A newly developed contact detection method designed for the interaction between flexible slender structures and rigid sheaves is proposed. The former are discretized by means of two-dimensional beam finite elements based on the absolute nodal coordinate formulation. The contact detection relies on the geometrically exact intersection points of the third-order polynomial representing a beam element and the circular boundary of the sheave. The contact force is obtained from a spring–damper penalty formulation. The proposed method is applied to a numerical model of a pulley system, which is analyzed under static and dynamic conditions. Comparative simulations are performed employing a relevant, existing method based on an approximation of the polynomial by piecewise linear segments. In addition, a semi-analytical model is derived to serve as a reference. In the static case, convergence studies reveal a similar order of convergence for the exact as well as the segment method, however, with a significantly higher coarse-mesh accuracy of the exact one. This behavior is qualitatively reproduced by the dynamic results leading to a significant improvement in computational efficiency of the proposed method.

Model order reduction decreases the dimension of a mechanical system by introducing modal coordinates that retain important dynamic characteristics. Sliding beams, as found in telescopic structures, pose a fundamental challenge. Fixed modal coordinates fail to capture evolving system properties, and updating the modal basis during simulation causes modal coordinates to change meaning. The present work addresses this challenge by constructing a global reduction basis for a sliding beam. The global basis is constructed from snapshots in the form of modal matrices and compressed using proper orthogonal decomposition. Reduction is applied within a constraint multibody formalism with algebraically enforced constraints that permit continuous slider movement. The method is validated against an absolute nodal coordinate formulation of a sliding beam with a sliding joint. Different combinations of snapshot quantity and eigenmodes per snapshot are investigated and an error map is shown. A challenging test case involving a highly flexible beam subjected to time-dependent loading and slider movement demonstrates that the global reduction basis reduces computation time by approximately 90

Over the years, complex control approaches have been developed to control the motion of a bicycle. Reinforcement Learning (RL), a branch of machine learning, promises to be an automated approach for solving optimal control problems. By interacting with and observing an environment, a so-called agent is trained, ultimately leading to a learned controller. The present work introduces a pure RL approach to do path following with a virtual bicycle model while simultaneously stabilizing it laterally. The bicycle, modeled using the Whipple benchmark model and multibody system dynamics, has no stabilization aids. The observation of the environment consists of the minimal positional and velocity coordinates of the bicycle, as well as of information about the path ahead of the bicycle provided by moving preview points. Both path following and stabilization of the bicycle model are achieved exclusively by controlling the steering angle setpoint of the bicycle. Curriculum learning is applied as a state-of-the-art training strategy. Different settings for the RL approach are investigated and compared. The ability of the learned controllers to do path following and stabilization of the bicycle model traveling between 2 m/s and 7 m/s along complex paths including full circles, slalom maneuvers, and lane changes is demonstrated. Explanatory methods for machine learning are used to analyze the learned controller and identify connections to research in bicycle dynamics.

Large Language Models (LLMs) perform well on established code-generation and mathematical-reasoning benchmarks, but their capabilities in mechanics and spatial geometry, here denoted as mechanical engineering awareness, has not been quantified systematically. We present MecEng, a fully automated benchmark that evaluates LLMs on the creation of multibody simulation models from parameterized textual descriptions. The benchmark comprises 84 generic tasks on three difficulty levels, ranging from rigid-body systems with joints and contact to flexible multibody systems that require exact 3D geometry generation, tetrahedral finite-element meshing, and Hurty-Craig-Bampton model order reduction of machine parts. A dedicated pipeline with LLMs generates simulation-ready geometry from text using Netgen, and builds multibody system models for the code Exudyn, which are then verified against expert ground truth on several levels: system-graph isomorphism including graph node annotations, numerical solutions, and part-specific measures such as mass, geometry, and eigenfrequencies. In total, 32 open-weight and two proprietary LLMs are evaluated. On rigid-body tasks, the best open-weight model obtains an overall success rate of 86.0

The precision, stability, and performance of lightweight high-strength steel structures in heavy machinery is affected by their highly nonlinear structural dynamics. This, in turn, makes control more difficult, simulation more computationally intensive, and achieving real-time autonomy, using standard approaches, impossible. Machine learning through data-driven, physics-informed and physics-inspired networks, however, promises more computationally efficient and accurate solutions to nonlinear dynamic problems. This study proposes a physics-inspired real-time structural dynamics estimation framework using novel SLIDE-neural networks for the hydraulically actuated three-dimensional systems.1 It learns the dynamics of a system by utilizing physically known damping properties in a SLIDE window. For data acquisition, an algorithm is introduced from randomized initial configurations and hydraulic pressures in a system, along with a method to compute the SLIDE size. The new framework was evaluated across varying geometries, and 1-DOF and 2-DOF hydraulically actuated systems. Different sensor configurations while lifting various payloads were also tested. The SLIDE-trained network accelerated structural dynamics estimation solutions by a factor of 103 in reference to flexible multibody simulation batches and provided reasonable accuracy. Performance of new framework is compared with the sequential architectures such as RNN, LSTM and CNN. The SLIDE network was successfully trained in less time using standard parameters from PyTorch, ADAM optimizer. These results support the studies goal of providing robust, real-time solutions for control, robotic manipulators, structural health monitoring, and automation problems.

In computational engineering, enhancing the simulation speed and efficiency is a perpetual goal. To fully take advantage of neural network (NN) techniques and hardware, we present the SLiding-window Initially-truncated Dynamic-response Estimator (SLIDE), a deep-learning based method designed to estimate output sequences of mechanical systems and multibody systems, in particular, which are subject to forced excitation. A key advantage of SLIDE is its ability to estimate the dynamic response of damped systems without requiring the full system state to be known, making it particularly effective for flexible multibody systems. The method truncates the output window based on the decay of initial effects due to damping, which is approximated by the complex eigenvalues of the system's linearized equations and is only limited by the lack of transfer of internal states between evaluations. In addition, a second NN is trained to assess the accuracy of the surrogate model by estimating the error during inference, further enhancing the method's applicability. The method is applied to a diverse selection of systems, including the Duffing oscillator, a flexible slider-crank system, and an industrial 6R manipulator, mounted on a flexible socket. Our results demonstrate significant speedups from the simulation up to several millions, exceeding real-time performance substantially.

The floating frame of reference formulation (FFRF) is one of the most widely used computational methods for modeling linearly elastic flexible multibody systems. It offers a convenient and computationally efficient approach, particularly the nodal-based framework. An advantage of the FFRF is its ability to directly utilize 3D models created with CAD software and meshed with finite element tools, making it an appealing alternative to beam-element models for studying rotating machinery. However, it is well known that the FFRF is not suitable for rotordynamics applications because it fails to capture centrifugal stiffening. Centrifugal stiffening arises as rotating components, such as discs and blades, experience tensile forces that increase their natural frequencies, effectively enhancing structural stiffness. This study addresses this limitation for systems rotating around a fixed axis of rotation and presents a practical solution. The presented approach introduces an additional stiffness term into the FFRF equations of motion, which we demonstrate is essential for achieving accurate rotordynamics simulations. The significant improvements achieved with this approach over the conventional FFRF are demonstrated using three rotors discretized with 3D solid finite elements.

Understanding particle motion in snow avalanches is crucial for improving the representation of flow dynamics in numerical models. In this study, we develop and apply a general framework for testing and calibrating thickness-integrated flow models using in-flow sensor data from AvaNodes, radar measurements, and simulations with the com1DFA module of the open-source AvaFrame framework. This includes an implementation of particle tracking functionalities and focuses on assessing a modified Voellmy friction relation.Radar measurements of the avalanche front and three-dimensional AvaNode trajectories provide a comprehensive observational basis for model comparison. By minimizing the differences between measured and simulated velocities and front positions, we identify parameter sets that achieve high agreement with observed dynamics, yielding deviations below 5 %-10 % in maximum velocity and travel distance. However, the results reveal a trade-off between accurately reproducing particle vs. front behaviour, reflecting model limitations and the presence of equifinality in the parameter space.We also find that the simulated particle velocities are primarily controlled by initial position, contrasting with experimental observations that show more complex particle interactions. These findings underline the need for enhanced model formulations to better capture flow regime transitions and particle-scale effects. Our results highlight the potential of combining multiple measurement types for calibration and future improvements in avalanche modelling.

This work focuses on compliant joints in autonomous cells. These cells preserve the underlying geometry of a triangular mesh and enable self-reconfiguration using six-bar linkages. The six-bar linkages, essential for maintaining mesh geometry, are realized as 3D-printable compliant mechanisms. However, compliance in the hinges and deviations from the desired remote center of rotation results in positioning errors. Detailed multibody models have been developed using nonlinear beam elements to accurately represent the compliant mechanisms. In order to meet the required computational real-time performance, we propose surrogate models that can accurately predict positioning errors during self-reconfiguration. Finally, these errors are corrected by solving the inverse kinematics of a hyper-redundant manipulator using the static solution of a linearized model. Our study illustrates the benefits of utilizing a surrogate model, which reduces CPU time compared to beam elements. For the first time, we have successfully corrected positioning errors within a system of cells.

Efficient and accurate time integration methods are crucial for real-time simulation, optimization and control of constrained multibody systems. This paper presents new Lie group generalized-a methods that improve accuracy for multibody systems with large rotations. The proposed methods extend the widely used geom1 scheme by Brills and Cardona by introducing a a-modification that allows to systematically eliminate a Lie group-specific part of the leading error term without compromising second-order accuracy or zero stability. While optimal accuracy is achieved for a specific choice of a, the special case a = 1 offers notable algorithmic simplicity and minimal computational overhead. The original geom1 scheme is recovered by setting a = 0. Several numerical benchmarks demonstrate the potential of the proposed Lie group integrators compared to both the original geom1 method and conventional formulations based on Euler parameters or Cardan/Tait-Bryan angles.

In self-reconfigurable structures, the mechanical design of the joints is one of the most challenging tasks. Within this context, flexural pivots are widely adopted as compliant mechanisms due to their ideal design for achieving low rotational stiffness and high off-axis stiffness. To maximize performance, they are often optimized for specific application requirements. However, designing flexural pivots for self-reconfigurable structures with an arbitrary center of rotation remains a significant challenge. To address this, we propose an approach for optimizing the topology of beam-based flexural pivots undergoing large deflections, aiming to achieve an optimal configuration with an arbitrary center of rotation. To this end, both the stiffness-based objective function and the strain energy-based objective function are introduced. For the implementation, a geometrically exact beam element is utilized to establish a dual-layer ground structure for optimization. A genetic algorithm is employed to identify optimal configurations for flexural pivots, including traditional notch hinges and cross-spring pivots. Additionally, the influence of different objective functions and their corresponding parameters on the optimized topology is examined and verified. Ultimately, this approach yields optimal topologies in three representative examples with different centers of rotation, establishing a foundation for the design of compliant mechanisms with user-defined rotational behavior.

The precision, stability, and performance of lightweight high-strength steel structures in heavy machinery is affected by their highly nonlinear dynamics. This, in turn, makes control more difficult, simulation more computationally intensive, and achieving real-time autonomy, using standard approaches, impossible. Machine learning through data-driven, physics-informed and physics-inspired networks, however, promises more computationally efficient and accurate solutions to nonlinear dynamic problems. This study proposes a novel framework that has been developed to estimate real-time structural deflection in hydraulically actuated three-dimensional systems. It is based on SLIDE, a machine-learning-based method to estimate dynamic responses of mechanical systems subjected to forced excitations. Further, an algorithm is introduced for the data acquisition from a hydraulically actuated system using randomized initial configurations and hydraulic pressures. The new framework was tested on a hydraulically actuated flexible boom with various sensor combinations and lifting various payloads. The neural network was successfully trained in less time using standard parameters from PyTorch, ADAM optimizer, the various sensor inputs, and minimal output data. The SLIDE-trained neural network accelerated deflection estimation solutions by a factor of 10^7 in reference to flexible multibody simulation batches and provided reasonable accuracy. These results support the studies goal of providing robust, real-time solutions for control, robotic manipulators, structural health monitoring, and automation problems.

Remote center of motion (RCM) mechanisms are widely used because their center of rotation is outside the mechanical device. Usually, compliant RCM mechanisms use a linkage-based design with flexure hinges to achieve relative motion. It is still an open question to design a distributed compliant RCM mechanism using flexural beams. Addressing this, the paper proposes a generalized optimization approach for the design. The optimization approach is implemented in two steps. First, we use beams to establish a dual-layer ground structure. Using a genetic algorithm and considering the relative density of beams as variables, we obtain the optimized topology. Second, based on the topology and employing curved beams for size-shape optimization, we achieve optimized distributed compliant RCM mechanisms. Based on this approach, we explore and identify four distinct topologies and four detailed distributed compliant RCM mechanisms. With the comparison of stiffnesses and rotational axis shift, two kinds of optimized distributed compliant RCM mechanisms are considered. For verification, the commercial finite element software ABAQUS and experimental testing were utilized, demonstrating excellent alignment. Ultimately, this approach can be generalized for optimizing distributed compliant RCM mechanisms.

This work investigates the influence of terms representing the coupling of bending stiffness and dissipative effects with axial motion for highly flexible beams modeled with an arbitrary Lagrangian–Eulerian (ALE) formulation. In the current work, axially moving beams undergoing large deformations are numerically modeled using an absolute nodal coordinate formulation (ANCF) and an ALE framework. In the resulting beam element model, an ANCF beam is extended by an independent axial (Eulerian) coordinate which models the axial motion. The influence of terms dependent on the axial coordinate appearing in the equations of motion is the focus of the present investigation. It is shown that the role of these terms is crucial in modeling problems involving large bending of axially moving beams. The consistency of the investigated ALE modeling with a conventional Lagrangian modeling is verified by comparisons of results obtained by reproducing numerical examples with the two modeling approaches. An exclusion of the axial-coordinate-dependent terms from the model highlights their significance in ALE modeling of beams with large bending deformations. Finally, obtained results show agreement to an analytical solution and a semi-analytical solution derived for the quasi-static and dynamic numerical example, respectively.

Modular self-reconfigurable robots hold the promise of being capable of performing a wide variety of tasks. However, many systems fall short of either delivering this promised functionality due to constraints in system architecture or validating it on functional hardware prototypes. This paper demonstrates the functional capabilities of the Planar Adaptive Robot with Triangular Structure (PARTS) and documents the versatility of this robot system using a holistic approach that combines simulations and hardware demonstrations on a prototype with nine fabricated modules. PARTS is a two-dimensional modular robot consisting of modules with a shape-shifting triangular geometry capable of forming adaptable space-covering structures. Meta-modules and mesh restructuring techniques are presented as methods for achieving topological self-reconfiguration. The feasibility of these methods is demonstrated by applying them on a simulated reconfiguration example of 62 modules. The paper showcases the versatility of PARTS on the hardware prototype using task-specific configurations, including locomotion using a meta-module and a walker configuration, module-module interaction by establishing a bridge between two separated module clusters, and interaction with the environment using a gripper and supporting structure configuration. The results validate the versatility and emphasize the potential of the system’s design concept, motivating the transfer of the hardware architecture to the third dimension.

Computational models are conventionally created with input data, script files, programming interfaces, or graphical user interfaces. This paper explores the potential of expanding model generation, with a focus on multibody system dynamics. In particular, we investigate the ability of Large Language Model (LLM), to generate models from natural language. Our experimental findings indicate that LLM, some of them having been trained on our multibody code Exudyn, surpass the mere replication of existing code examples. The results demonstrate that LLM have a basic understanding of kinematics and dynamics, and that they can transfer this knowledge into a programming interface. Although our tests reveal that complex cases regularly result in programming or modeling errors, we found that LLM can successfully generate correct multibody simulation models from natural-language descriptions for simpler cases, often on the first attempt (zero-shot). After a basic introduction into the functionality of LLM, our Python code, and the test setups, we provide a summarized evaluation for a series of examples with increasing complexity. We start with a single mass oscillator, both in SciPy as well as in Exudyn, and include varied inputs and statistical analysis to highlight the robustness of our approach. Thereafter, systems with mass points, constraints, and rigid bodies are evaluated. In particular, we show that in-context learning can levitate basic knowledge of a multibody code into a zero-shot correct output.

The algorithms identifying machine health and predicting maintenance needs require accurate information about the machine's state. Because of the great amount of collected data and limited data buffering and data transfer capabilities in many hydraulic machinery applications, the data should be processed in real time. The real-time requirement demands computationally efficient simulation models, while the self-correcting nature of estimation algorithms allows models with lower precision to be used. The study combines the novel low-fidelity surrogate models with an Unscented Kalman Filter (UKF) for the real-time state estimation of the coupled mechanical systems. The surrogate-assisted modeling approach reduces the model complexity and improves computational efficiency while maintaining high accuracy. A hydraulic forestry crane case study is investigated, and the computational efficiency and numerical accuracy of the developed observers are evaluated. The encoder measurements are provided by the high-fidelity model. The high-fidelity model introduces imperfections in the form of the frictional forces in the hydraulic cylinders, which induce approximately 2 % error in actuated force. The case study results demonstrate that the surrogate-based state observer delivers estimations within the real-time computational range. It shows a maximum accuracy deviation of 7.31 % for unmeasured states compared to the high-fidelity model-based observer.

Abstract. Understanding particle motion in snow avalanches is essential for unravelling the driving processes behind transport phenomena and mobility. Our approach to investigating avalanche dynamics at the particle level combines data from a novel inflow sensor system, the AvaNodes, with radar measurements and simulation results from the thickness integrated flow module of AvaFrame, the open avalanche framework. The radar measurements offer a comprehensive view of the avalanche, serving as a reference for the AvaNodes' trajectories within it. This synthesis provides a holistic overview of the motion of avalanche particles and the front. The utilized com1DFA module in AvaFrame, equipped with a numerical particle grid method, enables a direct implementation of numerical particle tracking functionalities, facilitating a comparison between measurements and simulations. This unique combination prompts questions about the comparability of simulations and measurements on a particle level, yielding new insights into the thickness integrated model's ability to replicate real-scale snow avalanche particle behaviour assuming a modified Voellmy friction relation. Our work also highlights current limitations of comparing radar measurements and synthetic particle sensor systems with numerical simulation particles. Minimizing the differences between measured and simulated particle velocities and front positions allows to identify optimal parameter settings for an observed avalanche event at the Nordkette test site. Using the best-fit parameter values yields deviations below 5–10 % for the maximum velocities and the resulting travel lengths. Beyond the best-fit simulations, the applied optimization method shows a wide range of suitable parameter sets causing equifinality within the investigated parameter space. Additionally, the results show that there is a trade-off between the accuracy of an optimization on single observables or the simultaneous optimization of particle and front behaviour.

Motion reconstruction and navigation require accurate orientation estimation. Modern orientation estimation methods utilize filtering algorithms, such as the Kalman filter or Madgwick's algorithm. However, these methods do not address potential sensor saturation, which may occur within short time periods in highly dynamic applications, such as, e.g., particle tracking in snow avalanches, leading to inaccurate orientation estimates. In this paper, we present two algorithms for orientation estimation combining magnetometer and partially saturated gyrometer readings. One algorithm incorporates magnetic field vector observations and the full nonlinearity of the exponential map. The other, computationally more efficient algorithm builds on a linearization of the exponential map and is solved analytically. Both algorithms are then applied to measurement data from four different experiments, with two of them being snow avalanche experiments. Moreover, Madgwick's filtering algorithm was used to validate the proposed algorithms. The two algorithms improved the orientation estimation significantly in all experiments. Hence, the proposed algorithms can improve the performance of existing sensor fusion algorithms significantly.

As commonly known, standard time integration of the kinematic equations of rigid bodies modeled with three rotation parameters is infeasible due to singular points. Common workarounds are reparameterization strategies or Euler parameters. Both approaches typically vary in accuracy depending on the choice of rotation parameters. To efficiently compute different kinds of multibody systems, one aims at simulation results and performance that are independent of the type of rotation parameters. As a clear advantage, Lie group integration methods are rotation parameter independent. However, few studies have addressed whether Lie group integration methods are more accurate and efficient compared to conventional formulations based on Euler parameters or Euler angles. In this paper, we close this gap using the ℝ^3× SO(3) Lie group formulation and several typical rigid multibody systems. It is shown that explicit Lie group integration methods outperform the conventional formulations in terms of accuracy. However, it turns out that the conventional Euler parameter-based formulation is the most accurate one in the case of implicit integration, while the Lie group integration method is computationally the more efficient one. It also turns out that Lie group integration methods can be implemented at almost no extra cost in an existing multibody simulation code if the Lie group method used to describe the configuration of a body is chosen accordingly.