within the SSU method to account for the stability of robot motion. These parameters, represented as discrete hump waves, are intended to improve motion efficiency during locomotion. Furthermore, the trajectories for each swinging segment are determined through kinematic analysis. Experimental results validate the effectiveness of the proposed SSU multi-gait generation method, demonstrating the successful traversal of gaps and rough terrain. Full article
(This article belongs to the Section Locomotion and Bioinspired Robotics)
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25 pages, 11860 KiB  
Review
Recent Advances in Piezoelectric Compliant Devices for Ultrahigh-Precision Engineering
by Zeyi Wu, Zehao Wu, I-Ming Chen and Qingsong Xu
Micromachines 2024, 15(12), 1456; https://doi.org/10.3390/mi15121456 - 29 Nov 2024
Viewed by 916
Abstract
With advancements in small-scale research fields, precision manipulation has become crucial for interacting with small objects. As research progresses, the demand for higher precision in manipulation has led to the emergence of ultrahigh-precision engineering (UHPE), which exhibits significant potential for various applications. Traditional [...] Read more.
With advancements in small-scale research fields, precision manipulation has become crucial for interacting with small objects. As research progresses, the demand for higher precision in manipulation has led to the emergence of ultrahigh-precision engineering (UHPE), which exhibits significant potential for various applications. Traditional rigid-body manipulators suffer from issues like backlash and friction, limiting their effectiveness at smaller-scale applications. Smart materials, particularly piezoelectric materials, offer promising solutions with their rapid response and high resolution, making them ideal for creating efficient piezoelectric transducers. Meanwhile, compliant mechanisms, which use elastic deformation to transmit force and motion, eliminate inaccuracies induced by rigid-body mechanisms. Integrating piezoelectric transducers and compliant mechanisms into piezoelectric compliant devices enhances UHPE system performance. This paper reviews the recent advances in piezoelectric compliant devices. By focusing on the utilization of piezoelectric transducers and compliant mechanisms, their applications in perception, energy harvesting, and actuation have been surveyed, and future research suggestions are discussed. Full article
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22 pages, 7322 KiB  
Article
Design and Parameter Optimization of a Rigid–Flexible Coupled Rod Tooth Threshing Device for Ratoon Rice Based on MBD-DEM
by Weijian Liu, Xuegeng Chen and Shan Zeng
Agriculture 2024, 14(11), 2083; https://doi.org/10.3390/agriculture14112083 - 19 Nov 2024
Viewed by 593
Abstract
To solve the problem of the high loss rate of threshing devices during the mechanical harvesting of ratoon rice, we propose a method using the principle of rigid–flexible coupling in this paper to reduce losses. Through analysis of the forces and collisions on [...] Read more.
To solve the problem of the high loss rate of threshing devices during the mechanical harvesting of ratoon rice, we propose a method using the principle of rigid–flexible coupling in this paper to reduce losses. Through analysis of the forces and collisions on ratoon rice grains during the threshing process, it has been confirmed that changing the structure and materials of the threshing contact components can effectively reduce grain loss. A rigid–flexible coupling rod tooth was designed, and the overall structural parameters of the device were determined based on force analysis results and dimensional boundary conditions. The MBD-DEM coupling method was used to simulate the threshing process, and the force conditions of the threshing rod teeth and threshing drum were obtained. The influence of the feeding amount and of the flexible body thickness on the crushing of ratoon rice grains was analyzed. In order to obtain the device’s optimal parameter combination, a three-factor quadratic regression orthogonal rotation combination experiment was conducted with drum speed, flexible body thickness, and rod tooth length as experimental factors. The optimization results showed that when the drum speed, flexible body thickness, and rod tooth length were 684 r/min, 3.86 mm, and 72.7 mm, respectively, the crushing rate, entrainment loss rate, and uncleaned rate were 1.260%, 2.132%, and 1.241%, respectively. The bench test showed that it is feasible to use the MBD–DEM coupling method to measure the motion and force of ratoon rice. The rigid–flexible coupling threshing device can reduce the grain crushing rate while ensuring grain cleanliness. Compared with traditional threshing devices, the crushing rate and entrainment loss rate of the rigid–flexible coupling threshing device were reduced by 55.7% and 27.5%, respectively. The research results can provide a reference for the design of threshing devices for ratoon rice harvesters. Full article
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15 pages, 11324 KiB  
Article
Scalable O(log2n) Dynamics Control for Soft Exoskeletons
by Julian D. Colorado, Diego Mendez, Andres Gomez-Bautista, John E. Bermeo, Catalina Alvarado-Rojas and Fredy Cuellar
Actuators 2024, 13(11), 450; https://doi.org/10.3390/act13110450 - 9 Nov 2024
Viewed by 1048
Abstract
Robotic exoskeletons are being actively applied to support the activities of daily living (ADL) for patients with hand motion impairments. In terms of actuation, soft materials and sensors have opened new alternatives to conventional rigid body structures. In this arena, biomimetic soft systems [...] Read more.
Robotic exoskeletons are being actively applied to support the activities of daily living (ADL) for patients with hand motion impairments. In terms of actuation, soft materials and sensors have opened new alternatives to conventional rigid body structures. In this arena, biomimetic soft systems play an important role in modeling and controlling human hand kinematics without the restrictions of rigid mechanical joints while having an entirely deformable body with limitless points of actuation. In this paper, we address the computational limitations of modeling large-scale articulated systems for soft robotic exoskeletons by integrating a parallel algorithm to compute the exoskeleton’s dynamics equations of motion (EoM), achieving a computation with O(log2n) complexity for the highly articulated n degrees of freedom (DoF) running on p processing cores. The proposed parallel algorithm achieves an exponential speedup for n=p=64 DoF while achieving a 0.96 degree of parallelism for n=p=256, which demonstrates the required scalability for controlling highly articulated soft exoskeletons in real time. However, scalability will be bounded by the n=p fraction. Full article
(This article belongs to the Special Issue Actuators and Robots for Biomedical Applications)
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21 pages, 8999 KiB  
Article
An MPC-DCM Control Method for a Forward-Bending Biped Robot Based on Force and Moment Control
by Zhongshan Wei, Wenyan Deng, Zhengyong Feng, Tao Wang and Xinxiang Huang
Electronics 2024, 13(22), 4374; https://doi.org/10.3390/electronics13224374 - 8 Nov 2024
Cited by 1 | Viewed by 1004
Abstract
For a forward-bending biped robot with 10 degrees of freedom on its legs, a new control framework of MPC-DCM based on force and moment is proposed in this paper. Specifically, the Diverging Component of Motion (DCM) is a stability criterion for biped robots [...] Read more.
For a forward-bending biped robot with 10 degrees of freedom on its legs, a new control framework of MPC-DCM based on force and moment is proposed in this paper. Specifically, the Diverging Component of Motion (DCM) is a stability criterion for biped robots based on linear inverted pendulum, and Model Predictive Control (MPC) is an optimization solution strategy using rolling optimization. In this paper, DCM theory is applied to the state transition matrix of the system, combined with simplified rigid body dynamics, the mathematical description of the biped robot system is established, the classical MPC method is used to optimize the control input, and DCM constraints are added to the constraints of MPC, making the real-time DCM approximate to a straight line in the walking single gait. At the same time, the linear angle and friction cone constraints are considered to enhance the stability of the robot during walking. In this paper, MATLAB/Simulink is used to simulate the robot. Under the control of this algorithm, the robot can reach a walking speed of 0.75 m/s and has a certain anti-disturbance ability and ground adaptability. In this paper, the Model-H16 robot is used to deploy the physical algorithm, and the linear walking and obstacle walking of the physical robot are realized. Full article
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18 pages, 3777 KiB  
Article
Dynamic Analysis of Tethered Satellites with a Payload Moving Along a Flexible Tether
by Yohan Ahn, Woojae Jang, Jeonga Lee and Jintai Chung
Appl. Sci. 2024, 14(20), 9498; https://doi.org/10.3390/app14209498 - 17 Oct 2024
Viewed by 953
Abstract
This study investigates the dynamic behavior of a three-body tethered satellite system with a flexible tether, focusing on a scenario in which a payload is transported along the tether connecting two satellites. Traditional models use rigid tethers, limiting the analysis of complex dynamics [...] Read more.
This study investigates the dynamic behavior of a three-body tethered satellite system with a flexible tether, focusing on a scenario in which a payload is transported along the tether connecting two satellites. Traditional models use rigid tethers, limiting the analysis of complex dynamics such as tether deformation, slack, and rebound. To address these limitations, we employed the absolute nodal coordinate formulation (ANCF) to model the flexibility of the tether. We derived nonlinear equations of motion using Lagrange’s equation and solved them using the Newmark time integration method to obtain the dynamic responses of the satellite system. Our findings revealed that the Coriolis effect caused significant deviations in the payload trajectory as its mass and speed increased, leading to greater tether deformation and slack, and potential system destabilization. Additionally, axial force fluctuations in the tether varied notably as the payload moved, transitioning between tensile and compressive states. This study provides a more accurate representation of three-body tethered satellite systems by incorporating tether flexibility, offering valuable insights into the dynamic behavior and stability of the system. Full article
(This article belongs to the Section Aerospace Science and Engineering)
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