This study proposes a physiologically constrained multibody dynamic model based on prismatic-revolute compound joints to characterize the biodynamic responses of the seated human body under whole-body vibration (WBV). The anatomically-inspired model divides the human body into five rigid segments: head-neck complex, upper torso, middle torso, lower torso, and hip-and-thigh. Adjacent segments are interconnected by compound joints that integrate translational and rotational degrees of freedom (DOFs) to replicate the physiological kinematics of the human spine. The governing equations of motion are derived via the virtual power principle; linearization of the nonlinear dynamic equations yields analytical expressions for apparent mass (AM) and seat-to-head transmissibility (STHT). Experimental data from 20 seated subjects exposed to band-limited (0.5–20 Hz) random vertical vibration were adopted for the system model identification. A weighted least-squares objective function incorporating both AM and STHT was constructed, and a two-stage hybrid optimization strategy combining particle swarm optimization global search and gradient descent local refinement was implemented to enable efficient, high-precision identification of joint stiffness and damping parameters. Validation demonstrates strong agreement between model predictions and experimental measurements, with goodness of fit values exceeding 0.968 for seat-to-head transmissibility and 0.926 for apparent mass. Modal analysis identifies five distinct vibration modes in the frequency range from 1.24 to 8.30 Hz, dominated by pitch and vertical motions of the upper-body segments. The identified natural frequencies align well with previously reported experimental modal findings, verifying the model’s capability to capture intrinsic whole-body vibration transmission mechanisms. Compared to existing models, the proposed framework achieves a superior balance among model compactness, computational efficiency, and biomechanical fidelity through physiology-guided DOF reduction. The model provides a reliable numerical tool for seating system design and occupant-seat coupling dynamics analysis, and also supports segment-level vibration absorbed power calculation to facilitate WBV injury risk assessment and segment-specific frequency weighting research.
In recent years, abnormal lateral swinging has frequently occurred in the trailing car of Power Centralized EMUs operating in single-track tunnels. This phenomenon has severely compromised ride comfort and operational safety. The objective of this research is to investigate its underlying mechanism and evaluate effective mitigation strategies. Dynamic tests reveal that the trailing power car exhibits a 1.5 Hz yaw motion, causing the lateral Sperling index to exceed 2.97. Fluid-structure interaction (FSI) dynamics simulations are conducted to reproduce the abnormal vibration and clarify its excitation mechanism. The results indicate that intense unsteady aerodynamic loads, particularly the aerodynamic yaw moment, are the primary excitation source of the low-frequency forced vibration of the car body. Further analysis demonstrates that this forced vibration cannot be effectively mitigated through conventional suspension damper optimization. Three mitigation approaches are evaluated, including bogie suspension damper adjustment, inter-car lateral stiffness optimization, and active lateral actuation. The results show that conventional suspension damper optimization provides only marginal improvement. Therefore, two effective mitigation strategies are identified: optimizing the inter-car lateral stiffness and installing an active lateral Giant Magnetostrictive Actuator (GMA) between the car body and the bogie. Both strategies significantly suppress tunnel-induced yaw oscillations. This research provides a theoretical foundation and practical engineering solutions for addressing aerodynamically induced vehicle oscillations, offering critical guidance for improving train operational performance.
Lower limb exoskeletons are gaining attention in the literature for their ability to enhance end-user muscle torque generation; this is particularly advantageous for assisting in walking actions. However, maintaining upright balance often remains the user’s responsibility. Existing standing balance controllers have primarily focused on regulation of whole-body momentum, instead of using full-state feedback and optimal control. In the current study, a constrained optimal full-state feedback feet-in-place (FIP) balance controller for an active hip-knee-ankle exoskeleton was developed using model predictive control (MPC). An integrated human-exoskeleton multibody dynamic model of upright stance was developed for controller design and evaluation. The model was linearized for controller design. Multibody dynamic simulations assessed balance recovery and controller performance following support-surface translations under two scenarios: 1) without any active torque generation from the simulated human (MPC-only regulates balance); 2) providing a percentage of assistance to a simulated human with variable torque capabilities (human driven via linear quadratic regulator, LQR). In the first set of simulations, exoskeleton performance was assessed comparing MPC against unconstrained LQR. In the second, the exoskeleton was driven by MPC exclusively while human torques were produced via the LQR utilized in the first set. Criteria in the MPC/LQR objectives included those identified from human experiments: regulate center of mass deviations, changes in trunk pitch, and net torque application over the prediction horizon. Multibody dynamic simulation results suggest that applying either of LQR and MPC to exoskeleton control can provide restoring torques post-perturbation during standing. Unlike the LQR however, the MPC consistently maintained the zero moment point within the support polygon and actuator torques within limits, though MPC did in some cases struggle with convergence in the joint kinematics. This was more evident when adding a human-in-the-loop that concurrently tried to regulate balance according the LQR while the exoskeleton used MPC (second set of simulations). We conclude that MPC offers a viable near-optimal control law for constrained standing balance assistance.
Wear at the wheel–rail interface is a key factor affecting vehicle safety, dynamics, and maintenance strategies. The progressive modification of wheel and rail profiles due to wear can significantly influence stability, comfort, and operating costs, making accurate prediction of profile evolution essential. Traditional wear models often rely on simplified flat-contact assumptions, such as those in the FASTSIM algorithm, which fail to capture the real behavior under conformal contact conditions typical of worn surfaces, curves, and flange–rail interactions. This study proposes a wear model integrating a conformal contact formulation by extending the Kik–Piotrowski normal contact model with Blanco–Lorenzo’s coefficients and enhancing FASTSIM to handle non-elliptical and curved patches in the tangential problem. Implemented within a Simpack Rail multibody framework, the model reproduces realistic operating conditions. Comparisons with conventional non-conformal models highlight that the proposed approach achieves a superior balance between computational efficiency and physical accuracy, providing a more reliable tool for wear prediction and maintenance optimisation in railway systems.
Interactive multibody simulations, particularly within virtual reality environments for applications such as virtual assembly and operator training, require computationally efficient and numerically stable contact models. A significant challenge arises when handling user-driven interactions, such as grasping, where unpredictable motions can lead to large penetrations and instabilities in traditional penalty-based contact formulations. This paper presents the adaptation and verification of a smoothed offset geometric contact model for real-time interactive multibody simulations. The model redefines collision geometry by creating a volumetric cushion around objects, enabling the computation of smooth, penetration-free contact forces. A key contribution of this work is the adaptation of a model initially intended for computer graphics implementations, along with a novel experimental methodology, to identify the model’s primary parameters: the offset thickness and the contact stiffness, based on physical measurements of human fingertip deformation and gripping forces. The proposed model is benchmarked against a widely used nonlinear penalty model, demonstrating comparable dynamic behaviour with a computational speed-up of over 50
Efficiently and reliably determining all natural frequencies below a trial frequency is critical for analyzing the vibration characteristics of mechanical systems. The multibody system transfer matrix method (MSTMM) is a powerful tool for mechanical system dynamics analysis. The derived eigen-equation contains nonlinear functions of the eigenvalues, making the conventional methods (such as subspace iteration, QR iteration, etc.) for solving the generalized eigenproblem not applicable. The low order of its coefficient matrix makes it feasible to solve the equivalent nonlinear algebraic equation to determine the natural frequencies, but many methods for solving nonlinear equations locally converge, making it difficult to obtain all natural frequencies below a trial frequency. To overcome this difficulty, based on MSTMM, this paper proposes an improved automatic search method and its acceleration to efficiently determine all natural frequencies below a trial frequency. Firstly, the iterative step error formula of the square root iteration method which is globally and cubically convergent is modified to avoid the computational failure due to too small or large values and tedious calculation caused by the coefficient matrix determinant and its derivatives, thereby enhancing the computational efficiency and stability. Secondly, an iterative initial value estimation method is proposed to obtain an initial value iterating to the next natural frequency after already obtaining one natural frequency, where the required natural frequency multiplicity can be obtained by the proposed multiplicity determination method. Thirdly, a detection method is proposed to avoid missing natural frequencies due to root over-stepping. These contributions lead to an improved automatic search method (IASM). Further, the numerical deflation is introduced to accelerate the IASM, resulting in an improved accelerated automatic search method. Finally, the efficiency and reliability of the proposed methods are verified through comparative numerical simulations. The proposed methods are highly efficient, automatically performed and reliable.
Serpentine locomotion in snake robots is inherently susceptible to lateral slip induced by environmental interactions, leading to propulsion efficiency degradation and trajectory deviations. To address these tribodynamic coupling challenges, this study systematically investigates slip dynamics and parametric optimization strategies for high-efficiency serpentine propulsion. First, a hybrid Coulomb-viscous friction model is developed to characterize anisotropic contact constraints while ensuring numerical convergence. Based on this formulation, a generalized multibody dynamics framework incorporating passive wheel position parameters is established using planar rigid-body motion theorems. Numerical simulations comprehensively evaluate the sensitivity of frictional anisotropy, propulsion loss coefficient, and propulsion velocity to distinct control parameters. Subsequently, a genetic algorithm (GA) optimization framework is employed to determine optimal gait parameters, yielding an explicit empirical mapping between optimal initial angles and friction coefficient ratios to facilitate terrain-dependent parameter selection. Crucially, experimental validation on a physical prototype confirms the theoretical trends across varying friction conditions. Demonstrating significant enhancements in locomotion stability and efficiency, the proposed framework provides quantitative design guidelines and a theoretical basis for robust terrain-adaptive control of snake robots in unstructured environments.
Funicular load-bearing structures achieve exceptional efficiency because their shapes follow the natural trajectories of internal stresses. However, time-varying loads can disrupt funicularity if they have fixed geometries. Recently, the authors found that funicularity may be restored through shape adaptation mediated by a simple, novel feedback control law. In this work, we investigate the limit of slow adaptation—an important special case of the new structural paradigm that is relevant to real-world applications in which external loads also evolve slowly. By considering the quasi-static limit of the coupled Newtonian and shape dynamics, we develop a discrete, chain-like multibody model of a morphing column, which enables detailed examination and visualization of shape dynamics. We show that, despite the lack of Newtonian dynamics, the shape dynamics is rich and nonlinear because of large geometric changes. Illustrative examples of shape adaptation reveal cases of successful convergence to the target shape as well as sustained shape oscillations with repeated snapping. The prominent role of elastic buckling instability in shape convergence is highlighted. Linearized evolution equations are used to verify local convergence to the target shape, and a condition of non-local convergence from almost all initial configurations to the target configuration is also developed.
This paper is about an extension of a general purpose multibody dynamics solver for two-sided elastohydrodynamic lubricated contacts. The compressible Reynolds equation with a mass-conserving cavitation model is formulated as a mixed nonlinear complementarity problem, and solved in a monolithic way by means of a Newton Fischer Burmeister algorithm. Kinematic and hydraulic boundary conditions are taken directly from the multibody solver, and reaction forces are applied in a monolithic way. Solid contacts between rough surfaces are considered. An implicit 2D LuGre model is used for solid friction. Deformations of flexible bodies are considered by means of a component mode synthesis approach. The model order reduction scheme uses static mode shapes and normal mode shapes. Dedicated mode shapes are introduced in order to increase the accuracy of the deformations within the surfaces of the bearings. A special A-stable second-order-accurate hybrid-step integration scheme is used for the monolithic solution of the equations of motion and the Reynolds equation. The models are validated based on simple analytical solutions and published data. Finally, the methodology is applied to a variable speed reciprocating refrigeration compressor model with four flexible bodies and five two-sided elastohydrodynamic lubricated contacts.
The LuGre friction model is among the most frequently used models in multibody dynamical applications. It is common that the steady-state conditions of the model are described by a specific shape of the Stribeck characteristic, which is influenced by the Stribeck exponent (or shape factor) that depend on the properties of the contacting surfaces. The paper discusses the bifurcations in the case of the LuGre model with the three typical shapes of the Stribeck curve. To capture the essence of the nonlinear effects associated with friction, we consider a minimal mechanical model: a block sliding on a horizontal surface, which is subjected to a constant external force and the LuGre friction force with a viscous damping term. Despite the simplicity of the mechanical model, several equilibria of different types and bifurcations – including saddle-node and Hopf bifurcation – are pointed out. Various bifurcation scenarios are examined revealing rich phase-space structures with several coexisting equilibria and limit cycles. The paper highlights that one must be aware when choosing the parameters of the LuGre model – including the Stribeck exponent – since the bifurcation map can change significantly depending on the shape of the Stribeck characteristic.
Crane is a multibody system characterized by large displacements due to the coupling of its boom structure and pulley-rope system, both of which involve dynamic boundaries and dynamic loads. Since the boom undergoes significant deformation, conventional beam elements derived under the assumption of small deformations and rotations are not applicable. Due to the dynamic contact between pulley and rope, describing motion using material description is complex and insufficiently accurate. In this paper, the generalized strains of geometric nonlinearity beam element are derived to formulate the dynamic equations of the boom. The spatial description is adopted to characterize the relative motion between booms and the interaction between pulleys and ropes, leading to the establishment of elements with movable node. A model smoothing method is applied to filter out high-frequency oscillatory components of the system, significantly enhancing computational efficiency. Dynamic analysis of the crane system using the proposed method yields results with reasonable accuracy, which can provide support for the dynamic analysis of crane systems in engineering applications.
This paper presents a novel framework for the cooperative transport of a highly elastic membrane using multiple omnidirectional mobile robots, including scenarios involving additional payloads. Since model-based control approaches have enabled very versatile schemes for the transport of rigid bodies in previous works, this is also pursued for the transport of highly deformable objects, where two complementary object models are proposed. First, to capture large deformations and geometrically nonlinear effects arising during transport, a data-driven surrogate model based on a neural network is employed to predict quasi-static pretensioning forces for desired membrane deformations resulting from different payloads. Since the surrogate model is trained on quasi-static equilibrium configurations, it cannot predict the transient membrane dynamics and is therefore unsuitable as a prediction model for feedback control. Instead, a simplified multibody model is integrated into a distributed model predictive control scheme (DMPC) to account for the dynamic aspects of cooperative transportation. The surrogate is trained exclusively on finite element simulation data and provides force setpoints in real-time, which are then explicitly controlled within a cascaded control structure. The DMPC scheme coordinates the robots to both transport the tensioned membrane along a given reference path and exert the desired tensile forces. The proposed approach is validated experimentally using a custom-built robot platform transporting an elastic membrane along various paths and with different payloads, demonstrating precise tracking performance and satisfactory agreement between desired and achieved object deformations.
This work presents a complete framework for the modeling, workspace analysis, and trajectory planning of a tendon-driven continuum manipulator (TDCM). For modeling purposes, a Petrov–Galerkin Cosserat rod finite element formulation is adopted, and material parameters are identified through dedicated experiments. The identified model shows good agreement with the optical motion capture data, with a position error of no greater than 4.5
In the process of formulating and optimizing modern methods for accurate and effective modeling of mechanical systems, an important step is validation. The presented research aims to design a test bench devoted to the experimental investigation of an overconstrained mechanism based on a benchmark multibody system and to collect force measurements while the system is stationary or in motion. The hardware realization of a previously developed theoretical model is presented, with special attention paid to minimizing the effects of friction, drag, backlash, and manufacturing inaccuracies. In order to achieve this, low-friction, low-backlash joints are used, the lengths of all the links are adjustable, and the mechanism parts of various stiffnesses are designed. The system is also prepared to deliberately introduce assembly stresses by changing the links’ lengths. The stiffness of crucial components was experimentally verified, and the developed FEM model of the mechanism’s frame was validated against measurement data. Finally, the constructed test bench is demonstrated to perform measurements reliably, providing accurate, consistent results. The experimentally obtained force data are compared with the loads predicted by numerical analyses, confirming that the stand may be used to validate multibody modeling methods.
When trains operate in tunnel spaces, the poor elasticity of the rigid catenary and poor track smoothness induce severe fluctuations in the overall contact force. Meanwhile, complex aerodynamic behaviors, the pantograph’s structural characteristics and varying working heights, lead to large differences in the contact force distribution between the front and rear sliders. Ultimately, the poor relationship of pantograph and catenary increases operating costs and can even affect train operation safety. In order to reduce fluctuations of contact force and minimize difference between front and rear slider, this paper establishes a coupled dynamic model of catenary-pantograph during tunnel operation and designs a fuzzy PID strategy for subway train pantographs. The results show that: (1) When the train operates at speeds of 60 km/h, 70 km/h, and 80 km /h, the average difference between front and rear slider contact forces is 10.13 N, 13.81 N, and 18.06 N, respectively, which are key factors causing abnormal wear. (2) When the train operates at speeds ranging from 60 km/h to 80 km /h with fuzzy PID control applied to the pantograph, the average difference in front and rear slider contact forces is close to 0 N, and the total contact force is close to 120 N. (3) Fuzzy PID control can effectively reduce fluctuations in contact forces. When the train operates at speeds between 60 km/h and 80 km/h, the standard deviations of the contact force indicators show significant improvements: the front slider contact force is reduced by 32
The floating frame of reference formulation (FFRF) is widely used to model flexible multibody systems, such as wind turbines. With the development of longer and more flexible wind turbine blades, it is essential that geometrical nonlinear effects are considered to accurately capture the large deflections these structures experience. A method is presented that uses the FFRF to this end by partitioning a structure into sub-bodies, each with its own floating frame. The elastic deformation of the sub-bodies is represented by Hurty/Craig-Bampton component modes, calculated from an existing solid finite element (FE) model; the use of a high-fidelity FE model allows for capturing complex structural phenomena (e.g. three-dimensional effects) that can arise in wind turbine blades. Interface modes are used to reduce the number of interface degrees of freedom, which require a special treatment of the constraint equations needed to connect the sub-bodies. Conventional rigid multipoint constraints are also analysed. It is demonstrated that this FFRF-based multibody approach can compute accurate nonlinear responses when compared to standard solid finite element models, with a good compromise between computational cost and accuracy.
The complex vibration of high-speed railway track systems under seismic excitation greatly increases the derailment risk of electric multiple units (EMUs). To clarify the derailment mechanism and evaluate the performance of derailment protection devices, a comprehensive dynamic model incorporating seismic input, bridge response, vehicle multibody dynamics, and 3D multi-point contact among the wheelset, gearbox, traction motor, protection device, rail, and slab track was developed. Numerical simulations were performed under different train speeds and seismic intensities. Results show that the seismic-induced derailment of high-speed EMUs exhibits strong nonlinearity and frequent multi-point collisions, with wheelset lateral displacement being the key indicator for derailment evaluation. The protection device effectively limits lateral displacement and delays complete derailment under low- and medium-speed conditions but shows reduced effectiveness under high-speed operation or strong earthquakes, where failure may occur. Although the brake disc and gearbox provide limited buffering, they cannot replace the dedicated device. Working-domain analysis further indicates that the device remains functional when train speed is below 150 km/h and track lateral acceleration is under 10 m/s2. These findings offer theoretical support for seismic safety assessment and optimization of derailment protection devices for high-speed railway vehicles.
Remotely Operated Vehicle (ROV)–cable systems exhibit strong coupling and high dynamics, yet existing studies face notable limitations: cable models oversimplify hydrodynamic interactions and lack real-time coupling with ROV motion; control strategies largely address either ROV motion or cable deformation, with little integration; the influence of cable-related parameters on tension remains understudied. To address these, an integrated modeling and control framework is proposed, focusing on coupled modeling of cable and ROV motion control to capture bidirectional interactions, and quantify the influence of α (cable length–to–ROV absolute position ratio) and v max (the cable take-up/payout speed threshold) on cable tension. Specifically, the Arbitrary Lagrangian–Eulerian (ALE) method and the Absolute Nodal Coordinate Formulation (ANCF) method are used to model the cable with real-time mesh updating. A closed-loop collaborative controller combines dual-loop proportional-integral-derivative (PID) control for cable control and sliding mode control (SMC) for ROV motion control, to reduce dynamic mismatch. Simulations under two typical operation scenarios quantify the combined effects of α and v max on tension fluctuations and entanglement risk, further identifying optimal parameter settings. MATLAB/Simulink simulation results verify that the proposed framework can capture the bidirectional ROV–cable coupling mechanism, significantly improving the rationality of control decisions. This work advances coupling modeling, collaborative control, and parameter coordination, supporting deep-sea flexible system design.
Soft robots are increasingly expected to operate in unstructured environments where compliance, environmental coupling, and embedded sensing fundamentally shape their behavior. However, the Cosserat rod models commonly used in soft robotics originate from two largely independent traditions: robotics-driven formulations optimized for control or intuitive simplicity, and mechanics-driven formulations optimized for structural generality. Considered separately, neither tradition fulfills the requirements for sensing, fabrication, environmental interaction, and numerical reliability of modern soft robotic systems. Drawing on our modeling and design experience with soft robotic systems, we identified a set of design challenges that guided the development of a suitable Cosserat rod formulation. To address these challenges, we propose a Cosserat rod model expressed directly in strain coordinates, matching the quantities measured by embedded sensors and eliminating the need for global pose tracking. A finite-element discretization supports localized tactile forces and environmental interactions, while a globally singularity-free quaternion representation enables full floating-base capability. We demonstrate that a Petrov–Galerkin projection, in contrast to the existing Bubnov–Galerkin formulation in soft robotics, decouples the choice of velocity coordinates and virtual displacements from the configuration parametrization. This enables the dynamics to be expressed in terms of sensor-aligned velocity variables, such as nodal absolute velocities from reliable existing sensors, rather than parametrization-dependent strain rates. This alignment simplifies estimator and controller design and also yields a constant mass matrix as a computational benefit. In addition, the formulation provides a unified mechanism for embedding hardware-intended strain constraints directly through intrinsic Lagrange-multiplier enforcement, ensuring that the model evolves strictly within the robot’s physically realizable strain manifold. The resulting finite-element formulation is total Lagrangian, objective, locking-free, globally singularity-free, and path-independent. Robust convergence and a significant reduction in nonlinear solver iterations (98.4
This paper presents a method for computing the kinematics of single–degree-of-freedom closed-loop mechanisms using minimal coordinates combined with C^2 -continuous Hermite spline interpolation. Instead of solving nonlinear constraint equations at every time step, the proposed approach evaluates exact kinematics only at selected values of the independent parameter and reconstructs intermediate configurations through interpolation. Several rotational interpolation strategies are examined, including incremental and normalized quaternion schemes as well as Tait–Bryant angle interpolation. Two benchmark systems—a double wishbone suspension and a 3D slider-crank mechanism—are used to assess the accuracy of the interpolated kinematics. The results show that C^2 interpolation significantly improves the smoothness of angular velocities and accelerations, reducing oscillations in curvature terms. Dynamic simulations further demonstrate that interpolation continuity has a direct impact on mechanical-energy conservation: C^2 interpolation allows stable integration with larger step sizes, whereas C^1 interpolation produces noticeable energy drift and requires stricter time-step control. The study highlights the importance of interpolation smoothness for both kinematic accuracy and dynamic robustness. The conclusions provide perspectives for extending the method to multiple DOFs, comparing additional orientation-spline formulations, and systematically analysing which interpolation strategies, integrators, and solver parameters are best suited for different multibody system configurations.
