Multibody System Dynamics最新文献

Human motion capture technology is utilized in many industries, including entertainment, sports, medicine, augmented reality, virtual reality, and robotics. However, motion capture data only allows the user to analyze human movement at a kinematic level. In order to study the corresponding dynamics and muscle properties, additional sensors such as force plates and electromyography sensors are needed to collect the relevant data. Collecting, processing, and synchronizing data from multiple sources could be laborious and time-consuming. This study proposes a method to generate the dynamics and muscle properties of existing motion capture datasets. To do so, our method reconstructs motions via kinematics, dynamics, and muscle modeling with a musculoskeletal model consisting of 14 joints, 40 degrees of freedom, and 15 segments. Compared to current physics simulators, our method also infers muscle properties to ensure our human model is realistic. We have met International Society of Biomechanics standards for all terminologies and representations. Furthermore, our integrated musculoskeletal model allows the user to preselect various anthropometric features of the human performing the motion, such as height, mass, level of athleticism, handedness, and skin temperature, which are often infeasible to estimate from monocular videos without appropriate annotations. We apply our method on the Human3.6M dataset and show that our reconstructed motion is kinematically similar to the ground truth markers while being dynamically plausible when compared to experimental data found in literature. The generated data (Human3.6M+) is available for download.

For rigid multibody systems with redundant constraints, mathematical modeling and physical interpretation of the obtained results are impeded due to the nonuniqueness of the calculated reactions, which—in the case of load-dependent joint friction—may additionally lead to unrealistic simulated motion. It makes the uniqueness analysis crucial for assessing the fidelity of the results. The developed methods so far for the uniqueness examination—based on the modified mobility equation, the constraint matrix, or the free-body diagram—are not well suited for multibody systems described by relative coordinates. The novel method discussed in this paper breaks this limitation. The proposed approach is based on the divide-and-conquer algorithm (DCA)—a low-order recursive method for dynamic simulations of complex multibody systems. The devised method may be used for checking the joint-reaction uniqueness of holonomic systems with ideal constraints that fulfill some additional assumptions. The reaction-uniqueness analysis is performed when the main pass of the DCA is completed. An eight-step algorithm is proposed. In the case of the single-joint connections, it is sufficient to study the appropriate equations of motion. However, if the multijoint connection is present, then one of the numerical methods—known from the constraint-matrix-based or the free-body-diagram-based approach—has to be used, namely the rank-comparison, QR-decomposition, SVD, or nullspace methods; all of these approaches are discussed. To illustrate the devised method, a spatial parallelogram mechanism with a triple pendulum is analyzed.

This paper presents a new approach to modeling the contact force in continuous method of modeling an impact. This method considers the traditionally used Hertz spring force to represent the elastic behavior of the impact. A new nonlinear damping force is introduced to model the energy dissipation during the impact. Unlike the traditional spring-damping force elements used in some continuous contact force models, the introduced nonlinear damper can address impacts with non-permanent local deformation at the time of separation. We conduct both analytical and numerical investigations to mathematically express the damping factor as an explicit function of system parameters. In order to ensure that the presented force model can recover the desired restitution, an optimization approach is introduced and implemented to determine the optimal damping factor. The proposed force model is numerically verified on random systems. Finally, this new model is used to study the behavior of two colliding pendulums along with well-established piecewise and continuous approaches for modeling impacts.

We propose a unified approach to dynamic modeling and simulations of general tensegrity structures with rigid bars and rigid bodies of arbitrary shapes. The natural coordinates are adopted as a nonminimal description in terms of different combinations of basic points and base vectors to resolve the heterogeneity between rigid bodies and rigid bars in the three-dimensional space. This leads to a set of differential-algebraic equations with constant mass matrix free from trigonometric functions. Formulations for linearized dynamics are derived to enable modal analysis around static equilibrium. For numerical analysis of nonlinear dynamics, we derive a modified symplectic integration scheme that yields realistic results for long-time simulations and accommodates nonconservative forces and boundary conditions. Numerical examples demonstrate the efficacy of the proposed approach for dynamic simulations of Class-1-to-(k) general tensegrity structures under complex situations, including dynamic external loads, cable-based deployments, and moving boundaries. The novel tensegrity structures also exemplify new ways to create multifunctional structures.

We describe a framework that can integrate prior physical information, e.g., the presence of kinematic constraints, to support data-driven simulation in multibody dynamics. Unlike other approaches, e.g., Fully Connected Neural Network (FCNN) or Recurrent Neural Network (RNN)-based methods, which are used to model the system states directly, the proposed approach embraces a Neural Ordinary Differential Equation (NODE) paradigm, which models the derivatives of the system states. A central part of the proposed methodology is its capacity to learn the multibody system dynamics from prior physical knowledge and constraints combined with data inputs. This learning process is facilitated by a constrained optimization approach, which ensures that physical laws and system constraints are accounted for in the simulation process. The models, data, and code for this work are publicly available as open source at https://github.com/uwsbel/sbel-reproducibility/tree/master/2024/MNODE-code.

Shale gas reciprocating compressors are usually faced with problems such as wide working conditions, multiple wells, and variable loads, which makes the torsional vibration of the compressor crankshaft serious. In addition, there is an inevitable fit clearance between the moving pairs of the shafting, which will increase the torsional amplitude value of the shafting and amplify the resonance risk. This paper presents a torsional vibration calculation method and a torsional vibration suppression technique for reciprocating compressor crankshaft systems, considering the influence of fit clearance and flexibility. A rigid-flexible coupling dynamic model of compressor crankshaft system that considers crosshead pin clearance is established by combining multibody dynamics, collision dynamics, and finite element method. The torsional angular displacement, angular velocity, and force characteristics of the compressor crankshaft system, considering fit clearance and part flexibility, are solved and analyzed. Additionally, the dynamic characteristics of the sliding bearings are determined by considering their clearance, using the finite difference method and the pressure disturbance method. A finite element model of the compressor crankshaft system considering the mixed clearances is constructed. The torsional vibration characteristics of the compressor crankshaft system are compared and analyzed under different fit clearances. The accuracy of the proposed model is validated through compressor on-site operation experiments. The speed error between the experimental and simulated results is found to be only 1.2%. Finally, research on clearance configuration optimization is conducted. The results demonstrate that with a crosshead pin clearance of 0.07 mm and a sliding bearing clearance of 0.1 mm, the angular displacement amplitude of the shafting is reduced by 1.76%, the peak value of rubbing is decreased by 29.49%, and the resonance point of the crankshaft system is minimized. This research offers theoretical guidance for ensuring the stable and reliable operation of compressors.

This work contributes to the simulation, modeling, and characterization of nonlinear elastic bending behavior within the framework of geometrically nonlinear rod models. These models often assume a linear constitutive bending behavior, which is not sufficient for some complex flexible slender structures. In general, nonlinear elastic behavior often coexists with inelastic behavior. In this work, we incorporate the inelastic deformation into the rod model using reference curvatures. We present an algorithmic approach for simulating the nonlinear elastic bending behavior, which is based on the theory of Cosserat rods, where the static equilibrium is calculated by minimizing the linear elastic energy. For this algorithmic approach, in each iteration the static equilibrium is obtained by minimizing the potential energy with locally constant algorithmic bending stiffness values. These constants are updated according to the given nonlinear elastic constitutive law until the state of the rod converges. To determine the nonlinear elastic constitutive bending behavior of the flexible slender structures (such as cables) from the measured values, we formulate an inverse problem. By solving it we aim to determine a curvature-dependent bending stiffness characteristic and the reference curvatures using the given measured values. We first provide examples using virtual bending measurements, followed by the application of bending measurements on real cables. Solving the inverse problem yields physically plausible results.

Maintaining the capacity for sit-to-stand transitions is paramount for preserving functional independence and overall mobility in older adults and individuals with musculoskeletal conditions. Lower limb exoskeletons have the potential to play a significant role in supporting this crucial ability. In this investigation, a deep reinforcement learning (DRL) based sit-to-stand (STS) controller is developed to study the biomechanics of STS under both exoskeleton assisted and unassisted scenarios. Three distinct conditions are explored: 1) Hip joint assistance (H-Exo), 2) Knee joint assistance (K-Exo), and 3) Hip-knee joint assistance (H+K-Exo). By utilizing a generic musculoskeletal model, the STS joint trajectories generated under these scenarios align with unassisted experimental observations. We observe substantial reductions in muscle activations during the STS cycle, with an average decrease of 68.63% and 73.23% in the primary hip extensor (gluteus maximus) and primary knee extensor (vasti) muscle activations, respectively, under H+K-Exo assistance compared to the unassisted STS scenario. However, the H-Exo and K-Exo scenarios reveal unexpected increases in muscle activations in the hamstring and gastrocnemius muscles, potentially indicating a compensatory mechanism for stability. In contrast, the combined H+K-Exo assistance demonstrates a noticeable reduction in the activation of these muscles. These findings underscore the potential of sit-to-stand assistance, particularly in the combined hip-knee exoskeleton scenario, and contribute valuable insights for the development of robust DRL-based controllers for assistive devices to improve functional outcomes.

This paper presents the implicit inversion method (IIM), a recursive method to evaluate the Jacobian of the forward dynamics w.r.t. the system inputs, using intermediate results obtained from an O(n) forward dynamics algorithm. The resulting coefficient matrix, called the inertia-weighted input matrix (IWIM), can be used to significantly improve the performance of solving optimal control problems that take into account system dynamics for only the current time step. As the relationship between inputs and accelerations appears fixed within a time step, this matrix can be evaluated in the initialization step of the optimization. This means that the forward dynamics only needs to be solved once at the initialization of the optimization, rather than having to solve the equations in every iteration of the optimization. The method presented in this paper especially targets a case where the forward dynamics are calculated using an O(n) method and takes advantage of variables that are already known through the evaluation of that method. These quantities allow us to obtain the inertia-weighted input matrix without having to convert the system to its generalized coordinate form. Exploiting the shape of the resulting equation, it is even possible to avoid an explicit inversion of any matrices in the process. Finally, runtime comparisons between three different methods to calculate the IWIM are made for several examples.

This paper further develops the Udwadia–Kalaba-approach-based view for the study of the controller design of underactuated systems. A challenge issue of the controller design for such complex systems is to implement an effective control input due to the non-full-rank feature of the control force configuration space. It becomes more difficult especially for the situation in which the control constraints are, in general, incompatible with the modeling constraints. In this paper, the modeling constraints are further divided into the natural and underactuated constraints, which can well capture the proper physical descriptions of underactuated systems. The control input that minimizes the control error and cost function can be derived by matrix operations, and then an additional constraint will be designed fully to address the incompatibility between the modeling and control constraints. This allowed us to develop an approach with precise effectiveness, high stability, and good robustness, which is applicable for various typical cases of complex underactuated systems. Finally, several representative numerical examples, including the fixed-point stabilization and trajectory tracking of a mobile robot, and the trajectory tracking of a hovercraft, are presented to demonstrate the proposed method.