Rigid Body Research Articles

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.

Continuum Mechanics Applied to the Biomechanics of Motion.

Continuum Mechanics is the discipline that studies the motion and deformation of material bodies, and is at the basis of both Solid Mechanics and Fluid Mechanics. This works aims at highlighting how a basic education in modern Continuum Mechanics can be of fundamental importance not only in the Biomechanics of Tissue, but also in the Biomechanics of Movement. The latter is largely based on Rigid Body Mechanics, which can be considered as a simple particular case of the general theory of Continuum Mechanics. As an example, a straightforward methodology for the extraction of the angular velocity from motion analysis data is illustrated. The method is based on a quantity that is more primitive than the angular velocity: the spin tensor.

Strongly Coupled Simulation of Magnetic Rigid Bodies

Strongly Coupled Simulation of Magnetic Rigid Bodies

The Synthesis of Spherical Four-bars for Biomimetic Motion through Complete Solutions for Approximate Rigid Body Guidance

Abstract In this paper, we form a constrained optimization problem for spherical four-bar motion generation. Instead of using local optimization methods, all critical points are found using homotopy continuation solvers. The complete solution set provides a full view of the optimization landscape and gives the designer more freedom in selecting a mechanism. The motion generation problem admits 61 critical points, of which two must be selected for each four-bar mechanism. We sort solutions by objective value and perform a second order analysis to determine if the solution is a minimum, maximum, or saddle point. We apply our approximate synthesis technique to two applications: a hummingbird wing mechanism and a sea turtle flipper gait. Suitable mechanisms were selected from the respective solution sets and used to build physical prototypes.

The Interior Contact-Aided Rolling Element (I-CORE)

Abstract This work introduces an interior contact-aided rolling element (I-CORE) compliant mechanism that draws upon the concepts used for the contact-aided rolling element, cross axis flexural pivot, and pre-curved flexible beam. The I-CORE incorporates a bilinear compressive stiffness response with an initial tailorable stiffness governed by the flexural geometry, followed by a stiffness curve governed by the material stiffness at the contact point. The I-CORE mechanism can achieve 1 or 2 degrees of rotational freedom as well as 1 degree of translational freedom. The purpose of the present work was to introduce the I-CORE mechanism, as well as a pseudo-rigid-body replacement model (PRBM) of the I-CORE mechanism which was subsequently validated using both finite element analysis and bench top mechanical testing. A pseudo rigid body model was created for the I-CORE to simplify rapid adaptation of this mechanism to different design applications. This model was validated using both finite element analysis and benchtop mechanical testing under both compression and rotation loading conditions. Additionally, multiple configurations of the device were created and evaluated in order to test its sensitivity to certain design features including the flexure width, flexure thickness, and the radius of the rounded contact surfaces. It was found that the model is sensitive to the thickness of the flexures and that despite some limitations, the pseudo rigid body model is sufficiently accurate for initial design work. Some possible applications of the mechanism are proposed.

A Static/Dynamic Coupled Harmonic Balance Method for Dry Friction Systems Containing Rigid Body Modes

Abstract A harmonic balance method for under-constrained dry friction systems containing rigid body modes (HBM-RBM) is proposed. This method aims to overcome the encountered obstacle when applying the harmonic balance method to turbine blades damped by underplatform dampers. The inspiration for HBM-RBM comes from the free interface modal synthesis method. The key innovation involves deriving the elastic inversion of the singular stiffness matrix through the elimination of rigid body modes. In this way, the general HBM framework can be adopted, and the frequency response of under-constrained dry friction systems can be solved in a static/dynamic coupled manner. The accuracy and efficiency are both verified on a lumped parameter model and a finite element model of turbines with UPDs from a real gas turbine. A comparative study between the HBM-RBM and the commonly adopted way of imposing artificial grounding springs (HBM-AGS) is conducted. Results demonstrate that the HBM-RBM holds a significant advantage over HBM-AGS, as it eliminates the need for artificial grounding springs (AGS) and avoids the necessity for numerous trial cases to determine AGS stiffness.

Physics-informed neural network for nonlinear dynamics of self-trapped necklace beams

A physics-informed neural network (PINN) is used to produce a variety of self-trapped necklace solutions of the (2+1)-dimensional nonlinear Schrödinger/Gross-Pitaevskii equation. We elaborate the analysis for the existence and evolution of necklace patterns with integer, half-integer, and fractional reduced orbital angular momenta by means of PINN. The patterns exhibit phenomena similar to the rotation of rigid bodies and centrifugal force. Even though the necklaces slowly expand (or shrink), they preserve their structure in the course of the quasi-stable propagation over several diffraction lengths, which is completely different from the ordinary fast diffraction-dominated dynamics. By comparing different ingredients, including the training time, loss value, and L2 error, PINN accurately predicts specific nonlinear dynamical properties of the evolving necklace patterns. Furthermore, we perform the data-driven discovery of parameters for both clean and perturbed training data, adding 1% random noise in the latter case. The results reveal that PINN not only effectively emulates the solution of partial differential equations but also offers applications for predicting the nonlinear dynamics of physically relevant types of patterns.

Trajectory optimization and stability control for a novel unmanned intelligent wheel-legged vehicles on unstructured terrains

The trend of intelligent vehicles is currently expanding, and a new class of unmanned intelligent vehicles known as wheel-legged vehicles (WLVs) is emerging. WLVs excel in transportation on unstructured terrain by offering a unique combination of the efficiency of wheels on flat ground and the versatility of legs to tackle obstacles. To enhance the locomotion performance of WLVs on unstructured terrains, this paper presents a novel framework for improving their locomotion through nonlinear programming-based (NLP) trajectory optimization and stability control. The framework optimizes the vehicle’s body and wheel positioning while incorporating terrain information and employs a linear rigid body dynamic model for efficient motion planning. The stability control framework combines feedforward control using ground reaction forces with feedback control through joint PD control and utilizes model predictive control (MPC) to adjust the wheel slip ratio to prevent slip on steep slopes. Experimental validation on the real vehicle with torque-controlled wheels demonstrated the capability of driving over a 1 m height with a 30°slope at an average speed of 0.7 m/s and a maximum speed of 1.03 m/s. Our approach also enables the WLV to overcome obstacles, such as inclines, while dynamically negotiating these challenging terrains.

Dynamics Modeling and Motion Evaluation of a Near-Ground Tethered Balloon Cable System under Severe Wind Environments

Weather survival poses a significant challenge for the utilization of tethered balloons. The dynamic modeling of tethered balloon systems presents challenges due to the flexible nature of the cables and the intricate nature of gust forces. The present study introduces a new approach for modeling near-ground tethered balloon systems, which enables the analysis of their dynamic responses and performance evaluation under complex boundary conditions. First, finite cylindrical rigid bodies that are joined together by bushing forces to describe the dynamics of the tethered cable. The properties of the flexible cables under severe bending and translation can be illustrated by the dynamics model. Second, a three-dimensional dynamics model based on the multibody dynamics theory is created to deal with the interaction of the tethered balloon system and flexible cables. The dynamic responses of the tethered balloon system under challenging operating conditions are investigated, focusing on the number of cable segments and the place and direction of gust wind impacts. This model allows for precise assessment and optimization of the system’s overall performance to improve weather resistance. The results show that compared to computational fluid dynamics (CFDs) methods, the multibody system dynamics-based balloon model improved the solution time by 80%, with a pitch angle deviation of only 0.0016°. Moreover, the bushing model effectively reduced cable force and enabled accurate reflection of the system’s motion characteristics.

A novel freemium code SAND (v1.0) for generation of randomly packed beds

The main current approaches for generation of the packed bed models are based on rigid body dynamics (RBD) and Newton's laws (discrete element methods - DEM). This paper deals with the development and analysis of a novel code based on analytical geometry approach for the packed bed generation. The architecture and main algorithms of the novel code are described and clarified. The parameters of the packed bed generated via the novel code are compared with experimental data and packed beds generated via Blender (RBD), Yade (DEM). The novel code demonstrates many advantages, such as good correlation with experimental data, no overlaps between pellets in the packed bed, and a low computational time for packed bed generation. The packed bed model can be directly exported in .step format. Other advantages are also demonstrated and clarified. The novel code is attached to this paper and can be freely used by engineers and scientists.

Determination of the dynamic stiffness matrix of a rail damper and application to vibration decay rate

In this paper, the 6×6 dynamic stiffness matrix of a rail damper seen by a short section of rail is defined based on the force simplification theory, and a method to determine the matrix is presented. According to the method, frequency response functions (FRFs) between specific points on the rail as a rigid body are measured with hammer testing. These FRFs are then used to express the acceleration of the mass center of the rail as well as the rail's angular acceleration. As the third step, the equations of motion of the rail are established based on the laws of momentum and moment of momentum, from which the dynamic stiffness matrix can be worked out. The method is then applied to determine the dynamic stiffnesses of a typical damper, and the determined dynamic striffnesses are combined with an infinite periodic track model to stduy the effect of the damper on the verical and lateral vibration decay rates of the rail.

Low frequency, broadband and thin acoustic metamaterials for acoustic insulation

Elastic and locally resonant metamaterials can be used to improve the acoustic insulation properties of panels, particularly at low frequencies. Among the possible architectures, we are interested in the case of a very soft panel consisting of a porous material in which a periodic distribution of cylindrical inclusions is inserted. It has recently been established (JSV 571 (2024) 118005) that this configuration gives rise to a large and low-frequency transmission dip, explained by the coexistence of an elastic band gap and the destructive interference resulting from the interaction between an elastic resonance mode of the skeleton and a rigid body mode of the inclusions. The paper aims to describe the essential physical mechanisms involved in using a minimal lumped element model, the characteristics of which are extracted from the cell modes. The relevance of the minimal model is validated utilizing a comparison with reference results obtained using the finite element method. This approach focuses on the mechanisms involved and is not constrained by the choice of a particular geometric configuration (exact shape and size of the inclusion), allowing it to evolve.

Observation-based quantification of aerosol transport using optical flow: A satellite perspective to characterize interregional transport of atmospheric pollution

Interregional transport plays a significant role in haze formation with varying and disputable contribution extent. Current research on quantitatively analyzing interregional atmospheric pollution transport has mainly relied on meteorological and chemical models. However, these models are typically affected by uncertainties due to the assumptions and simplifications inherent in the numerical simulations and source emission estimations. In this study, a comprehensive optical flow framework is developed to offer a new perspective on quantitative characterization of interregional transport of atmospheric pollution based on synergistic observations from geostationary and sun-synchronous satellites. In this framework, the high-frequency continuous aerosol observing images are regarded as video in computer vision, and an aerosol dynamic optical flow algorithm is proposed by incorporating aerosol-specific assumptions and constraints, overcoming the limitation that traditional optical flow methods are typically confined to rigid bodies. Results demonstrate that the developed optical flow framework could distinguish the aerosol transport process from other dynamic processes of aerosol development and accurately capture the fast-changing details of transport processes. Moreover, the satellite-based optical flow framework achieves aerosol transport results comparable to those of widely accepted model-based methods, demonstrating the physical interpretation of pixel-based optical flow results and highlighting its effectiveness in quantitative characterization of the atmospheric pollution transport process via the Aerosol Transport Index (ATI). Furthermore, a case analysis of long-term assessments of interregional transport of atmospheric pollution indicates that Beijing acts as a “sink” of atmospheric pollution, and a downward trend could be found from the annually averaged transported aerosol net loadings due to the emission reduction policy. Compared with model-based methods, the satellite-based optical flow framework is directly grounded in observations and does not rely on emission inventories that take years to update. Therefore, it not only helps improve understanding the patterns of atmospheric pollution interregional transport, but also provides a more efficient and economical way to assess the effectiveness of regional joint control policy.

On the nonlinear dynamics of in-contact rigid bodies experiencing stick–slip and wear phenomena

In this paper, the dynamic behavior of one degree-of-freedom oscillator subject to stick–slip and wear phenomena at the contact interface with a rigid substrate is investigated. The motion of the oscillator, induced by a harmonic excitation, depends on the tangential contact forces, exchanged with the rigid soil, which are modeled through piecewise nonlinear constitutive laws, accounting for stick–slip phenomena due to friction as well as wear due to abrasion, already developed by the authors in a previous work. The nonlinear ordinary differential equations governing the problem are derived, whose solution is numerically obtained via a typical Runge–Kutta-based algorithm. The main target of this study is to analyze and discuss the strong nonlinear behavior, descending from the presence of stick–slip and wear phenomena, thus investigating the effect of the different interface modeling. In this framework, the analysis is carried out considering the whole evolution of non-smooth contact laws, starting from the virgin interface.